28278 + Interview Questions in Maths in Class 12 Page 173 InterviewSolution

8601.	Find the points at which the function f given by f(x)=(x-2)^(4)(x+1)^(3) haspoint of inflexion.
Answer» ANSWER :`x=-1`

Discussion

8602.	Statement I Pi_(r=1)^(n) (1+sec 2^(r)theta)=tan 2^(n)theta cot theta Statement II Pi_(r=1)^(n) cos (2^(r-1)theta)=(sin(2^(n)theta))/(2^(n)sin theta)
Answer» A B C D Answer :A

Discussion

8603.	Integrate the following functions: (cosx-sinx)/(1+sin(2x)
Answer» SOLUTION :`(cosx-sinx)/(1+sin2x) = (cosx-sinx)/(cosx+sinx)^2` `int(cosx-sinx)/(1+sin2x) DX` = `int (cosx-sinx)/9cosx+sinx)^2 dx` LET t = cosx+sinx. Then `dt = (-sinx+cosx)dx` therefore` int(cosx-sinx)/(1+sin2x) dx` =`int dt/t^2 = -1/t+c` = `-1/(cosx+sinx)+c`

Discussion

8604.	Evalute the following integrals int sqrt(x^(2) + 4)dx
Answer» `(X)/(2) sqrt(x^(2) + 4) + 2 sinh^(-1) ((x)/(2)) + C` `(x)/(4) sqrt(x^(2) + 4) + 2 sinh^(-1) ((x)/(4)) + c` `(x)/(2) sqrt(x^(2) + 4) - 2 sinh^(-1) ((x)/(2)) + c` `(x)/(2) sqrt(x^(2) + 4) + 2 sinh^(-1) ((x)/(4)) + c` ANSWER :A

Discussion

8605.	There are 10 different objects 1, 2, 3,…..…10 arranged at random in 10 places marked 1, 2, 3,…….…10. The probability that exactly five of these objects occupy places corresponding to their number is k/3600, thenk is_____.
Answer» ANSWER :`(11)`

Discussion

8606.	A and B six digits numbertotal numbers of ways of forming A and B so that (i) These numbes can be added without carrying at any stage, (ii) n_(2) can be subtracted form n_(1) without borrowing at any stage, is equal to.
Answer» ANSWER :`=45X(55)^(5)`.

Discussion

8607.	Find all values of x that satisfy the determinant equation \|{:(2x , 1), (x , x):}\| = 3
Answer» `-1` `-1` or 1.5 1.5 `-1.5` SOLUTION :Evaluate the 2 by 2 determinant to get `2x^(2) - X = 3` . Then factor `2x^(2) - x - 3 ` into `(2x- 3) ( x + 1)` and SET each factor to ZERO to get `x = (3)/(2)` or x = - 1 .

Discussion

8608.	If int_(0)^(infty) f(x)dx=(pi)/(2) andf(x) is an even function, then int _(0)^(infty)f(x-(1)/(x)) dx is equal to
Answer» `(PI)/(4)` `(pi)/(2)` `pi` None of these Answer :B

Discussion

8609.	If(1+1/(1!)+(1)/(2!)+......oo)(1-(1)/(1!) +1/(2!) -1/(3!) + ......oo)=
Answer» 1 `E^(-2)` `-e^(-2)` 0 Answer :A

Discussion

8610.	Solvetheequationgiventhat ithas multipleroot x^4 +2x^3 -3x^2 -4x +4=0
Answer» ANSWER :`1,1,-2.-2`

Discussion

8611.	If a,b,c are three non-coplanar vectors then match the items of List -I with those of List -II. The correct answer is
Answer» `{:(""A,B,C,D),((a)" "III,IV,V,II):}` `{:(""A,B,C,D),((a)" "IV,V,II,III):}` `{:(""A,B,C,D),((a)" "I,IV,V,III):}` `{:(""A,B,C,D),((a)" "I,IV,II,III):}` Answer :D

