Most Important PYQ'S For KCET | Mathematics

hello students welcome back to our favorite Channel physics previous year questions and the most important questions now the first question is on the four to five years questions first one if a and b are finite set and a is subset of B then subset you know the elements compulsory is first in case you said B yeah elements because a is subset of B so Union B is whole set B the number of elements in a union B that is equal to number of elements in Australia a union bien whole set whole set B so number of elements in a union B is equal to number of elements in B but our though so wrong next answer but next one number of elements in a intersection B a intersection B see common intersections see whole B ite so number of elements in a intersection B is equal to number of elements in a but but number of elements in a union B is equal to number of elements in b clear either number of elements in a union B is equal to number of elements in a plus number of elements in B and number of elements in a intersection B and foreign clear next one the value of cos Square 45 degree minus sine Square for 15 degree is is root 3 minus 1 divided by 2 root two so other simplification models root 3 minus 1 by 2 root 2 now whole Square Market a minus B whole square is shortcut method cos square a minus sine square B which is nothing but which is equal to cos a plus b into cos a minus B Anthony just simple cos a plus b into cos a minus B expand markally cos square a minus sine square B name 15 degree foreign a plus b UH 60 degree into cos a minus B 45 minus 15 30 degree cos 60 degree 100 1 by 2 cos 30 degree a is root 3 by 2 so simplify root 3 by 4 so option B clear yes three plus five plus seven plus so on to n terms I mean sum of N terms yeah series AP sum of N terms formula node a SN is equal to n by 2 into 2A plus direct formula direct formula based questions director substitute in the first term that is nothing but a in another first term a is 3 common difference any day common difference D is equal to Pi minus 3 2 difference n by 2 into 2 a Plus n minus 1. sum of N terms so n minus 1 into D is 2. to clear solvana n by 2 3 2 is a six two into n 2 N minus 2. so now 6 minus 2 4 plus 2 n iTunes is with a two common together two plus n so two two cancel n into 2 plus n is the answer n into two plus n under one the N plus two one so option one clear if 1 plus I divided by 1 minus I whole power m is 1 then the least positive integral value of M okay just a m value Nigeria so you can now is suppose 1 plus I divided by 1 minus I whole power m malva is rationalize rationalize one plus I divided by 1 plus I rationalization which is nothing but multiply a plus b into a plus b a plus b whole Square a plus b whole Square a plus a plus b into a minus b a square minus b square a square minus b square whole power m equal to 1. whole square is equal to a square plus b square plus 2 a B Nani list step by step uh a square minus I Square value no minus 1. so minus 1 which is equal to 1 next is minus 1 minus one plus two I divided by 1 minus into minus plus 1 plus 1 2. 2 whole power M now one M birdies m one one cancel so 2i by 2 power m is equal to 1 2 2 cancel again I power m equal to 1 is now foreign minus 1 into minus 1 plus 1 therefore I power 4 is equal to 1. M therefore value of M is equal to 4 M value no clear my easier questions if modulus of x minus 2 is less than or equal to 1 is equation uh modulus plus or minus modulus foreign see 2 minus 2 is plus 2 1 plus 2 again X greater than or equal to 2 minus 1 1 2 plus 1 3. so X and do one greater than or equal to K closed bracket 1 comma less than or equal to three so foreign next one if NC 12 is equal to n c 8 then n is equal to a direct question answer bandhu 20. hey easiest one if a condition must ensure n c x is equal to n c y now permutations and combinations then we can directly say that X Plus y must be equal to n and [Music] X Plus y equal to n 12 plus 8 which is equal to N Andre 20 equal to n um n c r equal to n c n minus r put x equal to R and y equal to n minus r foreign next one the total number of terms in the expansion of X plus a whole power 47 minus x minus a whole power 47 after simplification total number of terms is ili Java is 47 another odd number in case if it is odd then the last term is nothing but n plus 1 by 2. even n by 2 Plus 1 is 47 plus 1 divided by 2. 20 4. so the total number of terms in that expansion is only 24. clear option one in case you do 48 it is 48 by 224 24 plus 1 25 or binomial expansionally equation of line passing through the point 1 comma 2 and perpendicular to the line easiest question is point x 1 y 1 now our equation Now find out more because it is passing through the point x one y one and it is perpendicular to the line lines y equal to three x y equal to 3 x minus 1. perpendicular find out equation of line under x minus x 1 equal to M into sorry y minus y 1 equal to M into x minus x 1 first thing y equal to three x minus one y equal to MX plus C format MX plus c M value a no 3 slope perpendicular perpendicular means M1 is equal to minus 1 by m that's it minus 1 by 3. foreign 3y minus 6 equal to minus into x minus X Plus 1. X Plus 3y is seven X Plus 3y equal to 7 or X Plus 3y minus 7 equal to 0. option A clear equation of the line passing through the point and it is perpendicular to the line y equal to MX plus click next eccentricity of the ellipse first season of x square by a square plus y Square by b square equal to one another that is x square by 6 Square plus y Square by 4 Square equal to 1 usually a value 6 and B is 4. eccentricity formula eccentricity of that ellipse is root of 1 minus what b square divided by a square direct formula based question root of 1 minus b square by a square root of 1 minus B and 4 4 Square 16 a square is 6 Square 36 LCM totally root of 36 136 36 minus 60. 36 minus 16 20 by 36 root in the outside degree 2 root 5 root 36 answer 6. option 2 root 5 Y is foreign yes naughty next one the perpendicular distance of the point P of 6 7 8 from X Y plane see perpendicular distance and the radiation explained perpendicular distance from the X Y plane is nothing but simple one perpendicular distance X Y plane that means it is from z z axis that is magnitude of Z magnitude of Z value in foreign magnitude of Y that is nothing but 7 in case why is that plane melee perpendicular distance so perpendicular distance magnitude of z x is magnitude of X that is nothing but value is six so yavaga or perpendicular distance clear next the value of limit Theta tends to 0 1 minus cos 4 Theta divided by 1 minus cos 6 Theta easy question is limit Theta tends to 0 1 minus cos 2 Theta you know sine Square yeah 1 minus 2 sine Square Theta e formula but cos 4 Theta cos 4 Theta Reno 1 minus 2 sine Square C cos 2 Theta 1 minus 2 sine Square Theta cos 4 Theta Radu and the multiple of 2 sine Square divided by 1 minus cos 6 Theta under multiple of three twos are three times 1 minus 2 sine Square 3 Theta clear