28278 + Interview Questions in Maths in Class 12 Page 163 InterviewSolution

8101.	If a, b, c are in AP then ax + by +c=0 represents
Answer» a single line a family of CONCURRENT lines a family of PARALLEL lines Two lines which are not parallel Answer :B

Discussion

8102.	Let three numbers be A=2^2 xx 3^3 xx 5, B =7^2 xx 13 xx 17, C = 2xx 3 xx 5 xx 7 xx 11 xx 13 xx 17. A number is chosen from A or B and is factorized then a non unit factor of this number is selected if this factor divide C then the probability that it is taken from A is.
Answer» `(2)/(3)` `(3)/(7)` `(7)/(24)` `(1)/(3)`. Answer :D

Discussion

8103.	Solve the following linear programming problem graphically. Minimize Z=200 x+500 y subject to the constraints: x+2y ge10 3x+4y le 24 x ge0, y, ge0
Answer» ANSWER :(4,3)

Discussion

8104.	If P is a point on the parabola y^(2)=4ax such that the subtangent and subnormal at p are equal then the coordinates of P are
Answer» (a,2A) or (a,-2a) (2a,2`SQRT(2)a)` `(4A,-4a) or (4a,4a)` none Answer :A

Discussion

8105.	Assertion (A): The roots of the equation 2x^(2) - 15x + 4 = 0 are each increased by 3, then the new equation is 2x^(2)-27x + 67 = 0 Reason (R): The equation whose roots are increased by k then those of f(x) = 0 is f(x//k) = 0
Answer» Both A, R are true and R EXPLAIN Assertion Both A, R are true but R does't explain A A is true R is FALSE A is false R is true Answer :C

Discussion

8106.	We have a 12 square unit piece of thin material and want to make an open box by cutting small squares from the corners of our material and folding the sides up. The question is, which cut produces the box of maximum volume ?
Answer» ANSWER :`(DV)/(DX)=0`

Discussion

8107.	Find the shortest distance between the lines vecr=(1-lambda)hati+(lambda-2)hatj+(3-2lambda)hatk ,vecr=(mu+1)+(2mu-1)hatj-(2mu+1)hatk
Answer» ANSWER :`2sqrt(29)` UNITS

Discussion

8108.	If lim_(xtoI^(-)) prod_(n=0)^(oo)((1+x^(n+1))/(1+x^(n))^(x^n))=l then [1/l] is equal to __________
Answer» SOLUTION :`(1+x^(n+1))/(1+x^(n))=1+(x^(n)(x-1))/(1+x^(n))` So, `"In" (Pi_(n=0)^(N) (1+(x^(n)(x-1))/(1+x^(n)))^(x^(n)))=sum_(n=0)^(N) x^(n)"In"(1+(x^(n)(x-1))/(1+x^(n)))` `LE(x-1)(1/(1-x^(2))-1/(1-x^(3))+………-1/(1-x^(2k+1)))` so, limit `=2/e`

Discussion

8109.	Differentiate w.r.t.x, the following functions : sqrt(3x+2)+(1)/(sqrt(2x^(2)+4)).
Answer» ANSWER :`X GT -(2)/(3)`

Discussion

8110.	If ((sqrt3//2+(1//2)i)/(sqrt3//2-(1//2)i))^(120)=p+iq,then
Answer» `p=cos20^@,q=sin20^@` `p=-1,q=0` `p=0,q=1` `p=cos40^@,q=sin40^@` ANSWER :D

Discussion

8111.	Which of the following matrice is invertible? [[-1,-2,3],[2,1,-4],[-1,0,2]]
Answer» Solution :LET A=`[[-1,-2,3],[2,1,-4],[-1,0,2]]` `THEREFORE absA =[[-1,-2,3],[2,1,-4],[-1,0,2]]` =`-1[[1,-4],[0,2]]+2[[2,-4],[-1,2]]+3[[2,1],[-1,0]]` =-(2-0)+(4-4)+3(0+1) =2+0+3=`1 ne 0` `therefore` A is invertible.