Discussion

8612.	If a, b, c are three non-coplanar vectors and p, q, r are defined by the relations p=(b xx c)/([(a, b, c)]), q=(c xx a)/([(a, b, c)]) and r=(b xx a)/([a,b,c]), then a. p+b.q+c.r is equal to
Answer» 0 1 2 3 Solution :`ap+Bq+CR=(abxxc)/(["ABC"])+(bcxxa)/(["abc"])+(cBXXA)/(["abc"])` `=1+1-1=1`

Discussion

8613.	Ifvec(a),vec(b), vec(c)be threenon - zerovectors satisfyingthe condition vec(a) xx vec(b) = vec(c) and vec(b) xx vec(c) = vec(a) , then .
Answer» `vec(a), vec(b),vec(C)` are ORTHOGONAL is PAIRS `[vec(a),vec(b),vec(c)] = [vec(a)]^(2)` `[vec(a) vec(b) vec(c)] =[vec(c)]` `\|vec(b)\| = \|vec(c)\|` Answer :A::B::C

Discussion

8614.	Let f: R to R is defined by f(x)= {{:(,alpha+(sin [x])/(x),if x gt 0),(,2,if x =0),(,beta+[(sin x-x)/(x^(3))], if x lt 0):}where [y] denotes the integral part of y. If f is continuous at x=0, then beta-alpha=
Answer» `-1` 1 0 2 Answer :B

Discussion

8615.	By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/4)log (1+ tan x) dx
Answer» ANSWER :`pi/8log2`

Discussion

8616.	Statement-1 : In a double decker bus consisting of 5 seats on the ground floor and 5 on the first floor, the chance that two old person will take the ground floor and three children will take first floor while the five youth may take any floor is (""^5C_2xx2!xx""^5C_3xx3!xx5!)/(10!) Statement-2 Two person each make a single throw with a pair of dice. The chance that the throws are equal is coefficient of x^10 " in " (((1-x^6)/(1-x))^4)/((36)^2). Statement-3 : Given that x+y=2a, where a is constant and that all values of x between 0 and 2a are equally likely, then the chance that xy gt 3/4a^2 " is " 1/2.
Answer» TTT FTT FFT FTF Answer :A

Discussion

8617.	Statement - 1: consider an ellipse with foci at A(z_1) and B(z_2) in the argand plane if eccentricity of ellipse bee and it is known that origin is an interior point of the ellipse thene in (0, (\|z_1 + z_2\|)/(\|z_1\| + \|z_2\|)) and Statement - 2:If z_0 is the point interior to curve \|z- z_1\| + \|z-z_2\| = lambda rArr \|z_0 - z_1\| + \|z_0 - z_2\| lt lambda.
Answer» STATEMENT -1 is TRUE,Statement -2 is a correct explanation for Statement -1 Statement -1 is True, Statement -2 is True, Statement -2 is NOT a correct explanation for Statement -1 Statement -1 is True, Statement -2 is False. Statement -1 is False, Statement -2 is True. Answer :D

Discussion

8618.	int (x^(6) - 1)/(x^(2) +1)dx =
Answer» `(X^(5))/(5) - (x^(3))/(3)` + x + c `(x^(5))/(5) - (x^(3))/(3) + tan^(-1) ` x + c `(x^(5))/(5) -(x^(3))/(3) + x + tan^(-1)`x +C `(x^(5))/(5) -(x^(3))/(3) + x - 2TAN^(-1)`x +C Answer :D

Discussion

8619.	Find the centre and radius of the circle 2x^2 + 2y^2 - x = 0.
Answer» ANSWER :`1/4`

Discussion

8620.	int(dx)/(x^(4)-x^(2))=(1)/(x)+log\|f(x)\|+C then f(x) is given by
Answer» `(x+1)/(x-1)` `(x-1)/(x+1)` `((x-1)/(x+1))^(1//2)` `((x-1)/(x+1))^(2)` ANSWER :C

Discussion

8621.	If \|vecaxxvecb\|^2+\|veca.vecb\|^2=144and \|veca\|=4, then the value of \|vecb\| is
Answer» 1 2 3 4 Answer :C

Discussion

8622.	If the three points (0, 1), (0, -1) and (x, 0) are vertices of an equilateral triangle, then the values of x are
Answer» `SQRT3, SQRT2` `sqrt3, -sqrt3` `-SQRT5, sqrt3` `sqrt2, -sqrt2` ANSWER :B