simplify limit Theta tends to 0 1 minus plus 2 sine Square 2 Theta by 1 minus 1 plus 2 sine Square 3 Theta 2 km Next Step limit Theta tends to 0 2 sine Square 2 Theta by 2 sine Square 3 Theta 2 2 cancel again limit X tends to 0 sine X by X under one so limit Theta tends to 0 . sine Square 2 Theta sine Square two Theta divided by see 2 Theta hakana 2 Theta into ethetile balance foreign Square 3 Theta divided by n Karma again multiply and divided by 3 Theta but what was that whole Square whole Square clear history naughty either value one either value one so next one again two Theta whole Square under 4 Theta Square by nine Theta Square 4 by 9 option 1 clear next one the control positive statement of the statement of the statement if x is a prime number then X is odd Contra positive opposite if x is a prime number then X is ordered prime numbers that means If X is not odd X prime numbers if X is not odd then X is not prime number If X is not odd then Contra positive elements is not or then it is not prime number yes option 4 clear is next one if coefficient of variation is 60 and standard deviation is 24 then arithmetic means is equal to standard deviation standard deviation standard deviation that is nothing um SD standard deviation divided by coefficient of variation foreign coefficient of variation 60 into 100 simplify what is 0 0 cancel s a four into ten 40 option one next one the range of the function is equation is y equal to root nine minus x square so X na is Square nine in minus X plus root y yes to question I think so wrong either one Ninja X is root x square equal to minus y Square yes um any lateral difference y equal to root 9 minus x square x 9 in terms of yborcia so SBS y Square equal to 9 minus x square X now left side x square is equal to 9 minus y Square X is equal to root of 9 minus y square is important root either a value either value must run should imaginary negative Allah that means 9 minus y Square either a value of positive greater than or equal to zero zero either imaginary in parallel but must run should greater than or equal to 0 over so 9 minus y Square greater than or equal to 0 9 3 Square minus y Square greater than or equal to 0 a square minus b square a plus b into a minus bigger than or equal to 0 . 3 minus y there then y minus three Mark colony 3 plus y minus 3 minus less than or equal to 0 that means Y is y minus 3 less than or equal to 0 3 plus y less than or equal to 0. Y is less than or equal to 3 and Y is less than or equal to minus 3. and then minus 3 minus three and then minus 2 minus one zero one two three other value is minus three minus 2 minus 1 0 1 2 3 3 is closed bracket foreign yes zero Saha is so option two clear next one let F from R to R be defined by f of x equal to X power 4 then f of x 1 equal to one second f of x 1 equal to F of X2 last correct so consider x 1 power 4 equal to x 2 power 4. foreign chord of mine code of r code real numbers real numbers means foreign foreign Infinity is real numbers are real numbers therefore range is not equal to code domain therefore that is not onto on therefore this is neither one one nor not neither one one nor onto character next one yeah the range of secant inverse X foreign not defined not Define so in 99 secant inversely now 0 comma Pi minus Pi by 2 that is option option 4. foreign X Plus tan inverse Y is equal to 4 Pi by pi then cot inverse X Plus cot inverse Y is the easiest thing is 90 minus yeah 90 minus 90 minus necessity but first 90 minus cot inverse X Allah yes cot inverse X Plus 90 minus cot inverse Y which is equal to 4 Pi by 5. cot inverse XNA cot inverse is foreign X Plus cot inverse y 5 by minus 4 pi Pi by 5 cot inverse X Plus cot inverse y so option yeah two option b Hatta foreign X F of G of X power 1 by 3. next is F1 e f of x under eight X Cuba X 0. specifically Matra constant Allah Allah X power 1 by 3 now 8 constant ly X power one by three foreign X clear 8 x go find out G of f of x G of f of x under eight X Cube same thing X power 1 by 3 x 0 8 x Cube now substitute foreign X Cube clear ly two again X um which is not equal clear foreign healthy symmetric Matrix under what is the meaning that is and our skill symmetrics excuse me transpose the same laughs a transpose mardaga yeah minus difference zero Matrix except that zero Matrix here then the value of X and Y is equation Matrix questions Y is 0 1 2 which is equal to Pi six one eight Matrix addition a corresponding elements corresponding elements now two plus y 6 Plus 0 plus 1 2 X plus two which is equal to five six one eight additions foreign 2 plus y equal to 5 2x Plus 2 equal to 8. simplify y equal to 3 is x equal to three x two three option clearance X is 3 and Y is three option one binary operation star on R minus of minus 1 which is defined by a star b a equal to B plus 1 is foreign foreign by foreign foreign C plus one clear which is equal to is huh a divided by C plus one a n Reno a divided by C plus one simplified LCM um okay a divided by C plus one else so B plus C plus one which is equal to a numerator denominator denominator either denominator a divided by B plus 1 into C plus one either a into C plus 1 divided by B plus C plus 1 which is equal to a divided by B plus 1 into C plus one not equal therefore this is not associative so either associative nor combinative option C next one determinant just determine and expand model though x value now find out expand money left side three into one three minus X into x x square which is equal to 3 ones are for dosa 3 minus x square equal to Minus 5 X 3 plus 5 equal to x square 8 equal to x square x equal to plus r minus 2 root 2. foreign foreign then the value of determinant of K A which is equal to on the shortcut formula determinant of K into a k is nothing but any constant which is equal to K power n into determinant of a n under a order of the Matrix this is order of the Matrix order order three so determinant of K A is equal to K power 3 into determinant of a option t clear next one the area of a triangle with the vertices what is this that is four square units then the value of k or a k value and find out first area of the triangle formula area of the triangle which is equal to 1 by 2 x two y two One X three y three one x 1 y 1 x 2 Y 2 x 3 y 3 is in a simplified area no 4 which is equal to 1 by 2 into 1 1 x 1 y 1 K 0 x 2 Y 2 4 0 x 3 y 3 0 2 clear ly a row in the expand is a [Music] easy and uh expanded clearer is minus plus minus plus minus see 0 into minus zero beta 0 into anything is 0 plus 0 into anything is 0 minus 2 into 2 into K 1 k minus 4. uh 4 equal to 1 by 2 foreign minus into K minus K minus into minus plus 4. so K is equal to zero uh now next methods next is um yes minus into K yeah yeah area of the triangle magnitude magnitude so 4 is the equal to 2 to cancel magnitude of minus K plus 4 magnitude magnitude magnitude minus K plus 4 equal to 4 or minus K plus 4 equal to minus 4. K is 0 or K is 8. K value another zeros clear next one let Delta equal to on determinant value then