Discussion

8112.	Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15, -19), and R (1, -7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0. The radius of the in circle of triangle PQR is
Answer» 4 5 6 8 Solution :The coordinates of the INCENTER are given as FOLLOWS: `BAR(x) = (20(-8)+15(-15)+25(1))/(20+15+25) = -6` `bar(y) = (20(5)+15(-19)+25(-7))/(60) = -6` Hence, incenter I is (-6, -6). Now, the equation of side PR is `y+7 = (12)/(-9)(x-1)` or 4x-4 = -3y-21 or 4x+3y+17 = 0 Inradius is given as the distance of I from side PR, i.e., `(\|-24-18+17\|)/(5) = 5`

Discussion

8113.	If 0 lt a lt c, 0 lt b lt c then int_(0)^(oo) (a^(x)-b^(x))/(c^(x))dx=
Answer» `LN(B/C) - ln(a/c)` `(ln a- ln b)/(ln c)` `(1)/(ln (b/c))-(1)/(ln(a/c))` 0 Answer :C

Discussion

8114.	If in a DeltaABC, right angled at B, s - a = 3, s - c = 2, then the values of a and c respectively are
Answer» `2,3` `3,4` `4,3` `6,8` ANSWER :B

Discussion

8115.	The point in the xy-plane which is equidistant from the points (2,0,3),(0,3,2) and (0,0,1) is
Answer» `(1,2,3)` `(-3,2,0)` `(3,-2,0)` `(3,2,0)` ANSWER :D

Discussion

8116.	int ((1)/(sqrt(x+2)-sqrt(x)))dx=....+c
Answer» `(3)/(2)(x+2)^((3)/(2))+(2)/(3)x^((3)/(2))` `(3)/(2)(x+2)^((1)/(2))+(2)/(9)x^((1)/(2))` `(3)/(2)(x+2)^((3)/(2))+(2)/(9)x^((3)/(2))` `(2)/(9)(x+2)^((3)/(2))+(2)/(9x` ANSWER :D

Discussion

8117.	Evaluate the definite integral in exercise overset(3)underset(2)(1)/(2)dx
Answer» ANSWER :`(64)/(3)`

Discussion

8118.	Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15, -19), and R (1, -7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0. The radius of the in circle of triangle PQR is The sum a + c is
Answer» 129 78 89 none of these Solution :The COORDINATES of D using section formula are (-5, -23/2) and `m_(PD) = -11//2.` The EQUATION of PD is 11x+2y+78=0 or a+c = 89

Discussion

8119.	AD is a median of the DeltaABC . If AE and AF are medians of the triangles ABD and ADC repectively , and AD=m_(1),AE=m_(2),AF=m_(3),then m_(2)^(2)+m_(3)^(2)-2m_(1)^(2)=
Answer» `a^(2)` `(a^(2))/(2)` `(a^(2))/(4)` `(a^(2))/(8)` ANSWER :d

Discussion

8120.	A die a rolled and let x denote twice the number appearing on its face. Mean of x is
Answer» 6 7 4 5 Answer :B

Discussion

8121.	The value of lim_(theta to 0)(1-cos 4theta)/(1-cos 6 theta) is
Answer» 1.`4//9` 2.`9//4` 3.`9//3` 4.`3//4` ANSWER :A

Discussion

8122.	Show that the Dirichletfunction[see Problem 1 . 14 . 4 (b)] is not integrable in theinterval [0,1].
Answer» Answer :THEREFORE, the limit of INTEGRAL sumsisnon-existent, . Whichmeans that theDirichlet FUNCTION is not INTEGRABLE on the interval [0,1]

Discussion

8123.	Find the derivative of (e^x)/(sin x) w.r.t. x.
Answer» Answer :`(E^(x)(SIN x-cos x))/(sin^(2)x), x NE npi, n in Z`

Discussion

8124.	The solution of (dy)/(dx) + 1 = e^(x + y)is
Answer» `E^(-(X + y)) + x + C = 0` `e^(-(x + y)) -x + c = 0` `e^(-(x + y)) + x + c = 0` `e^(-(x + y)) -x + c = 0` ANSWER :A

Discussion

8125.	Definite integration as the limit of a sum : lim_(ntooo)sum_(r=1)^(4n)(sqrtn)/(sqrtr(3sqrtr+4sqrtn)^(2))=...........
Answer» `(1)/(35)` `(1)/(14)` `(1)/(10)` `(1)/(5)` Answer :C

