28278 + Interview Questions in Maths in Class 12

1.	Dupose g(x) is the inverse of f (x) and f (x) has a domain x in [a,b]. Given f (a)= alpha and f (b) beta, then find value of int _(a) ^(b) f (x) dx + int _( alpha ) ^(beta) g (y) dy in terms of a,b, alpha and beta.
Answer» <P> ANSWER :`(p^(2))/(1+ p ^(2))`

Discussion

2.	Solve (x-1)(x-3)(x-5)(x-7)=9.
Answer» ANSWER :`4, 4+- SQRT(10)`

Discussion

3.	If the line x Cos alpha+y Sin alpha=p touches x^(2)/a^(2)-y^(2)/b^(2)=1 then a^(2) Cos^(2)alpha-b^(2) Sin^(2)alpha=
Answer» `2p^2` `p^2` p 2p Answer :B

Discussion

4.	Integrate the functions x(logx)^(2)
Answer» Answer :`(x^(2))/(2)(logx)^(2)-(x^(2))/(2)logx+(1)/(4)x^(2)+C`

Discussion

5.	In a class 30% of the student fail in Mathematics,20% of the student fail in English and 10% fail in bothIf he has failed in Mathematics, what is the probability that he has failed in English
Answer» SOLUTION :If he has FAILED in MATHEMATICS, then the probability thet he has failed in ENGLISH `P(B/A)=P((ACAPB))/(P(A))=(10/100)/(30/100)=1/3`

Discussion

6.	int sqrt((x - 1)/(x -2))dx =
Answer» `SQRT(x^(2)- 3X + 2) + (1)/(2) "cosh"^(-1)`(2x - 3) + C `sqrt(x^(2)- 3x + 2) - (1)/(2) "cosh"^(-1)`(2x - 3)+ C `sqrt(x^(2)- 3x + 2) + (1)/(2) "cosh"^(-1)`(2x + 3) + C `sqrt(x^(2)- 3x + 2) - (1)/(2) "cosh"^(-1)`(2X3) + C Answer :A

Discussion

7.	The slope of the normal to the curve y=2x^(2)+3sin x at x = 0 is ……….
Answer» 3 `(1)/(3)` `-3` `-(1)/(3)` ANSWER :D

Discussion

8.	If a+b+c=0 and \|{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}\|=0 then find the value of x
Answer» ANSWER :`x=0,+-SQRT(3/2(a^2+b^2+c^2))`

Discussion

9.	a_(1), a_(2), a_(3) ……….. Is an A.P. which of the following is true
Answer» 1. `a_(1) + a_(2) = a_(2) + a_(4)` 2. `a_(2) + a_(8) = a_(4) + a_(6)` 3. `a_(2) = 2a_(4)` 4. `a_(1) lt a_(2) lt a_(3) ………….` ANSWER :B

Discussion

10.	The value of a.b where a = 2i - 3j -k, b = 3i + 2j - 2k
Answer» ANSWER :2

Discussion

11.	Differentiate x^2sinx
Answer» SOLUTION :Let `y=x^2sinx` Then`dy/DX=d/dx(x^2).sinx+x^2d/dx(sinx)` `[therefore/dx(u.v)=(DU)/dx cdotv+u cdot(dv)/dx`

Discussion

12.	Two runner A and B start at the origin and run along positive x axis ,with B running three times as fast as A. An obsever, standeing one unit above the origin , keeps A and B in view.Then the maximum angle theta of sight between the observer's view of A and B is
Answer» `pi//8` `pi//6` `pi//3` `pi//4` Solution :`TAN theta = tan (theta_(2)-theta_(1))` `RARR tan theta =(3x-x)/(1+3xx)=(2x)/(1+3x^(2))` `Let y=(2x)/(1+3x^(2))` `rarr (dy)/(dx)=2(1-3x^(2))/(1+3x^(2^(2)))` and `(d^(2)y)/(dx^(2))=(-24x)/(1+3x^(2^(3)))lt0 for x =1//sqrt(3)` `therefore theta_(MAX)=pi//6`