foreign [Music] C1 Delta Ali X Y zedna multiply Modi C1 employs x y z into C1 C1 gamatra so Delta is equal to X Y is b y c z x square y Square Z Square x y z x y z x y z ISO next first trolley XNA common degree second really Y in a common third role common so x y z common again x y z x y z a b c x y z y z x z X Y is it is same with it is a b c x y z y z x z x y Stella so Delta is equal to Delta 1 so option B or Target the right question next one yeah if f of x is equal to e conditions which is continuous at x equal to 2 x continuous then the value of K is left hand limit must be equal to right hand limit lhl is equal to right hand limit left hand limit and limit X tends to left hand two that is 2 minus limit right hand limit 2 plus K into 2 square equal to 3 so K is equal to 3 by 4 option 3. explain the value of C in mean value theorem mean value theorem F dash of C is equal to F of B minus F of a divided by B minus a is first f of x one time differentiate two exactly replace F of b f all four minus F of a Android 2 divided by 4 minus 2 so really 2C is equal to F of 400 uh foreign this implies C is equal to 3 the value of C which is nothing but option a three foreign y Square equal to X where the tangent makes an angle of 45 degree tangent d y by D X Now find out so d y by DX 2 into why d y by DX which is equal to 1. by 4 tan Pi by 4 equal to 1 by 2y tan Pi by 400 1 equal to 1 by 2y e 2 Y and R 2 Y and beta y Namath y equal to 1 by 2. next question with x axis is the point that is one by two whole Square equal to X so X is equal to 1 by 4 therefore the points are 1 by 4 comma 1 by 2. 1 by 4 comma 1 by 2 values B option either next one the function f of x is equal to x square plus two x minus 5 is strictly increasing strictly increasing one the difference increasing Atmos strictly increasing increasing F dash of X another greater than or equal to 0 over strictly increasing strictly increasing just greater than the road closed intervals differences just increasing greater than or equal to zero foreign foreign foreign the rate of change of sphere with respect to its surface area above students the rate of changes that is DV by d s foreign DV by d r is equal to 4 by 3 pi r Cube differentiate 3 into R square three three cancel I2 Target d s by d r matadaga 4 Pi 2 r here I don't know divide my body one by two uh R by two our r value and the radius is 4 centimeter 4 divided by two two twos are two centimeter volume unit centimeter Cube Square necessity option two next one if y equal to tan inverse sine X Plus cos x divided by cos x minus sine X then d y by DX is equal to one but hey again first y equal to tan inverse okay foreign X by cos x tan X Plus cos x by cos x 1 cos by cos 1 minus sine by cos tan is tan inverse next tan Pi by foreign a plus b tan Pi by 4 plus b and Ray X clear tan inverse tan cancel Pi by 4 plus x equal to Y so Eva differentiate Mercury is differentiate with respect to X one so option option 4 clear next one if sine X equal to two t by 1 plus T square and tan y equal to two t by 1 minus t Square then d y by DX is equal to is huh first node is in consider Mana X is equal to sine inverse 2 T by 1 plus T Square direct formula sine 2 Theta divided by 1 plus Theta square that is nothing but two tan inverse t direct formula based y equal to tan inverse 2 T by 1 minus t Square 2 tan Theta by 1 minus tan Square Theta is equal to tan 2 Theta but inverse is 2 tan inverse t is 2 tan inverse T therefore X is equal to Y if a differentiate d y by DX is equal to X is differentiate one so option one clear ly sine uh 2T divided by 1 plus 2 T 1 plus T Square two t by 1 minus t Square now two tan inverse T and the variables so direct formula based question though clear next one the derivative of cos inverse 2x Square minus 1 with respect to cos inverse X with respect to either that means let V equal to cos inverse to x square minus 1 and U equal to cos inverse X this with respect to this that means d v by d u k EDU first DV by DX find out D U by DX cos inverse XNA differentiate minus one by root of 1 minus x square are the easy foreign um yes put t equal to tan Theta is foreign foreign [Music] cos Theta so V equal to cos inverse 2 cos Square Theta minus 1 2 cos Square Theta minus 100 cos 2 Theta now it's okay to Theta Andre you know cos inverse X so now uh cos 2 Theta Alpha so tune outside so V equal to 2 cos inverse X differentiate Mana DV by DX is equal to 2 cos inverse X now differentiate is minus 2 by root of 1 minus x square minus 1 by root of 1 minus x square to answer option a h if y equal to log of log X then d square y by d x square first one time differentiate muddy a problem log X is 1 by X is 1 by X log X but either answer Allah now in no one the time differentiate d square y by d x square is equal to foreign minus 1 by x square minus 1 by x square is foreign U into differentiation of V plus v into differentiation of U h that is minus 1 by X log X whole square into 1 plus log X 1 plus log X that is d square y by d x square minus 1 plus log x divided by minus 1 plus log X yes option a for demo option A h integration of X plus 3 e x e power x divided by X plus 4 whole Square DX is equal to yeah E power x total and outside X plus 3 X plus 4 minus 1 divided by X plus 4 whole square is E power x plus 4 divided by X plus 4 whole Square minus 1 by X plus 4 whole Square stay answerable yeah is E power x 1 by X plus 4 is 1 by um f of x plus F dash of X either a differentiation E power x f of x Plus E power x f of x f of x under 1 by X 1 by XNA differentiate minus 1 by X is x square character one by accident minus 1 by x square f of x E power x f of x plus C Stella plus C that is option C or Theta integration of either is equation foreign minus cos 2 Theta is 2 cos Square Theta minus 1 if bracket and remove uh minus minus into 1 minus minus into minus plus whole divided by cos x minus cos Theta into DX minus 1 plus 1 cancel 2 Common cos Square x minus cos Square Theta divided by cos x minus cos Theta into DX a square minus P Square a plus b into a minus B 2 Common a plus b electricity a minus B hmm cos x minus cos Theta into dx11 direct integration model though cos x naught integrate sine X foreign X watched blessing Marana okay it's option either option A 2 into sine X Plus X cos Theta correct X cos theta plus C clear yes integration x square plus 2X plus 5 into d x foreign a plus b whole square plus in micro though if root of x square plus a square root of x square plus a square is integration of root of x square plus a square DX is equal to X by 2 into root of x square plus a square plus a square by 2 into log of x plus root of x square plus a square plus c expand Mercury root of I think X Plus 1 whole Square plus 4 Allah 5 is 4 correct X by 2 x under X Plus 1 by 2 into root of x square plus a square is foreign plus a square by 2 that is 4 by 2 into log of x plus root of x square plus a square either plus c two twos are so the answer X Plus 1 by 2 into root of x square plus 2 X plus 5 plus 2 log X Plus root of x