Discussion

8623.	PQ is a vertical tower and A, B, C are three points on a horizontal line through Q, the foot of the tower and on the same side of the tower. If the angles of elevation of the top of the tower from A, B and C are alpha, beta, gamma respectively, then AB/BC =
Answer» `(COT alpha-cot GAMMA)/(cot beta - cot gamma)` `(cot alpha - cot beta)/(cot beta - cot gamma)` `(cot alpha - cot beta)/(cot alpha - cot gamma)` `(cot alpha - cot gamma)/(cot alpha - cot beta)` ANSWER :B

Discussion

8624.	Determine all real values of the parameter 'a' for which the equation 16x^4 - ax^3 + (2a + 17) x^2 - ax + 16 = 0 has exactly four distinct real roots that form a geometric progression.
Answer» ANSWER :170

Discussion

8625.	IF the angle between a pair of tangents drawn from a point P on the circle x^2+y^2+4x-6y+9 sin^2 a+13 cos^2a=0 us 2a, then the equation of the locus of P is
Answer» `x^2+y^2+4x-6y+4=0` `x^2+y^2+4x-6y-9=0` `x^2+y^2-4x+6y-4=0` `x^2+y^2+4x-6y+9=0` ANSWER :D

Discussion

8626.	If Z in C and area enclosed by the curves \|Z + bar(Z)\| + \|Z - bar(Z)\| ge 4 and \|Z\| le 2 is equal to (a pi - b) where a, b in N then the value of is
Answer» Solution :`\|Z + BAR(Z)\|+\|Z - bar(Z)\| ge 4` Let `Z = x + iy` `\|x\|+\|y\| ge 2` `\|z\| le 2` represent INTERIOR part of CIRCLE WHOSE radius is 2 and centre at origin Required area = `pi (2)^(2) - 4.1/2.2 = 4pi - 8` `a = 4, b = 8` then `b/(4a) = 8/16 = 0.5`.

Discussion

8627.	Refers to question 7, maximum value of Z+minimum value of Z is equal to
Answer» 12 1 `-13` `-17` Solution :Refers to solution 27, MAXIMUM value of Z+minimum value of Z =15-32=-17

Discussion

8628.	underset(-1)overset1inte^\|x\|dx=_______
Answer» SOLUTION :`UNDERSET(-1)overset(.1.)inte^\|x\|dx=2underset0overset1inte^\|x\|dx[becausee^\|x\|` is an even function] `=2underset0overset1inte^xdx=2[e^x]_0^1=2(e-1)`

Discussion

8629.	If r= hati +hatj+t (2hati-hatj+hatk) and r= 2hati+hatj-hatk+s (3 hati-5 hatj +2hatk) are the vector equations of two lines L_1 andL_2 then the shortest distance between them is
Answer» `9/(sqrt(59))` `(10)/(sqrt(59))` `(11) /(sqrt(59))` 0 Answer :B

Discussion

8630.	The probability that a non leap year will have 53 Wednesdays is
Answer» `(1)/(7)` `(2)/(7)` `(5)/(7)` `(6)/(7)` ANSWER :A

Discussion

8631.	Let p, q and r be three statements, then [ p rarr ( q rarr r ) ] harr [ ( p ^^ q) rarr r ],is a
Answer» tautology contradiction fallacy none of these Answer :A

Discussion

8632.	A point is moving along the curve y^(3)=27 x. The interval in which the abscissa changes at slower rate then the ordinate is ………..
Answer» `(-3,3)` `(-OO,oo)` `(-1,1)` `(-oo,-3)UU(3,oo)` ANSWER :C

Discussion

8633.	Write two different vectors having same magnitude.
Answer» ANSWER :An INFINITE of POSSIBLE ANSWERS.

Discussion

8634.	Find the equation of the ellipse whose vertices are (-4, 1) (6, 1) and one of the focal chord is x - 2 y - 2 = 0
Answer» ANSWER :`((x-1)^(2))/(25)+((y-1)^(2))/(16)=1`

