28278 + Interview Questions in Maths in Class 12

1.	If A is matrix of order m xx n and B is a matrix such that AB' and B'A are both defined, the order of the matrix B is
Answer» `mxxm` `nxxn` `nxxm` `mxxn` ANSWER :D

Discussion

2.	x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy
Answer» Answer :`(1)/(2sqrt2)log\|(X + sqrt2y)/(x - sqrt2y)\| = log\|x\| + C`

Discussion

3.	Differentiate the following functions with respect to x: (x^(2))/(4)- (y^(2))/(9)=1
Answer» ANSWER :`(9X)/(4Y)`

Discussion

4.	The locus of the poles of chords of the parabolay^(2) = 4pxwhich touch the hyperbolax^(2)//a^(2)-y^(2)//b^(2)= 1 is
Answer» ` 4p^(2)X^(2) +B^(2) y^(2) =4p^(2) a^(2) ` ` 4p^(2) x^(2) -b^(2) y^(2)=4p^(2)a^(2) ` ` 4p^(2)x^(2) +b^(2) y^(2) =4p^(2)b^(2) ` `4Q^(2)x^(2) -b^(2)y^(2) =4q^(2)a` Answer :A

Discussion

5.	The value ofunderset0overset(pi//2)int[cosx]dx=________
Answer» SOLUTION :`underset0overset(pi//2)INT[COSX]dx=underset0overset(pi//2)int0dx=0`

Discussion

6.	Integrate the following : int((x+sqrtx)(2x+1))/x^2dx
Answer» Solution :`INT((X+SQRTX)(2x+1))/(x^2)dx` =`int(2x^2+x+2x^(2/3)+x^(1/2))/(x^2)dx` =`int{2+1/x+2x^(-1/2)+x^(-3/2)}dx` `2x+In `absx`+`2x^(1/2)/(1/2)+x^(-1/2)/(-1/2)+C` `2x+In absx+4sqrtx-2/(sqrtx)+C`

Discussion

7.	From any point M two normals are drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 where a gt b which are at right angles and their corresponding tangents meet at N. Find the locus of the mid point of MN.
Answer» ANSWER :`X^(2)+y^(2)=(a^(2)+B^(2)) ((x^(2))/(a^(2))+(y^(2))/(b^(2)))^(2)`

Discussion

8.	The sum of series 1/2! + 1/4! + 1/6! + …….. is
Answer» `(E - 1)^(2)/(2E)` `(e^(2) - 1)/(2e)` `(e^(2) - 1)/2` `(e^(2) - 1)/e` ANSWER :A

Discussion

9.	Find the equation of a line parallel to x-axis and passing through the origin
Answer» Answer :The direction cosines of the x-axis are 1, 0, 0. THEREFORE we any ASSUME the direction ratios of the REQUIRED line as 1, 0, 0. Since it PASSES through the origin, the required equation is `(x-0)/1 = (y-0)/0 = (z-0)/0`

Discussion

10.	int(1)/(sin^(2)x+2sin x cos x +5 cos^(2)x)dx=
Answer» `(1)/(3) TAN^(-1) [ (1)/(3) (tan X + 1) ] + C ` `tan^(-1) [ (tan x + 1)/(SQRT(3)) ] + ` C `(1)/(sqrt(2)) tan^(-1) [ (tan x + 1)/(sqrt(2)) ] +C ` `(1)/(2) tan^(-1) [ (tan x + 1)/(2) ] + C ` Answer :D

Discussion

11.	A=[{:(0,1,2),(1,2,3),(3,a,1):}]and A^(-1)=[{:(1/2,-1/2,1/2),(-4,3,c),(5/2,-3/2,1/2):}] then a=...... and c= .........
Answer» 1,1 1,-1 1,2 `-1,1` ANSWER :B

Discussion

12.	If A = [(a,b),(c,d)] such that A satisfies the relation A^(2)-(a+d) A=O then inverse of A is
Answer» I A (a+d)A none of these ANSWER :D