square plus 2 X plus 5 plus c so option 1 by 2 is option one character X Plus yes yes wrong mistake log X Plus log X Plus root of x square plus a square clear integration of 0 to Pi by 2 um Edo one another I equal to one next I equal to 0 to Pi by 2 tan oh oh sorry yes tan 90 minus thetana huh Allah Court minus foreign X 90 minus Theta divided by tan power 7 90 minus X Plus cot power 7 90 minus 6. foreign yes tan power 7 90 minus x divided by cot power 7 90 minus X Plus tan power 7 90 minus X so next 0 to 90 minus Theta is 10 power 7x plus cot power 7 x DX is one and two aerodyne I plus I 2 i 0 to 90 no delay denominator numerator can be directly added tan power 7x plus cot power 7X tan power 7x plus cot power 7x divided by tan power 7x plus cot power 7x Area 1 DX questions iandra Pi by 4 option two clear yes next one see integral minus Phi 2 5 modulus of X plus 2 DX is equal to modulus so first minus now minus Phi lip first minus mother plus two and a minus 5 2 minus 2 exactly X plus 2 into DX next e minus five that is plus value is x square by 2 minus 2X upper limit minus 2 lower limit minus 5 plus x square by 2 plus 2X Pi minus 2. apply Maadi minus two and apply minor minus two apply four by two minus 4 by 2. minus 2 into minus 2 minus 4 minus it to minus plus 4. minus lower limit of confused minus minus lower limit foreign minus 5 Square 25 by 2 minus 2 Pisa 10 minus into minus plus in my stone minus as it is plus 5 Square 25 by 2 10. 25 by 2 plus then minus lower limit minus 2 square is 4 by 2 minus minus into minus plus 4. clear yes four minus two two minus minus into minus plus 25 by 2 minus 10 plus 25 by 2 plus 10 minus 2 plus 4 plus 2 clear yes 25 by 2 plus 25 by 2 50 by 2 again 25 plus 4 which is equal to 29 calculations Miss marbedema calculations minus Pi by 2 2 plus pi by 2 DX by E power E power sine X is equal to property minus a to a f of x DX zero to a f of x plus F of minus X DX same property integral definite integral Ali minus Pi by 2 to Pi by 2 with Ray zero to Pi by 2 f of x same as it is f of x Plus F of minus X under x0 minus X plus 1 DX yes 0 to 90 1 by E power sine X Plus 1 Plus E power minus sine X now now 1 by E power sine X oh 1 by E power sine X Plus 1 is okay plus LCM E power sine X is foreign X into 1 is the same as it is 1 plus 1 into E power sine X E power sine X into DX your denominator is same numerator can be directly added 0 to 90 E power sine X Plus 1 1 plus E power sine X upper limit Pi by 2 lower limit zero so apply more than any option optional Pi by 2 is the answer option 4 clear I equal to 0 to Pi by 2 1 divided by a square sine Square X plus b square cos Square X DX is equal to multiply OK multiply and divided by cos Square X body multiply and divide by cos Square X no delay cos Square X by cos Square X into 1 by a square sine Square x b square cos Square X is secant Square X [Music] a square into sine Square by cos Square trans Square X Plus b square into DX now put Tan x equal to tan and the Saku differentiate secant Square X DX equal to DT answer 0 to 90 secant Square X DX DT divided by a square into T square plus b square a square one by a square 0 to 90 DT sorry foreign T square plus b square by a square one divided by one plus one divided by 1 plus T square or 1 divided by a square plus X Square 1 by a into tan inverse X by a foreign by a clear upper limit Infinity 0. so is 1 divided by a b tan inverse Infinity huh 1 divided by secondary 1 by a into tan inverse X by Ayla is tan inverse X by a into B foreign minus tan inverse 0 by anything is 0 Infinity by anything is infinity only clear 1 divided by either 1 divided by a b foreign therefore pi divided by 2 a b now available next one the area of the region bounded by the curve y equal to x square y equal to x square on the rough diagram hakana parabola y equal to x square and the line y equal to 16. the line y equal to 16. 0 comma 16 is x square rhetor under 16 will substitute X Value Plus R minus four birthday 4 comma 16 my sorry zero Alva 16 and 16 sorry 80 minus 4. y value is a necessity 4 minus 4 and Y is x square the line y equal to 16. area this region 0 to 16 X into d y 0 to 16 x and the no root y d y integration of root y power 3 by 2 by 3 by 2 upper limit sixteen lower limit zero sixteen power three by two by three by two minus zero sixteen square roots foreign foreign two two the four divided by 3 into 4 Cube 4 power 4 256 by 3. 4 under 256 a three area of the region bounded by the curve y equal to cos x is 0 and x is foreign yes e region plus e region okay integrate so area is equal to zero to it is to Pi by 2 0 to Pi by 2 positive so cos positive Plus Pi by 2 to Pi Pi by 2 to Pi into negative cos minus minus cos x DX cos now integrate sine X Pi by 2 0 minus integrate sine X Pi by 2 pi so simplify sine 90 under 1 minus sine 0 0. minus sine Pi 0 minus into minus minus into minus lower limit applied minus so minus into minus plus 1 plus sine 90 is 1 1 plus 1. 2 option A clear the degree of the differential equation order method degree first highest derivative one the question Ali highest derivative order questions order degree highest power of the derivative is degree Illinois highest derivatives one so degree is one and order is 2. foreign General solution General Solutions d y by DX 1 minus d y by 1 minus y equal to DX just integrate log 1 minus y minus minus one equal to X plus c stay e minus huh OK log huh answer it's okay [Music] um foreign minus log 1 minus y equal to X plus c log a minus log B is log a by b e that equal to X plus C so option a clear the integrating factor of the differential equation d y by DX plus p y equal to Q format whole equation x in the Divide body plus 2 by X into y equal to x d y by DX plus p y equal to Q format p d x 1 by X now integrate log X log x square e Power log x square is x square answer option a clear if a equal to vectors a dot b must be equal to zero a dot b must be equal to zero so a and Ray 2i plus Lambda J plus K dot I plus 2 J plus 3 K must be equal to zero dot product same same not DOT products same cross products two into one two plus two Lambda Plus 3 equal to 0. 5 2 Lambda plus 5 equal to 0 Lambda equal to Minus 5 by 2 option 4. if a b c or unit vectors such that a plus b plus C is equal to zero then the value of a dot b b dot c c dot a is equal to is determinant of a determinant modulus of B modulus of C or magnitude which is nothing but one unit vector and rather magnitude another which is always equal to 1. foreign a square plus b square plus C square plus 2 a dot b b dot c c dot a equal to 0. 1 plus 1 1 2 a dot b b dot C dot a equal to zero foreign if a and b are unit vectors the angle between a and b for root 3 a minus B to be a unit Vector question over here but a angular foreign a square plus b square minus 2 a B equal to 1. 