Discussion

8126.	int_(0)^(pi//2)log(sinx)dx=
Answer» ANSWER :`-(PI)/(2) LOG 2`

Discussion

8127.	Using binomial theorem show that 1^(99) + 2^(99) +3^(99) + 4^(99) + 5^(99) is divisible by 5
Answer» Solution :`1^(99) + 2^(99) + 3^(99) + 4^(99) + 5^(99)` = 1+ (5-3)^(99) + 3^(99) + (5-1)^(99) + 5^(99) = 1 + (5^99- "^(99)C_1 5^(98). 3^1 + ^(99)C_2 5^(97). 3^2 - ... 3^(99)) + 3^99 - (1- ^(99)C_1 5^1 + ^(99)C_2 5^2 - ... - 5^(99)) + 5^(99)` = `(3xx5^(99) - "^(99)C_1 5^(98). 3^1 + ^(99)C_2 5^(97). 3^2 - .... + ^(99)C_(98) 5^1. 3^(98)) + (^(99)C_15^1 - ^(99)C_2 5^2 + ... -^(99)C_98 5^(98)) ... (1) which is divisible by 5 as each term is a multiple of 5

Discussion

8128.	(d)/(dx) ( sqrt(x sin x))= …… (0 lt x lt pi)
Answer» `(x SIN x + cos x)/(sqrt(x sin x))` `(x cos x)/(2 sqrt(x sin x))` `(x cos x + sin x)/(2 sqrt(x sin x))` `(1)/(2 sqrt(x sin x))` ANSWER :C

Discussion

8129.	On a multiple choice questions with three possible answers for each of the five questions, whatis the probability that a candidate would get 4 or more correct answers just by guessing ?
Answer» ANSWER :`(11)/(243)`

Discussion

8130.	Given the scatterplot graph above, ten students at Welton Academy were polled at random at their usage of the school's new physics centered social media app, E=MC shared. The app was developed to encourage students to discuss physics Curricula and concepts in ways that mirrored social media trends in 2013. Students were asked how many times they logged into the app each day as well as how many posts they actually made using the app. With the given data,what conclusions can be drawn about this group of students?
Answer» The majority of students POLLED logged in more times PER day than they POSTED The majority of students polled posted more times per day than they logged in. The majority of students polled logged in and posted an EQUAL number of times No relationship can be drawn between logins per day and POSTS per day. Answer :A

Discussion

8131.	Let A=[[ 1 , sin theta , 1 ],[-sin theta , 1 , sin theta],[-1 , -sin theta , 1 ]], where 0 le theta le 2 pi, then,
Answer» `DET(A) =0` ` Det(A) in (2, INFTY ) ` `Det (A) in (2,4) ` `Det(A) in [2,4]` ANSWER :D

Discussion

8132.	A coin is tossed until a head appears or tail appears 4 times in succession. Find the probability gettinga head it is known that tail occured at least twice .
Answer» ANSWER :`(3)/(4)`

Discussion

8133.	All the letters of the work ANIMAL are permuted in all possible ways and the permutations thus formed are arranged in dictionary order. IF the rank of the work ANIMAL is x, then the permutation with rank x, among the permutations obtained by permuting the letters of the word PERSON and arranging the permutations thus formed in dictionary order is
Answer» ENOPRS NOSPRE NOEPRS ESORNP Answer :D

Discussion

8134.	If (n,theta)=prod_(n=1)^(n)((1+tan^(2)(2""^(n)theta))/((1-tan^(2)(2""^(n)theta))^(2))) then find the value of 8f (3,(pi)/(8))?
Answer» SOLUTION :`f(n,THETA)=underset(n=1)overset(n)prod(((1+tan^(2)(2^(n)theta))/(1tan^(2)(2^(n)theta)))^(2).(1)/(a+tan^(2)(2^(n)theta)))=underset(n=1)overset(n)prod(COS^(2)(2^(n)theta))/(cos^(2)(2.2^(n)theta))` `=(cos^(2)2theta)/(cos^(2)2^(2)theta).(cos^(2)2^(2)theta)/(cos^(2)2^(3)theta).(cos^(2).2^(3)theta)/(cos2^(2).2^(4)theta).........(cos^(2)2^(n)theta)/(cos^(2)2^(n+1)theta)` `f(n,theta)=(cos^(2)2 theta)/(cos^(2)2^(n+1)theta)` `f(3,(PI)/(8))=(cos^(2)""(pi)/4)/(cos^(2)(2^(4).(pi)/(8)))=((1)/(sqrt2))^(2)/((1)^(2))=1/2` So, `8f(3,(pi)/(8))=4.Ans."]"`