Discussion

13.	Which of the following is/are correct ? (i) Adjoint of a symmetric matrix is also a symmetric matrix. (ii) Adjoint of a diagonal matrix is also a diagonal matrix. (iii) If A is a square matrix of order n and lambda is a scalar, then adj (lambda A)= lambda^(n) adj(A) (iv) A (adj A) = (adj A) A = \|A\| I
Answer» Only (i) (II) and (III) (iii) and (IV ) (i), (ii) and (iv) ANSWER :D

Discussion

14.	If x=a (cos t +t sin t)" and "y= a (sin t -t cos t), find (d^(2)y)/(dx^(2)).
Answer» ANSWER :`(sec^(3)t)/(at), 0 lt t lt (PI)/(2)`.

Discussion

15.	Vectors a and b are such that \|a\|=1,\|b\|=4 and a.b=2." If " c=2axxb-3b, then the angle between b and c is
Answer» `(pi)/(6)` `(5PI)/(6)` `(pi)/(3)` `(2pi)/(3)` Solution :Now , `\|axxb\|^(2)=\|a\|^(2)\|b\|^(2)-(ab)^(2)=16-4=12` ` and \|c\|^(2)=(2axxb-3b)(2axxb-3b)` `=4\|axxb\|^(2)+9\|b\|^(2)=412+916=192` `rArr \|c\|=8sqrt(3)` Again now `bc = b(2axxb-3b)2(baxxb)-3\|b\|^(2)` `=-3\|b\|^(2)=-48` `therefore cos theta=(bc)/(\|b\|\|c\|)=-(48)/(4*8sqrt(3))=-(SQRT(3))/(2)` `therefore theta = (5pi)/(6)`

Discussion

16.	Maximum number of +1/2 spin electrons in Cr which have \|l x m\| =2
Answer» 5 4 11 2

Discussion

17.	int (2 + cos x//2)/(x + sin x//2)dx =
Answer» LOG`\|x + sin""(x)/(2)\| + `C `(1)/(2) log \| x + sin ""(x)/(2) \| + C ` `2 log \| x + sin""(x)/(2)\| + C ` `-(1)/(2) log\| x + sin""(x)/(2) \|` + C Answer :C

Discussion

18.	The tengent line at (a/sqrt(8),a/sqrt(8)) to the curve x^(2//3)+y^(2//3)=a^(2//3) is parallel to the line
Answer» `x=-y` `x=y` `x=0` `y=0` ANSWER :A

Discussion

19.	If f(x) = (x-1) (x-2) (x-3) " for ' x in [0,4] then the value of c in (0,4) satisfying Lagrange's mean value theorem, is
Answer» `3 +- (sqrt2)/(3)` `2 +- (2 sqrt3)/(3)` `2 +- (sqrt3)/(2)` `3 +- (sqrt3)/(3)` ANSWER :B

Discussion

20.	Determine whethera ** b = "GCD" {a,b} "on" Noperations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.
Answer» Solution :for all `a,B in N, GCD {a,b} in N ` `IMPLIES ab in N` ` implies ` is a binary OPERATION on N.

Discussion

21.	y"' + 2y'' + y' = 0
Answer» ANSWER :ORDER 3; DEGREE 1

Discussion

22.	If vec(a) and vec(b), are two collinear vectors, then which of the following are incorrect : (A) vec(b)=lambda vec(a), for some scalar lambda (B) vec(a)=+-vec(b) ( C ) the respective components of vec(a) and vec(b) are not proportional (D) both the vectors vec(a) and vec(b) have same direction, but different magnitudes.
Answer» ANSWER :ALTERNATES (B), ( C ) and (D) are INCORRECT.