3 into units so magnitude of a magnitude of b n 1. minus 2 root 3. magnitude of a into magnitude of B cos Theta format equal to 1 clear yes next 3 plus 1 4 minus 2 root 3 into either one one's a one cos Theta equal to 1 is 4 minus 1 3 is 1 root three one root three cancel so root 3 by 2 equal to cos Theta root 3 by 2 value 60 degree now 60 degree now 30 degree now fast Vega 30 degree so cos Theta equal to 30 degree clear yes reflection of the point in X Y plane reflection in X Y plane reflection in y z plane or reflection in exact plane and the carries reflection of the point x y z on X Y plane X Y plane melee Reflections that is minus that a state same thing reflection of this point is clear option D next one the plane 2x minus 3y plus six Z minus 11 is equal to 0 makes an angle sine inverse Alpha with x axis x axis is a miss marbley the value of alpha is equal to 27 until okay foreign the value of the alpha sine we know that the angle between the line and plane angle between line and plane is sine Theta is equal to a DOT none is B a dot b director mabena is a foreign divided by um 49 root 4900 7 so 2 by huh 2 by 7 option b clear next one a box has hundred pens of which 10 are defective defective the probability that out of a sample of five pens drawn one by one with replacement replacement and at most one defective questions at most one defective at most Andre maximum one defective at most at least Allah at least five times but at most effective but minimum is clear yes probability of the pens are defective anonymous 10. so 1 by 10 the probability which is not defective are not defective one minus P of D which is 1 minus 1 by 10 LCM nine by 10. under defective foreign but zero defective under not defective defective Allah nine by ten one time nine by ten two time three or five next one defective that is nine by ten one two three four answer five times Plus 9 by 10 nanodu four times now next is foreign see the yellow subscribe two events A and B will be independent independent events P of a intersection B is equal to P of a DOT P of B is A and B are mutually exclusive mutually exclusive events P of a intersection b equal to 0 over foreign foreign foreign minus P of b b yes option to clear the probability distribution of X is the value of K is 0.3 plus K plus 2 K plus 2K foreign one Zana Forza so K is equal to point one four so option a clear the Shaded region in the figure is the solution set of the equation shaded region is to options foreign foreign see This Is The Answer clear next one clear see the set okay 60 Questions yeah the set a has four elements and the set B has five elements then the number of injective mappings that can be defined from A to B is shortcut formula is m p n now the bigger elements in a set of a has four elements and B another five elements the number of injective mappings the bigger elements under five element five p four expand Mari NP Arna five factorial by 5 minus four is one factorial five factorial 120 so option next one is next one let F from R to R be defined by f of x equal to two X plus six which is bijective mapping that F inverse of X is given by F pin version of find out Simple Thing y equal to 2x plus 6 in case y minus six equal to two x x equal to Y by 2 minus 3 is F inverse x equal to why is X by 2 minus 3 first answer so option a clear next one let's start with a binary operation defined an R by a star b equal to a plus b by 4. uh B commutative so option b same question is the value of sine inverse COS of 53 by five fifty three by five sine inverse cos in terms of 150 300 10 pi plus 3 Pi by five first quadrant ten pi plus Theta first quadrant sine inverse cos 3 Pi by 5. sine the cause is a COS the sign change sine inverse cos no sign for Metals sine 90 minus Theta is Pi Pi minus 6 Pi which is equal to minus Pi by 10 so option D minus Pi by 10. next one if three tan inverse X Plus cot inverse x equal to Pi then x equal to 3 tan inverse X nano two tan inverse X Plus tan inverse X Plus cot inverse x equal to piant value ninety two tan inverse x equal to Pi in the 19th minus 90. so 2 tan inverse x equal to 90 to tan inverse Excel tan inverse x equal to Pi by 4 so x equal to tan Pi by 4 value is 1 so option b clear um the simplified form of tan inverse X by y minus tan inverse x minus y by X Plus y first thing tan inverse X by y minus tan inverse numeratory method denominator really is one plus y by X okay X by y minus tan inverse a minus B by 1 plus a B Tan inverse a minus tan inverse B an inverse a minus minus into minus plus tan inverse B equal to okay tan inverse X by y plus cot inverse is in Reverse X by y minus tan inverse 145 degree 45 degree tan inverse X Plus cot inverse x equal to 90. X by Y is tan inverse theta plus cot inverse Theta is equal to 90 90. 90 minus Pi by 4 in pi by 4 Ella so Pi by 4 is the answer option 2 clear yes next one if x y z are all different and not equal to 0. uh okay then the value of x inverse y inverse Z inverse is equal to First nodima determinant foreign Plus x y y z z x plus x y z equal to 1 plus X Plus y plus Z okay X Y plus y z plus z x equal to minus X Y dash Z whole thing now x y z in the Divide body stay so 1 by Z 1 by x 1 by y minus 1. Z inverse X inverse y inverse equal to minus 1. X inverse five inverse Z inverse that is equal to minus 1 clear my simplification is that is 27 so yes a direct question is foreign X next tan inverse pi x minus tan inverse pi x 0 sine inverse X by pi minus sine inverse X by pi 0 again cot inverse X by pi x plus tan inverse pi x cot inverse pi x Plus tan inverse pi x clear yes 1 by pi either value n o sine inverse theta plus Tau cos inverse Theta Theta and then of L word actually inverse sine inverse X Plus cos inverse X is equal to 90. 0 0 tan inverse X Plus cot inverse X is 90. 90 outside again 1 by pi into 90 one zero zero one irano identity Matrix identity Matrix divided by two that is option D or one by two into identity Matrix if x into y equal to E power x minus y then d y by D X is so take log on both sides log x y equal to log E power x minus y so e value x minus so log X Y is log a plus log b equal to x minus y so direct again differentiate Madi 1 by X Plus Y into sorry log no differentiate mother 1 by y y in a differentiate d y by DX 1 minus d y by d x foreign minus 1 by X y plus log Y X Plus log X log 1 by X Y into ill it's okay foreign because yeah in case 1 minus foreign so just take log on both sides y log x equal to x minus log is so x minus foreign yeah differentiate Mana uh so yes notice why log X Plus y equal to X why in common together log X plus one cross multiply Amanda log X Plus 1 U by V rule d y by D X is equal to V Square V into differentiation of u 1 minus U into differentiation of V Stella so next step okay d y by D X is equal to 1 plus log X 1 plus log X X cancel other minus 1 divided by 1 plus log X whole Square so answer n log X by 1 plus log X whole Square foreign next node if a is a matrix of order M cross n and B is a matrix such that a b Dash and B Dash a are both defined the order of the Matrix B first thing um foreign B Dash M cross n is matrix multiplication foreign foreign next one the value of E power x into 1 plus X DX divided by cos Square E power x dot X is put E power x dot