Discussion

13.	If 'a' is the coefficient of the middle term in the expansion of (1 + x)^(2n) and b,c are the coefficients of two middle terms in the expansion of (1 + x)^(2n -1) then
Answer» a + B = C `a = b+ c b= c+a b + c = 2A ANSWER :B

Discussion

14.	Draw the graph of the relation (y-x)^(2)=x^(3)
Answer» SOLUTION :We have `(y-x)^(2)=x^(3)` We must have `x GE0` `rArr y-x=+-x^(3//2)` `rArr y=x+x^(3//2)`………………(i) or `y=x-x^(3//2)`…………..(ii) Function (i) is an INCREASING function and always non-negative. So its graph LIES above the x-axis. Function (ii) meets the x-axis, where `x-x^(3//2)=0` or `x=0,1` When `x to infty, x - x^(3//2) to -infty` From these information, we can plot the graph of functions as shown in the following figure.

Discussion

15.	STATEMENT-1 : Forn ne N, n gt 1 , 2^(n) gt 1 n ^((n-1)/(2)) and STATEMENT-2 : A.M. of distinct positive number is greater then G.M.
Answer» Statemant-1 is True , STATEMENT-2 is True, Statement -2 is a correct explanation for Statement-1 Statemant-1 is True , Statement-2 is True, Statement -2 is NOTA correct explanation for Statement-1 Statement-1 is True, Stetement-2 is False. Statement-1 is False, Statement-2 is True ANSWER :1

Discussion

16.	If A is squarematrix of order 3, then consider the following statements I. If \|A\|=0 , then \|AdjA\|=0 II. If \|A\| ne 0 , then \|A^(-1)\|=\|A\|^(-1) Which of the above statements is / are ture ?
Answer» Both I and II Neither I nor \|\| I only II only Answer :A

Discussion

17.	Solvethe equationx^4-2x^3+ 4x^2+ 6x-21=0 the sumoftwoof rootsbeingzero.
Answer» ANSWER :`+- SQRT(3) ,1+- sqrt(6) i`

Discussion

18.	Find the area of the parallelogy whose diagonals are determined the vectors 2hati+hatk and hati+hatj+hatk.
Answer» Answer :`(SQRT(6))/(2)` SQ. units

Discussion

19.	Show that the function given by f(x)=3x+17 is strictly increasing on R.
Answer» Solution :We have `F(x)=3xx1+0=3gt0` for all `"x"inRtherefore` f is strictly INCREASING on R

Discussion

20.	If the equation 2hxy+2gx+2fy+c=0represents two straight lines, then show that they form a rectangle of area (\|fg\|)/(h^2) with the coordinate axes.
Answer»

Discussion

21.	For k in N, let N_(k) = {km : m in N} Suppose a,b in N and N_(a) cap N_(b) = N_( c) for some c in N, then
Answer» c=ab c=a+B c=hcf(a,b) c=lem(a,b) ANSWER :D

Discussion

22.	Out of 8 gentlemen and 5 ladies a committee of 5 is to be formed. Find the number of ways in which this can be done so as to include atleast 2 ladies.
Answer» ANSWER :881

Discussion

23.	If A+B+C=180^(@), then sin 2 A+sin 2B-sin2C=
Answer» `4sinA cos B SIN C` `4 cos A sin B sin C` `4 cos A cos B sin C` `4COS ASIN B cos C` Answer :C

Discussion

24.	Write the order and degree of the differential equation given by : ((d^2y)/dx^2)^(3/2)=1+(dy/dx)^5
Answer» SOLUTION :ORDER = 2, DEGREE = 3

Discussion

25.	Let x_(1), x_(2), …, x_(15) be 15 distinct numbers chosen from 1, 2, 3, …., 15. Then the value of (x_(1)-1) (x_(2)-1) (x_(3)-1) …(x_(15)-1) is
Answer» always `le 0` 0 always EVEN always ODD ANSWER :b

Discussion

26.	lim_(n rarr oo) sum_(k=1)^(n) k/(n^(2)+k^(2))=
Answer» `1/2 LOG 2` `2 log 2` `1/3 log 2` `3 log 2` ANSWER :A

