28278 + Interview Questions in Maths in Class 12 Page 176 InterviewSolution

8751.	A ladder 20 feet long is leaning against a wall. The bottom of the ladder is 16 feet away from the wall. If the upper end of the ladder slide along wall is lambda times the lower end of the ladder pull along the ground. Find the value of lambda.
Answer» ANSWER :`(4)/(3)`

Discussion

8752.	If f(x) and g(x) are differentiablefunction for 0 le x le 23 such thatf(0) =2, g(0) =0 f(23) =22 g (23) =10. Thenshow that f(x)=2g(x) for at least one x in the interval (0,23)
Answer»

Discussion

8753.	Consider a parabola P touches coordinate axes at (4,0) and (0,3). Length of latus rectum of parabola P is
Answer» `72/125` `144/125` `288/125` `576/125` ANSWER :D

Discussion

8754.	The triangle PQR is incribed in the circle x^(2)+y^(2)=25.If Q=(3,4) and R=(-4,3) then /_QPR=
Answer» `(PI)/2` `(pi)/3` `(pi)/4` `(pi)/6` ANSWER :C

Discussion

8755.	If the radius of a sphere is measured as 7m with an error of 0.02 m, then find the approximate error in calculating its volume.
Answer» ANSWER :`=3.92 PI (m)^(3)`

Discussion

8756.	int_(-pi//2)^(pi//2) sin^(2) x cos^(2) x(sin x + cos x) dx=
Answer» 0 `(11)/(4)` `(15)/(4)` `(4)/(15)` ANSWER :D

Discussion

8757.	The cartesian equation of a line is (x-5)/(3)=(y+4)/(7)=(z-6)/(2).Write its vector form.
Answer» ANSWER :A

Discussion

8758.	Using integration, find the area of region bounded by the triangle whose vertices are (-1,0),(1,3)" and "(3,2).
Answer» ANSWER :4

Discussion

8759.	Relation given by 'R={(1,1),(2,2),(2,1)} is :
Answer» REFLEXIVE only symmetric only transitive only equivalence relation Answer :D

Discussion

8760.	Let P(x,y) be a point inside the equilateral Delta ABC such that d(P, AB) + d(P, AC) + d(P, BC) = K where k is the altitude of the Delta then Statement - 1 area of the region of p (x,y) or of (Delta ABC) Statement - 2, For equilateral tringle if d (P,AB) + d(P,AC) + d(P,BC) = k then P will lie inside the pedal triangle of Delta ABC
Answer» STATEMENT - 1 is TRUE, statement -2 is true, statement-2 is a correct explanation fro 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 :C

Discussion

8761.	Let , p q, r and s be four statements, then ~[ ( p ^^ q) rarr ( r vee s ) ] is equivalent to
Answer» <P>p `^^`Q `^^ ~ R ^^ ~ s ` `p ^^ q ^^ r ^^ s ` `p ^^ q ^^ ~ r ^^ s ` `p ^^ q ^^ r ^^ ~ s ` ANSWER :A

Discussion

8762.	If A=[{:(-1,2,0),(-1,1,1),(0,1,0):}] then show that A^(-1)=A^2
Answer» ANSWER : `A^(-1)=A^2`

Discussion

8763.	If vec(a),vec(b)andvec(c) are any three vectors, then vec(a)xx(vec(b)xxvec(c))=vec(a)xx(vec(b)xxvec(c)) if and only if
Answer» `VEC(B),vec(C)` are COLLINEAR `vec(a)andvec(c)" are collinear "` `vec(a)andvec(b)" are collinear "` none Answer :A::C::D

Discussion

8764.	The ratio in which the line x+y=4 divides the line joining the points (-1, 1) and (5, 7) is
Answer» 1:2 2:1 1:3 3:1 Answer :A

Discussion

8765.	The rule of an "obstaclecourse" specifiesthat at the n^(th) obstacle a person has to tos a fair 6sided die n times. If the sum of points in these n tossesis bigger than 2^(n), the person is said to have crossed the obstacle.Q. The maximum obstaclesa person can cross :
Answer» 4 5 6 7 Answer :A

Discussion

8766.	Determine whether each of the following relations are reflexive , symmetric and transitive : Relation R in the set A of human beings in a town at a particular time given by R = {(x,y)} : x and y live in the same locality }
Answer» SOLUTION :N/A