x equal to T differentiate X into E power X Plus E power x into 1. d x equal to DT E power x common E power x into X Plus 1 d x equal to DT 11 to substitute Mana E power x into 1 plus X under DT cos Square t cos square is secant Square t secant Square integrate tan substitute E power x dot X Plus option B hagya next one if x y z or not equal and right Muro not equally there which is not equal to 0 and 1 yes some simple operations use model though R2 implies R2 minus R1 R3 implies R3 minus R1 Modi foreign log X log y log Z next log 2 log 2 log 2 log 3 log 3 log 3 log 2 log 3. R2 minus R1 law R2 minus R1 foreign X log a minus log B log a by B it is oh sure okay log 2 Common into log 3 common log X log y log Z 1 1 1 1 1 1 1 you again answer is okay properties of the determinants option three clear the value of this integration is see E power x illi tan inverse X is Plus one divided by x square plus one is E power x tan inverse X into x square plus 1 by x square plus 1 plus 1 by x square plus 1 DX I think is tan inverse X answer integration of E power x f of x plus F dash of X is a differentiation is clear if 2 into 2 dot b sorry 2 into a dot b equal to magnitude of a b then the angle between a and b we know that a dot b is equal to magnitude of a magnitude of B into cos Theta which is equal to magnitude of a DOT magnitude of B either so cos Theta equal to 1 by 2 so Theta is equal to 60 degree now that's it option D clear if X power M and Y power n is equal to X Plus Y into M plus n then d y by DX is equal to either X Plus y power M plus n n things okay log X power m y power n which is equal to M plus n log X Plus y log a into B log a plus log B is log M Power n M log X plus n log Y which is equal to M plus n log X Plus y clear okay it differentiate M into log X 1 by X Plus n into log y k 1 by Y into Y is d y by D X which is equal to M plus n constant login 1 by X Plus y d y by DX foreign minus is M plus n by X Plus y equal to this one into this M plus n by X Plus y minus M by X is d y by DX X Plus Y into N is a y equal to X Plus Y into X just cross multiply X Plus Y into n X Plus Y into n minus M plus n into y Ada X into M plus n X into M plus n minus X Plus Y into m foreign X into n x n plus y n minus m y minus n y divided by y which is equal to x m x n minus MX and Y by X see clear foreign x n minus m y by y x n minus m y by X you do cancel I2 d y by d x equal to Y by X option y by X option 4 clearly split Mari differentiate marriages LCM don't find out the general solution of cot theta plus tan Theta General solution find out cause sine by cos equal to 2 this LCM cos Square theta plus sine Square Theta foreign Pi by 2 so Theta is equal to n Pi by 2 plus minus 1 power n Pi by 4. option B the value of minus Pi by 4 to plus pi by 4 sine power 1 R 3 x cos 4 1/4 x DX in the problems foreign X Plus F of minus X DX is zero first f of x actually F of minus X Maadi Sinai odd functions zero here this is an odd function so the value name just zero option D clear the length of the lattice rectum of the parabola 4y square plus 3x plus 3y plus 1 equal to 0 is in order first length of the lattice under y Square equal to 4 a x format is 4 y square plus 3y equal to minus 3x minus 1. foreign three by eight whole Square foreign clear minus 9 by 64 100 minus 3x minus 1. next is really [Music] um y square plus 3 by 8 whole Square which is equal to minus 3x minus 1 plus 9 by 64. yeah B whole Square characters um next y square plus 3 by 8 whole Square foreign by four foreign foreign X plus one plus nine divided by 400 16 bharata 16 yes minus 3 by 4 x foreign by 16. Clear Eyes to yes 9 by 64 so minus one by four birthday and 9 by 64 again 1 by 4 no common three by four and one on common yes each title three by four is minus three by four X Plus 48 birthday yes okay foreign that is equal to 4 a X clear is rectum is equal to 4 into a 4 into minus 3 by 16 for Forza therefore lattice rectum is equal to minus 3 by 4. so three by four clear is a problem but it's all models foreign X power 5 divided by X power 4 x power 3 d x a x power 5 Common X power three common degree x minus 1 divided by again x minus 1 DX integration x square DX X power 3 by 3 plus C option b next one the differential coefficient of log to the base 10 per into x with respect to log to the base x 10 is differential coefficient Now find out let U equal to log 10 x and V is equal to log X 10. foreign [Music] foreign Stella into one birthday no yes a log X is 1 by U minus 1 divided by 1 by U whole Square so you you know minus U Square meaning log Tan x so log 10 x whole Square minus clear yes option two the slope of the tangent to the curve x equal to but the X at the point 2 comma 1 . first x equal to 2 now substitute at x equal to 2 2 equal to T square plus three T minus eight so finally T square plus three T minus 10 equal to 0 multiply model 10 so plus minus Sandra t equal to Minus 5 comma 2 factors substitute y equal to minus 1 here minus 1 equal to 2 T Square minus 2T minus 5. 2 T Square minus 2T minus 5 plus 1 minus 4 equal to 0. I'll divide mod committee two in the T Square minus t minus 2 equal to 0 . yes minus 200 t equal to 2 comma minus 1 1 2 2 so now slope find out at T is equal to 2 X d y by DX that is d y by DT whole divided by D X by D T at t equal to two foreign Plus 3. at t equal to 2 clear yes so t equal to 2 now substitute minor four twos are eight minus 2 divided by 4 plus 3. so 4 4 6 6 by 7. character six by seven yes six by seven the real part of real part not really either one by one minus cos theta plus I sine Theta is rationalize so 1 minus cos Theta minus I sine Theta divided by 1 minus cos Theta minus I sine Theta a plus b into a minus B a square minus b square I Square under minus 1 minus into minus plus sine Square Theta clear next naughty 1 minus cos Theta Andre 2 sine Square Theta by 2 minus I into sine 2 Theta 2 sine Theta cos Theta are they sine Theta 2 sine Theta by 2 cos Theta by 2. 2 sine Theta by 2 cos Theta by 2 whole divided by lowest 1 minus cos Theta under 2 sine Square Theta by 2. whole Square Maadi 4 sine power 4 Theta by 2. Plus sine Theta is sine Square Theta by 2 cos Square Theta by 2. 