Discussion

8635.	(i) If y=asin(log x) then prove that x^(2)(d^2y)/(dx^2)+x(dy)/(dx)+y=0.(ii) If y=acos(log_(e)x)+bsin(log_(e)x), then prove that x^2y_2^2+x*y_(1)+y=0.
Answer»

Discussion

8636.	I xx (a xx i) + j xx (a xx j) + k xx (a xx k)=
Answer» 3a 2a a 0 Answer :B

Discussion

8637.	"^(74)C_(37)-2 is divisibl by
Answer» `37^(2)` `38` `36` none of these Solution :`(a)` `'^(74)C_(37)-2` `=^(37)C_(0)^(2)+^(37)C_(1)^(2)+^(37)C_(2)^(2)+....^(37)C_(37)^(2)-2` `='^(37)C_(1)^(2)+^(37)C_(2)^(2)+....^(37)C_(36)^(2)` is DIVISIBLE by `37^(2)` (as each `'^(37)C_(1)`, `'^(37)C_(2)`, `'^(37)C_(3)`, ….`'^(37)C_(36)` are divisible by `37`)

Discussion

8638.	(i) If (1,2),(3,-4),(5,-6) and (c,8) are concyclic, then find c. If (2,0),(0,1),(4,5) and (0,c) are concyclic then find c.
Answer» ANSWER :(i) 19 or 3 (II) `14/3`

Discussion

8639.	Evaluate the following :[[x,1,-1],[2,y,1],[3,-1,z]]
Answer» SOLUTION :`[[X,1,-1],[2,y,1],[3,-1,z]]=[[x,0,-1],[2,y+1,1],[3,z-1,z]]` (`C_2=C_2+C_3`) `x[[y+1,1],[z-1,z]]-1[[2,y+1],[3,z-1]]` =x(yz+z-z+1)-(2z-2-3y-3) xyz+x-2z+3y+5 xyz+x+3y-2z+5

Discussion

8640.	If x=a+b, y=a omega+b omega^2,z=a omega^2+bomega show that x^2+y^2+z^2=6ab
Answer» SOLUTION :`L.H.S.=x^2+y^2+z^2` `=(a+b)^2+(aomega+bomega^2)^2(aomega^2+bomega)^2` `=a^2+b^2+2ab+a^2omega^2+b^2omega^4+2abomega^3+a^2omega^4+b^2omega^2+2abomega^3` `=a^2+a^2omega^2+a^2omega+b^2+b^2omega+b^2omega^2+2ab+2ab+2ab` `=a^2(1+omega^2+omega)+b^2(1+omega+omega^2)+6AB` `=0+0+6ab=6ab=R.H.S."(PROVED)"`

Discussion

8641.	I= int (dx)/( 1+ e^( x) )
Answer» ANSWER :`I= "In" ( e^X)/( 1+ e^x) + C = x - "In" (1+ e^x) + C`.

Discussion

8642.	Find the coefficient of x^(3) in the expansion of (2-x+5x^(2))^(6).
Answer» SOLUTION :N/A

Discussion

8643.	The value of "log"_2(7+sqrt(2+sqrt(2+sqrt(2+.....))))/(sqrt(18sqrt(18sqrt(18.....))) is : -
Answer» `1/2` -1 -2 2

Discussion

8644.	Relation "perpendicular" in the straight lines in a plane is :
Answer» reflexive symmetric transitive equivalence Answer :B

Discussion

8645.	State with reason whether the following functions have inverse g : {5, 6, 7, 8} rarr {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)}
Answer» Solution :5 and 7 have the same IMAGE 4, so G is not one-one and hense no inverse

Discussion

8646.	Evaluateint[cos^-1((1-tan^2x)/(1+tan^2x))+sin^-1((2tanx)/(1+tan^2x))]dx.
Answer» SOLUTION :`INT[cos^-1((1-tan^2x)/(1+tan^2x))+sin^-1((2tanx)/(1+tan^2x))]dx.=int[cos^-1cos2x+sin^-1sin2x]2x=int(2x+2x)dx=int4xdx=4x^2/2+C=2x^2+C`