Discussion

27.	Find (dy)/(dx): x=t + (1)/(t) and y= t - (1)/(t)
Answer» ANSWER :`(t^(2)+1)/(t^(2)-1)`

Discussion

28.	If P(A) = 0.8, P(B) = 0.5 and P(B/A)= 0.4, find P (AnnB)
Answer» <P> SOLUTION :P(B/A)=0.4`RARR` `(P(ANNB))/(P(A))`=0.4 `rArr (P(AnnB))` = 0.4xx(P(A)) =0.4xx0.8=0.32

Discussion

29.	A die is thrown 5 times. If getting an even number is a success, what is the probability of 3 successes ?
Answer» SOLUTION :P=p(EVEN number)`=3/6=1/2` q=p(non even number)`=1/2` `THEREFORE`P(SUCCESS)=`p=1/2`,p(failure)=`q=1/2` p(3 success in 5 THROWS)`=^5C_3p^3q^3=10.(1/2)^5=10/32=5/16`

Discussion

30.	Given regression co-efficient of y on x is 0.4 and r(x,y) = (2)/( sqrt(10)), then the regression co-efficient of x on y is
Answer» 1 `0.2` `SQRT(10)` 2 Answer :A

Discussion

31.	If (x-1)^4-16=0,then the sum of non-real complex values of x is
Answer» 2 0 4 3 Answer :A

Discussion

32.	If A is matrix of order mxxn and B is a matrix such that AB^T and B^TAbothare defined , then order of matrix B is …………..
Answer» `mxxm` `nxxn` `nxxm` `mxxn` ANSWER :D

Discussion

33.	Find the area under the given curves a given line :y=x^2,x=1,x=2and x-axis
Answer» SOLUTION : AREA `=overset2underset1intydx=overset2underset1int x^2dx=[x^3/3]_1^2` `1/3[2^3-1^3]=7/3`sq.units

Discussion

34.	If P(A) = 0.8, P(B) = 0.5 and P (B\|A) = 0.4, find (i) P(A cap B) (ii) P(A\|B) (iii) P(A cup B)
Answer» ANSWER :(i) 0.32, (II) 0.64 , (III) 0.98

Discussion

35.	y" + 2y' + sin y = 0
Answer» ANSWER :ORDER 2; DEGREE 1

Discussion

36.	Find the equation of line of intersection of the planes3x-y+ z=1 and x + 4 y -2 z =2.
Answer» ANSWER :`(X- (6)/(13))/(-2 //13)= (Y - (5)/(13))/(7//13)= (z=0)/(1)`

Discussion

37.	Examine the consistency of the system of linear equtions in 1 to 6 3x-y-2z=2 2y-z=-1 3x-5y=3
Answer» ANSWER :`[{:(-5),(-3),(-6):}]ne[{:(0),(0),(0):}]`

Discussion

38.	From the three pairs of lines given below, identify those which uniquely determine a plane : (i)intersecting pair, (ii) parallel pair, (iii) a pair of skew lines.
Answer» Solution : Out of given three pairs , (i) Intersecting pair and (II) PARALLEL pair of LINES determine a PLANE.

Discussion

39.	LetP(n) : s^ngtnAAn in N and2^kgt k, AAn = K thenwhichof thefollowingis trueAAk ge2?
Answer» `2^kgt 5 Kgt 1` `2^(k+1)gt 2kgt k+1` ` 2^kgt2(k +1) gt k` NONEOF these Answer :B

Discussion

40.	cos x = b for what b do the roots of the equation form an A.P?
Answer» `-1` `1/2` `sqrt(3)/2` NONE of these Answer :A

Discussion

41.	Consider a triangle ABC, where c,y,z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a,b, c respectively. Let the letters R,r S,Delta denote the circumradius, inradius semi-perimeter and area of the triangle respectively. The valur of (c sin B+b sin C)/(x)+ (a sin C +c sin A)/(y)+(b sin A+a sin B)/(z) is equal to
Answer» `R/r` `S/R` 2 6 Answer :D

Discussion

42.	Find derivatives of the following functions.In tan x
Answer» Solution :`y = In (TAN x) [because d/DX(In u) = (l DU)/(u dx) dy/dx = 1/(tan x). d/dx (tan x) = sec^2x/tan x (1 + tan^2 x)/tan x =COT x + tan x`