2 sine Theta by 2 comma neither 2 sine Theta by 2 into sine Theta by 2 minus I cos Theta by 2 whole divided by 4 sine Square Theta by 2 comma 4 sine Square Theta by 2.0 sine Square Theta by 2 plus cos Square Theta by 2. sine Square theta plus cos Square Theta 1. sine Theta by 2 minus I cos Theta by 2 whole divided by 2 sine Theta by ah yes 2 sine Theta by 2 here I don't know split marcolana sine Theta by 2 sine Theta by 2 1 so cos by sine cot illegal party no one by two so other answer real part 1 by 2 option is 2 I equal to Pi by 2 I equal to Pi by 4. clear next one tan inverse x square plus y Square equal to Alpha then d y by D X is equal to first n minor is in right side x square plus y Square equal to tan Alpha you have differentiate money is into d y by DX zero yes so d y by d x equal to minus 2X divided by 2y minus X by y option a next one the simplified form of I power n uh oh n plus 1 I power n plus 2 I power n Plus 3. first I power n plus I power n dot I power 1 plus I power n dot I power 2 plus I power n dot I power 3. I power n plus I into I power n I Square under minus 1 minus I power n I Square under minus 1 already in on the is zero l a option A the two curves huh is first one slow find out differentiate Mana Square minus 3x 3x into two y d y by DX plus minus y square into 3 equal to zero either in the d y by DX foreign I think so yes so in case question another mistakes minus 6 x y d y by d x equal to 3 y Square is minus 3y Square equal to 6 x y d y by d x cross multiply 3x square minus 3y Square by 6 x y equal to d y by D X that is Let It Be m one another so then differentiate same thing three x square or one term three x square into y equal d y by DX Plus Y into 3 x square 6x foreign into 3 x square minus 3 y Square equal to minus 6 x y lost d y by D X is equal to minus 6 x y divided by 3 x square minus 3y Square m m 1 into M2 a no difference foreign yes perpendicular I cut each other at right angles so perpendicular option b clear the equation of the normal to the curve Y into 1 plus x square equal to 2 minus X where the tangent crosses the x axis yes you know same previous problem that is 2 comma zero point next is the same type of problems [Music] d y by D X at 2 comma 0 find out Mercury new Andre is so is approximately I think so one nimsha y Andre d y by DX Plus into 2 x plus x square into d y by DX equal to foreign minus 1 minus Square y by plus x square so minus 1 by yes minus one by five normal equation of the normal Android perpendicular to the line is 1 by m minus 1 by m minus into minus plus 1 by 1 by 5. y minus y 1 0 equal to either value anything 5 into x minus x 1 so y equal to 5x minus 10 5 x minus y 5x minus y minus 10 equal to 0 a my cancer clear now problem necessity so the maximum value of 1 divided by X power x is maximum value under d y by DX 0 substitute first d y by DX y equal to 1 by X power x clear yes next log substitute log y equal to log y Hakuna yes X power minus X that means log is minus X log X clear yes if I got d y by DX find out money 1 by Y into d y by DX is equal to minus X non and one term minus X by X Plus Theta but alone minus log X into minus 6 minus 1 clear d y by DX is equal to Y into minus 1 minus log X put d y by DX is equal to 0 d y by D X is equal to 0 so 0 is equal to Y into minus 1 minus log X minus log X l i minus 1 minus 1 is equal to log X is 1 equal to X that is X is equal to 1 by eina x value so next foreign the solution for the differential equation d y by y plus e to DX by x equal to 0 direct integration model will last a so integrate log y plus log X equal to log C Anthony log a plus log B log a b is so X Y is equal to C is the answer therefore the solution is option C is the highest derivative 2 Alpha d square y by d x square yes degree on the polynomial functions so degree is not defined yes option D clear next one if a and b are unit vectors then what is the angle between A and B either repeated question repeated question see now is either clearer next problem solve Mana here the 11th term in the expansion of X Plus 1 by root X whole power 14 equal to foreign R minus 1 into X power n minus r minus 1 into a power R minus 1 is in a substitute 14 see 11 minus 1 10 x power 14 minus 11 minus 1 11 minus okay n minus r minus 1 null bracket highlights okay 1 divided by root X power R minus so either simplified thousand one divided by X I think so check Martini yes one thousand one divided by X option foreign a plus b equal to minus C either whole square is a square plus b square plus 2 a on a no cos Theta on the directive B cos Theta equal to C Square substitute allowed to know 9 plus 25 plus 2 into 3 into 5 cos Theta equal to 49. so 25 9 Allah 34 34. 30 cos Theta equal to 15. so 15 twos are cos Theta is equal to 1 by 2 so Theta and nodu 60 degree C3 means Pi by 3 clear if a b c a b c value each one of a b c is perpendicular to the sum of the remaining Dot [Music] each one of a b and c is perpendicular to the sum of the other two so last C Dot B plus a equal to 0. a dot b b dot C dot a element is a plus b plus C whole square is equal to a square plus b square plus C square plus 2 a dot b dot C and C Dot a either a value 0 foreign Plus 25 . 15 a plus b plus C whole Square though A plus b plus C Matra root together option C clear if the straight lines this 2 are perpendicular perpendicular M1 into M2 equal to minus 1 then the value of K first M1 because 2 plus 3 d y by d x equal to 0. so d y by D X Andre minus 2 by 3. 1 plus K into d y by d x equal to zero so d y by d x equal to minus 1 by k evalu equal to minus 1 so M1 under a minus 2 by 3 m 2 means minus 1 by k equal to minus 1. so finally I'll get K is equal to minus 2 by 3 Estella K is minus 2 by 3 is option C orthog I don't know the rate of change of area of the circle with respect to its radius area of the circle area is equal to one second Pi R square rate of change d a by d r is equal to 2 into Pi into r so 2 into Pi into R under 2 centimeter two two 4 pi or Pi is the easier problems sorry probability Allah yes area lying between the curves y Square equal to 2X and y equal to X on the parabolism so in case y equal to X oh sorry do y Square equal to 2X and y equal to X K 0 substitute y equal to X in this equation 0 to 2 X terms y d x y Andrea root 2 x minus this line that is X DX clear is X power 3 by 2 by 3 by 2 0 to 2. minus X my integrate x square Y 2 0 to 2. clear our applied root 2 into 2 by 3 x power 3 by 2. 2 power 3 by 2 minus x square by 2 Alpha so 2 power 3 by 2 sorry for nimsha 3 by 12 square 2 Square by 2. so either root 2 cube root 2 Cube 2 into root 2. 2 root 2 into 2 root 2 divided by 3 minus 2. so 2 to the four photos are eight by three minus 2 that is equal to 2 by 3 answer 2 by 3 optional next one if P of a intersection b is 7 by 10 P of B is 17 by 20 where P stands for probability then P of A over B conditional probability is a direct formula is p of A over B is p of a intersection B divided by P of B P of a intersection B and 7 by 10 divided by 17 by 20. the coefficient of variation of two distributions are 60 and 70 the standard deviations are 21 and 16 then their means mean is equal to standard deviation by coefficient of variation into 100 arithmetic mean one and arithmetic mean two clear Ness is the probability of these two being is is see 52 cards now first thing probability of these two being is 52 cards two total possibility sorry foreign foreign two so either simplify Maadi NCR n factorial by n minus r factorial into R factorial so it's going to simplify modern MK 1 divided by 221 it simplifies so next one if sine inverse X Plus sine inverse Y is equal to Pi by 2 then x square is equal to simple question though is it a first huh sine inverse x equal to Pi by 2 minus sine inverse y sine inverse x equal to Pi by 2 minus cos inverse y but then again root of 1 minus y square is an assigned in terms of Berkeley