Discussion

8647.	Statement I Ifalpha , betaare roots of 6x^(2) + 11x + 3 = 0 ", then " cos^(-1) alphaexists but notcot^(-1) beta ( alpha gt beta). Statement II Domain ofcos^(-1) x" is " [-1, 1].
Answer» ANSWER :a

Discussion

8648.	It is given that at x = 1, the function x^4-62x^2+ax+9 attains its maximum value, on the interval [0,2]. Find the value of a ?
Answer» SOLUTION :`f(X)=x^4-62x^2+ax+9,[0,2]f(x)=4x^3-124x+a` SINCE, f(x) attains MAXIMUM at x =1, f(x) = 0 at x =1 `thereforef(x)=0rArr4-124+a=0` a=120

Discussion

8649.	Integrate the following int(sinx)/(cos^3x)dx
Answer» Solution :`INT(SINX)/(cos^3x) DX` [PUT cosx=t then sinx dx=-dt] `int((-dt)/t^3)=-int-t^3 dt` `-t^(-2)/-2+C=(1/2t^2)+C.

Discussion

8650.	If bar(mu)=bar(a)-bar(b),bar(v)=bar(a)+bar(b),\|bar(a)\|=\|bar(b)\|=2 then \|bar(mu)xx bar(v)\|=……..
Answer» `2sqrt(16-(bar(a).bar(b))^(2))` `2sqrt(4(bar(a).bar(b))^(2))` `sqrt(16-(bar(a).bar(b))^(2))` `sqrt(4-(bar(a).bar(b))^(2))` Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

Find the points at which the function f given by f(x)=(x-2)^(4)(x+1)^(3) haspoint of inflexion.

Statement I Pi_(r=1)^(n) (1+sec 2^(r)theta)=tan 2^(n)theta cot theta Statement II Pi_(r=1)^(n) cos (2^(r-1)theta)=(sin(2^(n)theta))/(2^(n)sin theta)

Integrate the following functions: (cosx-sinx)/(1+sin(2x)

Evalute the following integrals int sqrt(x^(2) + 4)dx

There are 10 different objects 1, 2, 3,…..…10 arranged at random in 10 places marked 1, 2, 3,…….…10. The probability that exactly five of these objects occupy places corresponding to their number is k/3600, thenk is_____.

A and B six digits numbertotal numbers of ways of forming A and B so that (i) These numbes can be added without carrying at any stage, (ii) n_(2) can be subtracted form n_(1) without borrowing at any stage, is equal to.

Find all values of x that satisfy the determinant equation |{:(2x , 1), (x , x):}| = 3

If int_(0)^(infty) f(x)dx=(pi)/(2) andf(x) is an even function, then int _(0)^(infty)f(x-(1)/(x)) dx is equal to

If(1+1/(1!)+(1)/(2!)+......oo)(1-(1)/(1!) +1/(2!) -1/(3!) + ......oo)=

Solvetheequationgiventhat ithas multipleroot x^4 +2x^3 -3x^2 -4x +4=0

If a,b,c are three non-coplanar vectors then match the items of List -I with those of List -II. The correct answer is

If a, b, c are three non-coplanar vectors and p, q, r are defined by the relations p=(b xx c)/([(a, b, c)]), q=(c xx a)/([(a, b, c)]) and r=(b xx a)/([a,b,c]), then a. p+b.q+c.r is equal to

Ifvec(a),vec(b), vec(c)be threenon - zerovectors satisfyingthe condition vec(a) xx vec(b) = vec(c) and vec(b) xx vec(c) = vec(a) , then .

Let f: R to R is defined by f(x)= {{:(,alpha+(sin [x])/(x),if x gt 0),(,2,if x =0),(,beta+[(sin x-x)/(x^(3))], if x lt 0):}where [y] denotes the integral part of y. If f is continuous at x=0, then beta-alpha=

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/4)log (1+ tan x) dx

int (x^(6) - 1)/(x^(2) +1)dx =

Find the centre and radius of the circle 2x^2 + 2y^2 - x = 0.

int(dx)/(x^(4)-x^(2))=(1)/(x)+log|f(x)|+C then f(x) is given by

If |vecaxxvecb|^2+|veca.vecb|^2=144and |veca|=4, then the value of |vecb| is

If the three points (0, 1), (0, -1) and (x, 0)﻿ are vertices of an equilateral triangle, then﻿ the values of x are

PQ is a vertical tower and A, B, C are three points on a horizontal line through Q, the foot of the tower and on the same side of the tower. If the angles of elevation of the top of the tower from A, B and C are alpha, beta, gamma respectively, then AB/BC =

Determine all real values of the parameter 'a' for which the equation 16x^4 - ax^3 + (2a + 17) x^2 - ax + 16 = 0 has exactly four distinct real roots that form a geometric progression.