Discussion

8767.	Determine whether each of the following relations are reflexive , symmetric and transitive : Relation R in the set A of human beings in a town at a particular time given by R = {(x,y)} : x is exactly 7 cm taller than y }
Answer» SOLUTION :N/A

Discussion

8768.	Determine whether each of the following relations are reflexive , symmetric and transitive : Relation R in the set A of human beings in a town at a particular time given by R = {(x,y): xis wife of y }
Answer» SOLUTION :N/A

Discussion

8769.	Determine whether each of the following relations are reflexive , symmetric and transitive : Relation R in the set A of human beings in a town at a particular time given by R = {(x,y): xis fatherof y }
Answer» SOLUTION :N/A

Discussion

8770.	The range of the function f(x)=""^(7-x)P_(x-3) is
Answer» {1, 2, 3, 4} {1, 2, 3, 4, 5, 6} {1, 2, 3} {1, 2, 3, 4, 5} ANSWER :C

Discussion

8771.	Water jet coming out of a stationary horizontal tube at speed v strikes horizontally a massive wall moving in opposite with same speed. Water come to rest relative to wall after striking. Treating A as cross-section of jet and density of water as rho. Select the correct alternative(s)
Answer» force exerted on the WALL is `2rhoAv^(2)` force exerted on the wall is `4rhoAv^(2)` rate of CHANGE of kinetic ENERGY of water jet STRIKING the wall is `8 rhoAv^(3)` rate of change of kinetic energy of water jet striking the wall is zero Answer :B::D

Discussion

8772.	Maximum value of tanA/2.tanB/2. tanC/2 in a triangle is equal to
Answer» ANSWER :`1/(3sqrt(3))`

Discussion

8773.	Show that P(n,n)=P(n,n-1)"For all positive integers."
Answer» SOLUTION :L.H.S.`=""^nP_n=(N!)/((n-n)!)=(n!)/(01)=(n!)/1=n!` `R.H.S.=""^nP_(n-1)=(n!)/((n-n+1)!) =(n!)/(1!)` `:.L.H.S.=R.H.S.`

Discussion

8774.	The mean marks of 120 students is 20. It was later discovered that two marks were wrongly taken as 50 and 80instead of 15 and 18. The correct mean of marks
Answer» `19.19` `19.17` `19.21` `19.14` ANSWER :A

Discussion

8775.	The modulus of ((3 + i) (2 - i))/(1 +i) is
Answer» 5 `SQRT5` `5sqrt2` `sqrt5//sqrt2` ANSWER :A

Discussion

8776.	If f(x) = sqrt(x^(2)+4)"then" int(f(x))/(x^(6))dx is equal to
Answer» `((f(x))^(3)((f(x))^(2)-10))/(120x^(5))+C` `((f(x))^(3)((f(x))^(2)-4))/(6x^(5))+C` `((f(x))^(3)((f(x))^(2)-2))/(20X^(5))+C` `((f(x))^(3)(x^(2)-6))/(6x^(5))+C` Answer :A

Discussion

8777.	If veca.vecb=sqrt15,\|vecb\|=sqrt3 and angle between veca and vecb" is "pi/3, find \|veca\|
Answer» ANSWER :`\|veca\|=2sqrt5`

Discussion

8778.	If the tangent at the point P (2,4) to the parabola y^(2)=8x meets the parabola y^(2)=8x+5 at Q and R then the midpoint of QR is
Answer» (2,4) (4,2) (7,9) none Answer :A

Discussion

8779.	Find unit vector in the direction of vector bar(a) = (2bar(i)+3bar(j)+bar(k))
Answer» Answer :`(2BAR(i)+3BAR(j)+bar(K))/(sqrt(14))`

Discussion

8780.	For two data sets each of size 5 the variances are given by 4 and 5 and the corresponding means are given to be 2 and 4 respectively. Then find the variance of the combined data.
Answer» ANSWER :`11//2`

Discussion

8781.	For A=a^2+b^2+c^2,B=ab+bc+ca,(a^3,b^3c^3-3abc)^2 is equal to
Answer» `\|{:(B,A,B),(B,B,A),(A,B,B):}\|` `\|{:(A,B,B),(B,B,A),(B,A,B):}\|` `\|{:(B,B,A),(B,A,B),(A,B,B):}\|` NONE of these Answer :A

Discussion

8782.	n different letters are placed in n different addressed envelopes at random. Find the probability that (i) no letter is placed in right envelope i.e., all the letters are placed in wrong envelopes. (ii) atleast one letter is placed in right envelope.
Answer» Answer :`1 - {(1)/(\|UL(2)) - (1)/(\|ul(3)) + (1)/(\|ul(4))...+(-1)^(n) (1)/(\|ul(n))}`