Discussion

8135.	If the foci of the ellips(x^(2))/( 25)+ ( y^(2))/( 16) =1 and the hyperbola(x^(2))/(4) - ( y^(2))/( b^(2) ) =1 coincide ,then b^(2)=
Answer» 4 5 8 9 Answer :B

Discussion

8136.	If the sum of odd terms and the sum of even terms in (x + a)^n are p and q respectively then 4pq =
Answer» `(X+a)^(2N) - (x -a )^(2n)` `(x^2 -a^2)^(2n) + (x + a)^(2n)` `(x^2 - a^2)^N - (x - a)^(2n)` `(x^2 +a^2)^n + (x - a)^(2n)` ANSWER :A

Discussion

8137.	Let P , Q and R are three co-normal points on the parabola y^2=4ax. Then the correct statement(s) is /at
Answer» <P>algebraic sum of the slopes of the normals at P,Q and R VANISHES algebraic sum of the ordinates of the points P,Q and R vanishes centeroid of the traingle PQR lies on the AXIS of the parabola Circle cicrcumscribing the traingle PQR passes through the vertex of the parabola. Answer :A::B::C::D

Discussion

8138.	For a sequence lt a_(n) gt, a_(1) =5 and (a_(r+1))/(a_(r))=(1)/(2) AA r, then overset(oo)underset(n=1)Sigma a_(2n-1) is
Answer» `20//7` `20//5` `20//3` 20 Answer :C

Discussion

8139.	If I=intsec^2x cosec^(4)x dx=Acos^2x-cot^3x+Btanx+Ccotx+D Then 3(A-C+B) equals
Answer» ANSWER :8

Discussion

8140.	Solve the following LPP using graphical method :Minimizz = 8x + 10y ,subject to 2x +y ge , 2x + 3y ge 15,y ge 2,x ge 0, y ge 0
Answer» SOLUTION :Z has MINIMUM value 52 when ` X= 3/2 `and y=4

Discussion

8141.	Consider the quadratic trinomial function y=ax^(2)+bx+c,ane0,a,b,cinR. We know that on rectangular cartesian coordinate system the above equation represents a parabola, whose axis is parallel to axis of y. The characteristics of this parabola can be further analysed by rewriting the equation as following: y=a(x+b/(2a))^(2)+((4ac-b^(2))/(4a)). So, the vertex of the parabola is (-b/(2a),(4ac-b^(2))/(4a)). Focus of the parabola is (-b/(2a),(4ac-b^(2)+1)/(4a)). Latus rectum of the parabola is 1/\|a\| Holding one or two of the parameters a, b, c constant we can find family of parabolas satisfying some very significant properties. If a and b remain constant but c varies, then the family of parabolas
Answer» have COMMON axis have common focus have common directrix pass through a FIXED point Answer :A

Discussion

8142.	Consider the quadratic trinomial function y=ax^(2)+bx+c,ane0,a,b,cinR. We know that on rectangular cartesian coordinate system the above equation represents a parabola, whose axis is parallel to axis of y. The characteristics of this parabola can be further analysed by rewriting the equation as following: y=a(x+b/(2a))^(2)+((4ac-b^(2))/(4a)). So, the vertex of the parabola is (-b/(2a),(4ac-b^(2))/(4a)). Focus of the parabola is (-b/(2a),(4ac-b^(2)+1)/(4a)). Latus rectum of the parabola is 1/\|a\| Holding one or two of the parameters a, b, c constant we can find family of parabolas satisfying some very significant properties. If b and c are constant but a varies from member to member, then the parabolas of the family
Answer» have COMMON directrix have common axis touch a common line at a FIXED point are equal parabolas Answer :C

Discussion

8143.	Consider the quadratic trinomial function y=ax^(2)+bx+c,ane0,a,b,cinR. We know that on rectangular cartesian coordinate system the above equation represents a parabola, whose axis is parallel to axis of y. The characteristics of this parabola can be further analysed by rewriting the equation as following: y=a(x+b/(2a))^(2)+((4ac-b^(2))/(4a)). So, the vertex of the parabola is (-b/(2a),(4ac-b^(2))/(4a)). Focus of the parabola is (-b/(2a),(4ac-b^(2)+1)/(4a)). Latus rectum of the parabola is 1/\|a\| Holding one or two of the parameters a, b, c constant we can find family of parabolas satisfying some very significant properties. If a and c held constant but b is allowed to vary, then the family of parabolas
Answer» have COMMON axis pass through a common point touch a common LINE at a FIXED point none of these Answer :B