IF the angle between a pair of tangents drawn from a point P on the circle x^2+y^2+4x-6y+9 sin^2 a+13 cos^2a=0 us 2a, then the equation of the locus of P is

If Z in C and area enclosed by the curves |Z + bar(Z)| + |Z - bar(Z)| ge 4 and |Z| le 2 is equal to (a pi - b) where a, b in N then the value of is

Refers to question 7, maximum value of Z+minimum value of Z is equal to

underset(-1)overset1inte^|x|dx=_______

If r= hati +hatj+t (2hati-hatj+hatk) and r= 2hati+hatj-hatk+s (3 hati-5 hatj +2hatk) are the vector equations of two lines L_1 andL_2 then the shortest distance between them is

The probability that a non leap year will have 53 Wednesdays is

Let p, q and r be three statements, then [ p rarr ( q rarr r ) ] harr [ ( p ^^ q) rarr r ],is a

A point is moving along the curve y^(3)=27 x. The interval in which the abscissa changes at slower rate then the ordinate is ………..

Write two different vectors having same magnitude.

Find the equation of the ellipse whose vertices are (-4, 1) (6, 1) and one of the focal chord is x - 2 y - 2 = 0

(i) If y=asin(log x) then prove that x^(2)*(d^2y)/(dx^2)+x(dy)/(dx)+y=0.(ii) If y=acos(log_(e)x)+bsin(log_(e)x), then prove that x^2*y_2^2+x*y_(1)+y=0.

I xx (a xx i) + j xx (a xx j) + k xx (a xx k)=

"^(74)C_(37)-2 is divisibl by

(i) If (1,2),(3,-4),(5,-6) and (c,8) are concyclic, then find c. If (2,0),(0,1),(4,5) and (0,c) are concyclic then find c.

Evaluate the following :[[x,1,-1],[2,y,1],[3,-1,z]]

If x=a+b, y=a omega+b omega^2,z=a omega^2+bomega show that x^2+y^2+z^2=6ab

I= int (dx)/( 1+ e^( x) )

Find the coefficient of x^(3) in the expansion of (2-x+5x^(2))^(6).

The value of "log"_2(7+sqrt(2+sqrt(2+sqrt(2+.....))))/(sqrt(18sqrt(18sqrt(18.....))) is : -

Relation "perpendicular" in the straight lines in a plane is :

State with reason whether the following functions have inverse g : {5, 6, 7, 8} rarr {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)}

Evaluateint[cos^-1((1-tan^2x)/(1+tan^2x))+sin^-1((2tanx)/(1+tan^2x))]dx.

Statement I Ifalpha , betaare roots of 6x^(2) + 11x + 3 = 0 ", then " cos^(-1) alphaexists but notcot^(-1) beta ( alpha gt beta). Statement II Domain ofcos^(-1) x" is " [-1, 1].

It is given that at x = 1, the function x^4-62x^2+ax+9 attains its maximum value, on the interval [0,2]. Find the value of a ?

Integrate the following int(sinx)/(cos^3x)dx

If bar(mu)=bar(a)-bar(b),bar(v)=bar(a)+bar(b),|bar(a)|=|bar(b)|=2 then |bar(mu)xx bar(v)|=……..

If the three points (0, 1), (0, -1) and (x, 0) are vertices of an equilateral triangle, then the values of x are

(i) If y=asin(log x) then prove that x^(2)(d^2y)/(dx^2)+x(dy)/(dx)+y=0.(ii) If y=acos(log_(e)x)+bsin(log_(e)x), then prove that x^2y_2^2+x*y_(1)+y=0.