Discussion

8783.	IF A = [{:(3,,1),(-1,,2):}] then A^(2) -5A is equal to
Answer» I `-I` 7I `-7I` ANSWER :D

Discussion

8784.	If u, v and w are functions of x, then show that (d)/(dx) (u.v.w) = (du)/(dx) v.w + u.(dv)/(dx).w + u.v.(dw)/(dx) in two ways- first by repeated application of product rule, second by logarithmic differentiation. Using product rule
Answer» ANSWER :`(du)/(DX) (v-W).(DV)/(dx).U + w+ (u.v) (dw)/(dx)`

Discussion

8785.	The setof real values of x for which the inequality \|x-1\|+\|x+1\|lt 4 always holds good is
Answer» `(-2,2)` `(-OO,-2)UU(2,oo)` `(-oo,-1]uu[1,oo)` `(-2,-1)uu(1,2)` ANSWER :A

Discussion

8786.	If a = 2hat(i) + 3hat(j) +hat(k),b = hat(i)- 3 hat(j)- 5hat(k) and c=3hat(i)-4hat(k), then match the items of List - I with those of List - II.
Answer» `{:(A,B,C,D),(IV,III,II,i):}` `{:(A,B,C,D),(iv,iii,ii,V):}` `{:(A,B,C,D),(iv,iii,i,ii):}` `{:(A,B,C,D),(i,ii,iii,v):}` Answer :A

Discussion

8787.	Let n be a natural number. Then the range of the function f(n)=""^(8-n)P_(n-4),4lenle6, is
Answer» {1, 2, 3, 4} {1, 2, 3, 4, 5, 6} {1, 2, 3} {1, 2, 3, 4, 5} Answer :C

Discussion

8788.	A five digit number is formed by the digits 1,2,3,4,5 with no digit being repeated. The prohability that the number is divisible by 4, is
Answer» `(1)/(5)` `(2)/(5)` `(3)/(5)` `(4)/(5)` Answer :a

Discussion

8789.	Function whose jump (non-negative difference of LHL and RHL) of discontinuity is greater than or equal to one. Is/are
Answer» `f(x) = {{:((e^(1//x)+1)/(e^(1//x)-1)",",x lt 0),((1-cos x)/(x)",",x gt 0):}` `g(x) = {{:((x^(1//3)-1)/(x^(1//2)-1)",",x gt 1),((log x)/(x-1)",",(1)/(2) lt x lt 1):}` `U(x)={{:((sin^(-1)2x)/(tan^(-1)3x)",",x in [0, (1)/(2)]),((\|sin x\|)/(x)",",x lt 0):}` `V(x) = {{:(log_(3)(x+2)",",x gt 2),(log_(1//2)(x^(2)+5)",",x lt 2):}` Answer :A::C

Discussion

8790.	What do the marching soldiers under the windows represent?
Answer» The Dawn of Prussia in the DEFEAT of FRENCH people The defeat of Prussia The VICTORY of French None of these Answer :A

Discussion

8791.	Integration of some particular functions : int(x^(4)+3x^(2)+1)/(x^(2)+3)dx=....+c
Answer» `(X^(3))/(3)+TAN^(-1)((x)/(sqrt(3)))` `x^(2)+(1)/(sqrt(3))tan^(-1)((x)/(sqrt(3)))` `(x^(3))/(3)+(1)/(sqrt(3))tan^(-1)((x)/(sqrt(3)))` `(x^(3))/(3)+tan^(-1)((x)/(sqrt(3)))` Answer :C

Discussion

8792.	If 2^(x)=8^(x+4)
Answer» `4` `6` `8` `64` ANSWER :B

Discussion

8793.	Find derivatives of the following functions.a^(In x)
Answer» SOLUTION :`y = a^(In X). In a. d/dx(In x) [because d/dx(a^u) = a^u. In a. (du/dx) a^(In x). In a. 1/x = (a^(In x) INA)/x)`