Discussion

43.	Which one of the following equals the average of x and 1//x?
Answer» `(X+ 2)/(x)` `(x^2 + 1)/(2X)` `(x + 1)/(x^2)` `(2x^2 + 1)/(x)` Answer :B

Discussion

44.	Consider a triangle ABC, where c,y,z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a,b, c respectively. Let the letters R,r S,Delta denote the circumradius, inradius semi-perimeter and area of the triangle respectively. If cot A+cot B+ cot C= k ((1)/(x^(2))+ (1)/(y^(2))+(1)/(z^(2))), then the value of k is
Answer» `R^(2)` RR `Delta` `a ^(2)+b^(2) +c^(2)` ANSWER :C

Discussion

45.	The mean of 5 observation is 4.4 and their variance is 8.24 . If three of the observations are 1,2 and 6, find the other two observations .
Answer» ANSWER :4 and 9

Discussion

46.	Consider a triangle ABC, where c,y,z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a,b, c respectively. Let the letters R,r S,Delta denote the circumradius, inradius semi-perimeter and area of the triangle respectively. If (bx)/(c) +(cy)/(a)+(az)/(b) =(a^(2) +b^(2)+c ^(2))/(k), then the value of k is
Answer» R S 2R `3/2R` ANSWER :C

Discussion

47.	The value of ..............
Answer» Solution :`(A)= int_(-pi)^(x) ubrace(cos 2x. cos 2^(2)x. cos 2^(3)x. cos 2^(4) x. cos 2^(5)x)_(f(x))")"dx` `I=2 int_(0)^(pi) f(x) dx` [f(x) is EVEN] `I=2.2 int_(0)^(pi//2) f(x) dx` `:' f(pi-x) = f(x)` `I= 4 int_(0)^(pi//2) f(x) dx =4 l_(1)` Now, `l_(1)= int_(0)^(pi//2) f(x)dx` `l_(1)=-l_(1)` `:' f(pi/2 -x)=-f(x)` `l_(1)=0` `IMPLIES l=0`

Discussion

48.	How many 4 letter words can be formed using the letters of the word 'PROPORTION'.
Answer» ANSWER :758

Discussion

49.	Statement -1 alpha = e^((i2 pi)/7) and f (x) = A_(0) + underset(k=1)overset(20)sum A_(k)x^(k) , " then " f(x) + f(alphax) + f(alpha^(2)x) + …..+ f(alpha^(2)x) = 5(A_(0)+A_(7)x^(7) + A_(14)x^(14)) Statement -2 : The least argument of a complex number z, satisfying\|z-16i\| ge 8 " is " pi/3 rStatement -3 Maximum argumentof the complex number z, satisfying\|z-16i\| ge 8 " is "(2pi)/3
Answer» F T T F T F FF F T F T ANSWER :A

Discussion

50.	Ifsin theta+ cosectheta=2,thenthevalueofsin ^6 theta+ cosec^6 thetais equal to
Answer» `0` `1` `2` `2^3` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Dupose g(x) is the inverse of f (x) and f (x) has a domain x in [a,b]. Given f (a)= alpha and f (b) beta, then find value of int _(a) ^(b) f (x) dx + int _( alpha ) ^(beta) g (y) dy in terms of a,b, alpha and beta.

Solve (x-1)(x-3)(x-5)(x-7)=9.

If the line x Cos alpha+y Sin alpha=p touches x^(2)/a^(2)-y^(2)/b^(2)=1 then a^(2) Cos^(2)alpha-b^(2) Sin^(2)alpha=

Integrate the functions x(logx)^(2)

In a class 30% of the student fail in Mathematics,20% of the student fail in English and 10% fail in bothIf he has failed in Mathematics, what is the probability that he has failed in English

int sqrt((x - 1)/(x -2))dx =

The slope of the normal to the curve y=2x^(2)+3sin x at x = 0 is ……….