Discussion

23.	A car moving with a speed of 40 km/h can be stopped by applying brakes after at least 2m. If the same car is moving with a speed of 80 km/h., what is the minimum stopping distance ?
Answer» 2 m 4 m 6 m 8 m Answer :A

Discussion

24.	On using elementary column operations C_(2)toC_(2)-2C_(1) in the following matrix equation [{:(1,-3),(2,4):}]=[{:(1,-1),(0,1):}]*[{:(3,1),(2,4):}] we have :
Answer» `[{:(1,-5),(0,4):}]=[{:(1,-1),(-2,2):}][{:(3,-5),(2,0):}]` `[{:(1,-5),(0,4):}]=[{:(1,-1),(0,1):}][{:(3,-5),(2,0):}]` `[{:(1,-5),(2,0):}]=[{:(1,-3),(0,1):}][{:(3,1),(-2,4):}]` `[{:(1,-5),(2,0):}]=[{:(1,-1),(0,1):}][{:(3,-5),(2,0):}]` ANSWER :D

Discussion

25.	A family of curves is such that the slope of normal at any point (x, y) is 2(1-y). The area bounded by the curve y = f(x) of question number 1 and the line x+2y = 0 is
Answer» `(10)/(3)` SQ. UNITS `(4)/(3)` sq. units `(28)/(3)` sq. units `(16)/(3)` sq. units Answer :B

Discussion

26.	Let f:N rarr Ybe a function defined as f(x) = 4x + 3, where, Y = { y in N:y = 4x + 3for some x in N}. Show that f is invertible. Find the inverse.
Answer» SOLUTION :N/A

Discussion

27.	IF T_(n)dentoesthe numberof triangleformedwithn pointsin planenothreeof whichare collinearand If T_(n+1) - T_(n)= 36 then n=
Answer» 7 8 9 10 Answer :C

Discussion

28.	vec(a)=2hati-10hatj+2hatk,vec(b)=3hati+hatj+2hatk and vec( c )=2hati+hatj+3hatk then find vec(a)xx(vec(b)xxvec( c )).
Answer» ANSWER :`VEC(O)``

Discussion

29.	An aeroplane can carry a maximum of 200 passengers. A profit of Rs. 1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit ?
Answer» ANSWER :40 tickets of EXECUTIVE class and 160 tickets of economy class.

Discussion

30.	Find the probability that a non leap year contains exactly (i) 53 Sundays (ii) 52 Sundays ?
Answer» ANSWER :`(1)/(7), (6)/(7)`

Discussion

31.	If A and B are events such that P(A' cup B') = (2)/(3) and P(A cup B) = (5)/(9) , then P(A') + P(B') = ……….
Answer» ANSWER :`(10)/(9)`

Discussion

32.	Using elementary transformations, find the inverseof the matrices [(3,-1),(-4,2)]
Answer» ANSWER :`[(1,(1)/(2)),(2,(3)/(2))]`

Discussion

33.	Letf be a function defined by - f(x)={underset(1"",""x=0)((tanx)/(1) "", ""x ne 0). Statement -1 : x=0 is pointof minima of f Statement -2 : f'(0)=0.
Answer» Statement-1 is TRUE , statement -2 is true, statement -2 is a CORRECT EXPLANTION forstatement-1 Statement -1 is true, statement-2 is true, statement-2 is not acorrect explantion for statement-1 Statement-1 istrue , statement-2 is false. Statement-1 is false, statement-2 is true. Answer :B

Discussion

34.	Integrate the functions (sin^(8)-cos^(8)x)/(1-2sin^(2)xcos^(2)x)
Answer» ANSWER :`-(SIN2X)/(2)+C`

Discussion

35.	lim_(ntooo)(sin^(n)1+cos^(n)1)^(n) is equal to
Answer» `cot1` `TAN1` `COS1` `SIN1` ANSWER :D

Discussion

36.	Six balls are drawn successively from an urn containing 7 red and 9 black balls. Tell whether or not the trials of drawing balls are Bernoulli trials when after each draw the ball drawn is (i) replaced (ii) not replaced in the urn.
Answer» ANSWER :(i) BERNOULLI TRIALS, (II) Not Bernoulli TRAILS.