Discussion

8794.	Consider f(x)=4x^(4)-24x^(3)+31x^(2)+6x-8 be a polynomial function and alpha, beta, gamma are the roots (alpha lt beta lt gamma lt sigma), So,
Answer» <P>`sigma^(p)+1/(sigma^(ALPHA))+alpha^(r)+r^(sigma)=36` `sigma_(p)+1/(sigma^(alpha))+sigma^(r)+r^(sigma)=18` `int_(2alpha)^(2BETA) (x^(alpha+1)-5x^(r+1)+2beta\|x\|+1)/(x^(2)+4beta\|x\|+1)dx=2 In 2` `int_(2alpha)^(2beta) (x^(sigma+1)-5x^(r+1)+2beta\|x\|)+1/(x^(2)+4beta\|x\|+1) dx=In 2` Solution :ac `f(x)=(2x-1)(2x+1)(x-2)(x-4)`

Discussion

8795.	The radius of right circular cylinder of maximum volume which can be inscribed in a sphere of radius r is
Answer» R `r//2` `SQRT(2//3)r` `sqrt(3//2)r` ANSWER :C

Discussion

8796.	If \|{:(b+ c, b, c),(a, c + a, c),(a, b, a+b):}\| = k(a.b.c), then the value of k equals
Answer» 0 2 4 `-4` ANSWER :C

Discussion

8797.	Let A, B, C be real numbers such that (i) (sin A, cos B) lies on a unit circle centred at origin. (ii) tan C and cot C are defined. If the minimum value of (tan C – sin A)^(2) + (cot C – cos B)^(2) is a+bsqrt(2) where a, b in I, find the valueof a^(3) + b^(3).
Answer» ANSWER :19

Discussion

8798.	Tangents are drawn from a point P to the hyperbola x^2/2-y^2= 1 If the chord of contact is a normal chord, then locus of P is the curve8/x^2 - 1/y^2 = lambda where lambda in N .Find lambda
Answer» ANSWER :0.9

Discussion

8799.	Find the differential equations of the family of circles (i) touching the y-axis at the origin (ii) having centres on the y-axis and passing through the origin.
Answer» ANSWER :(i) `y^(2) - X^(2) = 2xy(dy)/(DX)` (ii) `(x^(2) - y^(2))(dy)/(dx) - 2xy = 0`

Discussion

8800.	The value of sec(2cot^(-1)2+cos^(-1)3/5) is equal to
Answer» `25/24` `-24/7` `25/7` `-25/7` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

A ladder 20 feet long is leaning against a wall. The bottom of the ladder is 16 feet away from the wall. If the upper end of the ladder slide along wall is lambda times the lower end of the ladder pull along the ground. Find the value of lambda.

If f(x) and g(x) are differentiablefunction for 0 le x le 23 such thatf(0) =2, g(0) =0 f(23) =22 g (23) =10. Thenshow that f(x)=2g(x) for at least one x in the interval (0,23)

Consider a parabola P touches coordinate axes at (4,0) and (0,3). Length of latus rectum of parabola P is

The triangle PQR is incribed in the circle x^(2)+y^(2)=25.If Q=(3,4) and R=(-4,3) then /_QPR=

If the radius of a sphere is measured as 7m with an error of 0.02 m, then find the approximate error in calculating its volume.

int_(-pi//2)^(pi//2) sin^(2) x cos^(2) x(sin x + cos x) dx=

The cartesian equation of a line is (x-5)/(3)=(y+4)/(7)=(z-6)/(2).Write its vector form.

Using integration, find the area of region bounded by the triangle whose vertices are (-1,0),(1,3)" and "(3,2).

Relation given by 'R={(1,1),(2,2),(2,1)} is :

Let , p q, r and s be four statements, then ~[ ( p ^^ q) rarr ( r vee s ) ] is equivalent to

If A=[{:(-1,2,0),(-1,1,1),(0,1,0):}] then show that A^(-1)=A^2

If vec(a),vec(b)andvec(c) are any three vectors, then vec(a)xx(vec(b)xxvec(c))=vec(a)xx(vec(b)xxvec(c)) if and only if

The ratio in which the line x+y=4 divides﻿ the line joining the points (-1, 1) and (5, 7)﻿ is﻿

The rule of an "obstaclecourse" specifiesthat at the n^(th) obstacle a person has to tos a fair 6sided die n times. If the sum of points in these n tossesis bigger than 2^(n), the person is said to have crossed the obstacle.Q. The maximum obstaclesa person can cross :

Determine whether each of the following relations are reflexive , symmetric and transitive : Relation R in the set A of human beings in a town at a particular time given by R = {(x,y)} : x and y live in the same locality }

Determine whether each of the following relations are reflexive , symmetric and transitive : Relation R in the set A of human beings in a town at a particular time given by R = {(x,y)} : x is exactly 7 cm taller than y }