sine inverse X is equal to sine inverse root of 1 minus y Square x square equal to 1 minus 5 Square so option A that's it clear the control positive of the converse of the statement if x is a prime number now it's all moderative already so the repeated question option X is another prime number yes option four next one next Sol Mana yes next nodi two dice are thrown simultaneously the probability of obtaining a total score of five six square thirty six numerator is just five foreign option three clear yes next one if a is equal to a matrix and a plus a transpose is equal to I um I is the unit Matrix of order two cross two and a t is the transpose of a then the value of theta is equal to a a transpose at minus minus sine 2 Theta sine 2 Theta cos 2 theta plus rows now columns The Interchange model cos 2 Theta is sine 2 Theta minus sine 2 Theta cos 2 Theta is equal to Identity Matrix 1 0 0 1. so add Mercury cos 2 Theta cos 2 Theta 0 2 cos 2 Theta 2 Matrix another equal again the other corresponding element so 2 cos 2 Theta is equal to 1 cos 2 Theta Andre 1 by 2 so 2 Theta and raised to 1 by 200 60 degree Theta will be 30 degree 30 degrees Pi by 6. clear foreign minus 1 2 then a square minus Phi a is equal to is Lambda I equal to zero so 3 minus Lambda 1 minus 1 2 minus Lambda equal to 0. multiplier minus into minus six minus 3 Lambda minus 2 Lambda plus Lambda Square substitute Lambda Square minus 5 Lambda plus 7 equal to 0 Lambda Lambda equal to a a square minus 5 a is I identity Matrix so minus 7 I option D clear the value of x if x into i j k is a unit Vector unit Vector within a magnitude root of x into I the x square plus x square plus x square which is equal to 1 so root 3 x square equal to 1 root three x equal to 1 x equal to 1 by root 3 once again plus or minus r minus option one in case the other through one Value Plus R minus maximum so our Target is yeah two X is equal to okay x square x square x square space 3 Square yes foreign minus 3 sine Theta represent a circle then the center and radius x square plus y Square equal to R means x minus H whole square plus y minus K whole square is equal to R square format cos Theta sine Theta separate x minus 2 by 3 equal to cos Theta and here y minus 1 divided by minus 3 equal to sine Theta here it is so sine Square theta plus cos Square Theta Australia which is equal to x minus 2 by 3 whole square plus y minus 1 by minus 3 whole Square whole square plus y minus 1 by minus 3 whole Square 3 Square on the 9 minus 3 Square 1 through 9A denominator same nine is equal to x minus 2 whole square plus y minus 1 whole Square so Center H comma K inverter Center is 2 comma 1 radius 3 so Center 2 comma 1 and radius three option two next one the vector equation of the plane which is at a distance distance from the origin and the normal from the origin is 2i minus 3j plus K vector equation first thing r dot n cap is equal to D or number n by magnitude of n n vector by magnitude of n n vector 2i minus 3j plus K divided by root of 4 plus 1 5 plus 9 14. is equal to distance 3 by root 40. answer r dot 2 I minus 3j plus k equal to 3. it is option one clear next one if cos Alpha cos beta cos gamma are the direction cosines of a vector then cos 2 Alpha cos 2 Beta And cos two gamma now on the equation cos Square Alpha plus cos Square beta plus cos Square gamma is equal to 1 so cos Square Theta 1 plus cos 2 Alpha by 2 on top plus 1 plus cos 2 Beta by 2 plus 1 plus cos 2 gamma by 2 equal to 1. denominator is same numerator can be directly added is in a cross multiply 1 plus 1 plus 1 3 plus cos two alpha cos 2 Beta cos 2 gamma equal to 2. so cos 2 Alpha plus cos 2 Beta plus cos 2 gamma equal to 2 minus 300 minus 1 option 3. next one the value of sine 1 degree sine 2 degree so on sine 359 degree in the problems first one first term not only lost okay second term last second term is sine one degree so minus sine 1 degree sine 2 degree minus sine 2 degree so on sine 180 degree zero option a clear integrating factor of integrating Factor no salt mod is already problem okay a whole equation are divided by x mark only d y by D X is equal minus y by x equal to X power 3 minus 3. integrating Factor integrating factor is equal to E power integral p d x minus y by ah 1 by X DX so E power 1 by X now integrate log X is 1 either a value X power minus 1 or 1 by X so option foreign 4 cross 3 Alpha so I think yes 3 cross 4 the option is option three Cross Four once again Three cross one the four cross three three and yes okay now next one the symmetric part of the Matrix symmetric plus skew symmetric format symmetric a plus a transpose by 2 is a transpose by two symmetric a plus a transpose by two yeah one two four six eight two two minus 2 7 plus a transpose rows the columns now interchange Maadi one six two two eight minus 2 4 2 7. so divided by two modern one plus one two eight six and eight sixteen zero six zero fourteen okay divided by two more one by two model three one four three four eight zero three zero seven three four eight zero three zero seven whatever is option two next one two dice are thrown simultaneously the probability of obtaining a total score foreign [Music] P of a intersection b equal to P of a DOT P of B it is 1 minus P of B Dash so 1 minus 2 by 3 and 1 minus 2 by 7. simplify Maadi is one by three and Eden Pi by seven 5 by 21 Nala Pi by 21 7 3 is a 21. clear ly the question next one okay um yes to Allah yeah okay find the value of Kendra is to know that is equal to one point two plus K plus K plus 2 K foreign one by one plus y square into d y by DX d y by DX into 1 minus 1 plus y Square equal to minus 1. so d y by d x 1 plus y Square minus 1 by 1 plus y Square equal to minus one so cross multiply minor d y by DX is equal to minus 1 minus y Square by y Square Arduino split Mercury minus 1 by y Square minus one even again d square y by d x square minus y power minus 2 y power minus 2 now differentiate minus 2 into y power minus three minus sorry minus 0 minus into minus plus 2 by y Cube into d y by DX so F of y n o 2 by y Cube option 2. clear yes one second one second 80 yes 0 to Pi by 2 so Pi by 4 is the answer if M and N are the order and degree of the differential equation then higher derivative highest derivative degree and Ray are derivative to highest power is three Allah one two three four five second derivative so next yearly is foreign I think option maximum foreign

Channel: PW Kannada

Views: 65,884

Keywords: Most Important PYQ'S For KCET, Mathematics, important chapters for kcet maths, kcet important questions, mathematics, matrices kcet important questions, most important mcqs mhtcet 2023, kcet 2022 important question, kcet 2021 important questions, mhtcet 2023 most important biology mcqs, kcet physics most important chapters, class 12 mathematics timetable, 2nd puc mathematics, most important chapters kcet, most important questions kcet, class 12 mathematics strategy, kcet, kcet 2023

Id: rTyUekLuTMw

Length: 230min 53sec (13853 seconds)

Published: Mon May 15 2023