Discussion

8144.	Integrate thefunction in Exercise. (1)/(x- sqrt(x))
Answer» ANSWER :`( :.t=sqrt(X)-1)`

Discussion

8145.	Letalpha and betabe the values of x obtained form the equationlambda^(2) (x^(2)-x) 2lambdax +3 =0 and if lambda_(1),lambda^(2) be the two values oflambda for whichalphaand betaare connected by the relationalpha/beta + beta/alpha = 4/3 . then find the value of(lambda_(1)^(2))/(lambda_(2)) + (lambda_(1)^(2))/(lambda_(1)) and (lambda_(1)^(2))/lambda_(2)^(2) + (lambda_(2)^(2))/(lambda_(1)^(2))
Answer» ANSWER :`68/3, 178/9`

Discussion

8146.	If n is a positive integer, then (a+ib)^(m//n)+(a-ib)^(m//n)
Answer» `2(a^n+b^2)^(m//2n)COS[m/nTan^(-1)b/a]` `2(a^n+b^2)^(m//2n)SIN[m/nTan^(-1)b/a]` `2(a^n+b^2)^(m//2n)cot[m/nTan^(-1)b/a]` `2(a^n+b^2)^(m//2n)TAN[m/nTan^(-1)b/a]` ANSWER :A

Discussion

8147.	Evaluate int_(0)^(pi//6) cos^(7) 3x dx
Answer» ANSWER :`16/105`

Discussion

8148.	The vector equation of the line 3x-2=2y+1=3z-3 is
Answer» `barr=(2)/(3)hati-(1)/(2)hatj+hatk+lambda(2hati+3hatj+2hatk)` `barr=hati+hatj+hatk+lambda(2hati+3hatj+hatk)` `barr=lambda(2hati+3hatj+2hatk)` `barr=2hati+3hatj+2hatk+lambda((2)/(3)hati-(1)/(2)hatj+hatk)` ANSWER :A

Discussion

8149.	int (dx)/(sin(x-a)sin(x-b)=......+C
Answer» `SIN(b-a)LOG\|(sin(x-b))/(sin(x-b))\|` `"COSEC"(b-a)log\|(sin(x-b))/(sin(x-b))\|` `"cosec"(b-a)log\|(sin(x-b))/(sin(x-a))\|` `sin(b-a)log\|(sin(x-a))/(sin(x-b))\|` ANSWER :C

Discussion

8150.	The value of int_(0)^(pi//2) (1+ 2 cos x)/( (2 + cos x)^(2) ) dx is
Answer» `-1//2` `2` `1//2` NONE of these Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

If a, b, c are in AP then ax + by +c=0﻿ represents﻿

Let three numbers be A=2^2 xx 3^3 xx 5, B =7^2 xx 13 xx 17, C = 2xx 3 xx 5 xx 7 xx 11 xx 13 xx 17. A number is chosen from A or B and is factorized then a non unit factor of this number is selected if this factor divide C then the probability that it is taken from A is.

Solve the following linear programming problem graphically. Minimize Z=200 x+500 y subject to the constraints: x+2y ge10 3x+4y le 24 x ge0, y, ge0

If P is a point on the parabola y^(2)=4ax such that the subtangent and subnormal at p are equal then the coordinates of P are

Assertion (A): The roots of the equation 2x^(2) - 15x + 4 = 0 are each increased by 3, then the new equation is 2x^(2)-27x + 67 = 0 Reason (R): The equation whose roots are increased by k then those of f(x) = 0 is f(x//k) = 0

We have a 12 square unit piece of thin material and want to make an open box by cutting small squares from the corners of our material and folding the sides up. The question is, which cut produces the box of maximum volume ?

Find the shortest distance between the lines vecr=(1-lambda)hati+(lambda-2)hatj+(3-2lambda)hatk ,vecr=(mu+1)+(2mu-1)hatj-(2mu+1)hatk

If lim_(xtoI^(-)) prod_(n=0)^(oo)((1+x^(n+1))/(1+x^(n))^(x^n))=l then [1/l] is equal to __________

Differentiate w.r.t.x, the following functions : sqrt(3x+2)+(1)/(sqrt(2x^(2)+4)).