If a+b+c=0 and |{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 then find the value of x

a_(1), a_(2), a_(3) ……….. Is an A.P. which of the following is true

The value of a.b where a = 2i - 3j -k, b = 3i + 2j - 2k

Differentiate x^2sinx

Two runner A and B start at the origin and run along positive x axis ,with B running three times as fast as A. An obsever, standeing one unit above the origin , keeps A and B in view.Then the maximum angle theta of sight between the observer's view of A and B is

If 'a' is the coefficient of the middle term in the expansion of (1 + x)^(2n) and b,c are the coefficients of two middle terms in the expansion of (1 + x)^(2n -1) then

Draw the graph of the relation (y-x)^(2)=x^(3)

STATEMENT-1 : Forn ne N, n gt 1 , 2^(n) gt 1 n ^((n-1)/(2)) and STATEMENT-2 : A.M. of distinct positive number is greater then G.M.

If A is squarematrix of order 3, then consider the following statements I. If |A|=0 , then |AdjA|=0 II. If |A| ne 0 , then |A^(-1)|=|A|^(-1) Which of the above statements is / are ture ?

Solvethe equationx^4-2x^3+ 4x^2+ 6x-21=0 the sumoftwoof rootsbeingzero.

Find the area of the parallelogy whose diagonals are determined the vectors 2hati+hatk and hati+hatj+hatk.

Show that the function given by f(x)=3x+17 is strictly increasing on R.

If the equation 2hxy+2gx+2fy+c=0represents two straight lines, then show that they form a rectangle of area (|fg|)/(h^2) with the coordinate axes.

For k in N, let N_(k) = {km : m in N} Suppose a,b in N and N_(a) cap N_(b) = N_( c) for some c in N, then

Out of 8 gentlemen and 5 ladies a committee of 5 is to be formed. Find the number of ways in which this can be done so as to include atleast 2 ladies.

If A+B+C=180^(@), then sin 2 A+sin 2B-sin2C=

Write the order and degree of the differential equation given by : ((d^2y)/dx^2)^(3/2)=1+(dy/dx)^5

Let x_(1), x_(2), …, x_(15) be 15 distinct numbers chosen from 1, 2, 3, …., 15. Then the value of (x_(1)-1) (x_(2)-1) (x_(3)-1) …(x_(15)-1) is

lim_(n rarr oo) sum_(k=1)^(n) k/(n^(2)+k^(2))=

Find (dy)/(dx): x=t + (1)/(t) and y= t - (1)/(t)

If P(A) = 0.8, P(B) = 0.5 and P(B/A)= 0.4, find P (AnnB)

A die is thrown 5 times. If getting an even number is a success, what is the probability of 3 successes ?

Given regression co-efficient of y on x is 0.4 and r(x,y) = (2)/( sqrt(10)), then the regression co-efficient of x on y is

If (x-1)^4-16=0,then the sum of non-real complex values of x is

If A is matrix of order mxxn and B is a matrix such that AB^T and B^TAbothare defined , then order of matrix B is …………..

Find the area under the given curves a given line :y=x^2,x=1,x=2and x-axis

If P(A) = 0.8, P(B) = 0.5 and P (B|A) = 0.4, find﻿ (i) P(A cap B)﻿ (ii) P(A|B)﻿ (iii) P(A cup B)﻿

y" + 2y' + sin y = 0

Find the equation of line of intersection of the planes3x-y+ z=1 and x + 4 y -2 z =2.

Examine the consistency of the system of linear equtions in 1 to 6 3x-y-2z=2 2y-z=-1 3x-5y=3

From the three pairs of lines given below, identify those which uniquely determine a plane : (i)intersecting pair, (ii) parallel pair, (iii) a pair of skew lines.

LetP(n) : s^ngtnAAn in N and2^kgt k, AAn = K thenwhichof thefollowingis trueAAk ge2?

cos x = b for what b do the roots of the equation form an A.P?

Find derivatives of the following functions.In tan x

Which one of the following equals the average of x and 1//x?

The mean of 5 observation is 4.4 and their variance is 8.24 . If three of the observations are 1,2 and 6, find the other two observations .

The value of ..............

How many 4 letter words can be formed using the letters of the word 'PROPORTION'.

Ifsin theta+ cosectheta=2,thenthevalueofsin ^6 theta+ cosec^6 thetais equal to

If P(A) = 0.8, P(B) = 0.5 and P (B|A) = 0.4, find (i) P(A cap B) (ii) P(A|B) (iii) P(A cup B)