Determine whether each of the following relations are reflexive , symmetric and transitive : Relation R in the set A of human beings in a town at a particular time given by R = {(x,y): xis wife of y }

Determine whether each of the following relations are reflexive , symmetric and transitive : Relation R in the set A of human beings in a town at a particular time given by R = {(x,y): xis fatherof y }

The range of the function f(x)=""^(7-x)P_(x-3) is

Water jet coming out of a stationary horizontal tube at speed v strikes horizontally a massive wall moving in opposite with same speed. Water come to rest relative to wall after striking. Treating A as cross-section of jet and density of water as rho. Select the correct alternative(s)

Maximum value of tanA/2.tanB/2. tanC/2 in a triangle is equal to

Show that P(n,n)=P(n,n-1)"For all positive integers."

The mean marks of 120 students is 20. It was later discovered that two marks were wrongly taken as 50 and 80instead of 15 and 18. The correct mean of marks

The modulus of ((3 + i) (2 - i))/(1 +i) is

If f(x) = sqrt(x^(2)+4)"then" int(f(x))/(x^(6))dx is equal to

If veca.vecb=sqrt15,|vecb|=sqrt3 and angle between veca and vecb" is "pi/3, find |veca|

If the tangent at the point P (2,4) to the parabola y^(2)=8x meets the parabola y^(2)=8x+5 at Q and R then the midpoint of QR is

Find unit vector in the direction of vector bar(a) = (2bar(i)+3bar(j)+bar(k))

For two data sets each of size 5 the variances are given by 4 and 5 and the corresponding means are given to be 2 and 4 respectively. Then find the variance of the combined data.

For A=a^2+b^2+c^2,B=ab+bc+ca,(a^3,b^3c^3-3abc)^2 is equal to

n different letters are placed in n different addressed envelopes at random. Find the probability that (i) no letter is placed in right envelope i.e., all the letters are placed in wrong envelopes. (ii) atleast one letter is placed in right envelope.

IF A = [{:(3,,1),(-1,,2):}] then A^(2) -5A is equal to

If u, v and w are functions of x, then show that (d)/(dx) (u.v.w) = (du)/(dx) v.w + u.(dv)/(dx).w + u.v.(dw)/(dx) in two ways- first by repeated application of product rule, second by logarithmic differentiation. Using product rule

The setof real values of x for which the inequality |x-1|+|x+1|lt 4 always holds good is

If a = 2hat(i) + 3hat(j) +hat(k),b = hat(i)- 3 hat(j)- 5hat(k) and c=3hat(i)-4hat(k), then match the items of List - I with those of List - II.

Let n be a natural number. Then the range of the function f(n)=""^(8-n)P_(n-4),4lenle6, is

A five digit number is formed by the digits 1,2,3,4,5 with no digit being repeated. The prohability that the number is divisible by 4, is

Function whose jump (non-negative difference of LHL and RHL) of discontinuity is greater than or equal to one. Is/are

What do the marching soldiers under the windows represent?

Integration of some particular functions : int(x^(4)+3x^(2)+1)/(x^(2)+3)dx=....+c

If 2^(x)=8^(x+4)

Find derivatives of the following functions.a^(In x)

Consider f(x)=4x^(4)-24x^(3)+31x^(2)+6x-8 be a polynomial function and alpha, beta, gamma are the roots (alpha lt beta lt gamma lt sigma), So,

The radius of right circular cylinder of maximum volume which can be inscribed in a sphere of radius r is

If |{:(b+ c, b, c),(a, c + a, c),(a, b, a+b):}| = k(a.b.c), then the value of k equals

Let A, B, C be real numbers such that (i) (sin A, cos B) lies on a unit circle centred at origin. (ii) tan C and cot C are defined. If the minimum value of (tan C – sin A)^(2) + (cot C – cos B)^(2) is a+bsqrt(2) where a, b in I, find the valueof a^(3) + b^(3).

Tangents are drawn from a point P to the hyperbola x^2/2-y^2= 1 If the chord of contact is a normal chord, then locus of P is the curve8/x^2 - 1/y^2 = lambda where lambda in N .Find lambda

Find the differential equations of the family of circles (i) touching the y-axis at the origin (ii) having centres on the y-axis and passing through the origin.

The value of sec(2cot^(-1)2+cos^(-1)3/5) is equal to

The ratio in which the line x+y=4 divides the line joining the points (-1, 1) and (5, 7) is