If ((sqrt3//2+(1//2)i)/(sqrt3//2-(1//2)i))^(120)=p+iq,then

Which of the following matrice is invertible? [[-1,-2,3],[2,1,-4],[-1,0,2]]

Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15, -19), and R (1, -7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0. The radius of the in circle of triangle PQR is

If 0 lt a lt c, 0 lt b lt c then int_(0)^(oo) (a^(x)-b^(x))/(c^(x))dx=

If in a DeltaABC, right angled at B, s - a = 3, s - c = 2, then the values of a and c respectively are

The point in the xy-plane which is equidistant from the points (2,0,3),(0,3,2) and (0,0,1) is

int ((1)/(sqrt(x+2)-sqrt(x)))dx=....+c

Evaluate the definite integral in exercise overset(3)underset(2)(1)/(2)dx

Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15, -19), and R (1, -7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0. The radius of the in circle of triangle PQR is The sum a + c is

AD is a median of the DeltaABC . If AE and AF are medians of the triangles ABD and ADC repectively , and AD=m_(1),AE=m_(2),AF=m_(3),then m_(2)^(2)+m_(3)^(2)-2m_(1)^(2)=

A die a rolled and let x denote twice the number appearing on its face. Mean of x is

The value of lim_(theta to 0)(1-cos 4theta)/(1-cos 6 theta) is

Show that the Dirichletfunction[see Problem 1 . 14 . 4 (b)] is not integrable in theinterval [0,1].

Find the derivative of (e^x)/(sin x) w.r.t. x.

The solution of (dy)/(dx) + 1 = e^(x + y)is

Definite integration as the limit of a sum : lim_(ntooo)sum_(r=1)^(4n)(sqrtn)/(sqrtr(3sqrtr+4sqrtn)^(2))=...........

int_(0)^(pi//2)log(sinx)dx=

Using binomial theorem show that 1^(99) + 2^(99) +3^(99) + 4^(99) + 5^(99) is divisible by 5

(d)/(dx) ( sqrt(x sin x))= …… (0 lt x lt pi)

On a multiple choice questions with three possible answers for each of the five questions, whatis the probability that a candidate would get 4 or more correct answers just by guessing ?

Let A=[[ 1 , sin theta , 1 ],[-sin theta , 1 , sin theta],[-1 , -sin theta , 1 ]], where 0 le theta le 2 pi, then,

A coin is tossed until a head appears or tail appears 4 times in succession. Find the probability gettinga head it is known that tail occured at least twice .

If (n,theta)=prod_(n=1)^(n)((1+tan^(2)(2""^(n)theta))/((1-tan^(2)(2""^(n)theta))^(2))) then find the value of 8f (3,(pi)/(8))?

If the foci of the ellips(x^(2))/( 25)+ ( y^(2))/( 16) =1 and the hyperbola(x^(2))/(4) - ( y^(2))/( b^(2) ) =1 coincide ,then b^(2)=

If the sum of odd terms and the sum of even terms in (x + a)^n are p and q respectively then 4pq =

Let P , Q and R are three co-normal points on the parabola y^2=4ax. Then the correct statement(s) is /at

For a sequence lt a_(n) gt, a_(1) =5 and (a_(r+1))/(a_(r))=(1)/(2) AA r, then overset(oo)underset(n=1)Sigma a_(2n-1) is

If I=intsec^2x cosec^(4)x dx=Acos^2x-cot^3x+Btanx+Ccotx+D Then 3(A-C+B) equals

Solve the following LPP using graphical method :Minimizz = 8x + 10y ,subject to 2x +y ge , 2x + 3y ge 15,y ge 2,x ge 0, y ge 0

Integrate thefunction in Exercise. (1)/(x- sqrt(x))

If n is a positive integer, then (a+ib)^(m//n)+(a-ib)^(m//n)

Evaluate int_(0)^(pi//6) cos^(7) 3x dx

The vector equation of the line 3x-2=2y+1=3z-3 is

int (dx)/(sin(x-a)sin(x-b)=......+C

The value of int_(0)^(pi//2) (1+ 2 cos x)/( (2 + cos x)^(2) ) dx is

If a, b, c are in AP then ax + by +c=0 represents