Discussion

37.	Charge Q is given a displacement vec(r)=ahat(i)+bhat(j)in an electric field vec(E)=E_(1)+E_(2)hat(j). The work done
Answer» `Q(E_(1)a+E_(2)B)` `Qsqrt((E_(1)a)^(2)+(E_(2)b)^(2))` `Q(E_(1)+E_(2))SQRT(a^(2)+b^(2))` `Q(sqrt(E_(1)^(2)+E_(2)^(2)))sqrt(a^(2)+b^(2))` Solution :`(W)/(q)=vec(E),vec(R)=Q[E_(1)a+E_(2)b]`

Discussion

38.	Solve y(xy +1)dx+x(1+xy+x^(2)y^(2))dy = 0
Answer» ANSWER :`2x^(2)y^(2)log y - 2xy - 1 = CX^(2)y^(2)`

Discussion

39.	The mod-amplitude form of sin theta + icos theta is
Answer» `CIS THETA` cis `((pi)/(2) - theta)` cis `((pi)/(2) + theta)` cis `(theta - (pi)/(2))` ANSWER :B

Discussion

40.	Construct a 3xx4 matrix, whose elements are given by: (i) a_(ij)=(1)/(2)\|-3i+j\| (ii) a_(ij)=2i-j
Answer» ANSWER :`(i)[(1, (1)/(2),0,(1)/(2)),((5)/(2), 2,(3)/(2),1),(4, (7)/(2), 3,(5)/(2))](II)[(1,0,-1,-2),(3,2,1,0),(5,4,3,2)]`

Discussion

41.	The solution of the differential equation (dy)/(dx)=(y)/(x)+(phi(y//x))/(phi'(y//x)) is
Answer» `xphi((y)/(X))=k` `phi((y)/(x))=KX` `yphi((y)/(x))=k` `phi((y)/(x))=ky` ANSWER :B

Discussion

42.	Find the equation of normal to the hyperobla3x^(2) - 2y^(2) = 30 at (4, -3)
Answer» ANSWER :`RARR x- 2Y - 10 = 0`

Discussion

43.	Solve: (dy)/(dx)=(x-y+5)/(2(x-y)+7)
Answer» SOLUTION :N/A

Discussion

44.	Consider all the six digit numbers that can be formed using the digits 1, 2, 3, 4, 5 and 6, each digit being used exactly once. Each of such six digit numbers have the property that for each digit, not more than two digits smaller than that digit appear to the right of that digit. Q.Number of such six digit numbers having the desired property is :
Answer» 120 144 162 210 Answer :C

Discussion

45.	A tangent to the parabola y^2=4bx=0meets the parabola y^2=4ax in P and Q. Then the locus of the middle points of PQ is:
Answer» `x^2(2a+B)=4a^2y` `y^2(2a+b)=4a^2x` `x^2(2a+b)=2a^2y` `y^2(2a+b)=2a^2x` ANSWER :B

Discussion

46.	Consider all the six digit numbers that can be formed using the digits 1, 2, 3, 4, 5 and 6, each digit being used exactly once. Each of such six digit numbers have the property that for each digit, not more than two digits smaller than that digit appear to the right of that digit. Q. A six digit number which does not satisfy the property mentioned above, is :
Answer» 315426 135462 234651 None of these ANSWER :D

Discussion

47.	One amu is equal to :-
Answer» `1.57 xx 10^(-24) kg` `1.66 xx 10^(-24) kg` `1.99 xx 10^(-23) kg` `1.66 xx 10^(-27) kg` ANSWER :A

Discussion

48.	(Manufacturing problem): A manufacturer has three machines. I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for atleast 5 hours a day. She produces only two items M and N each requiring the sue of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machies are given in the follownig table: She makes a profit of Rs. 600 and Rs. 400 on items M and N respectively. How many of each item should be produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum profit?
Answer» ANSWER :RS. 4000

Discussion

49.	Let A = { a,b,c }, absB = {1,2} Determine all the relation from B to A .
Answer» SOLUTION :There are 64 RELATIONS from B to A as AY SUB set of `B xx A` is a relation from B to A .

Discussion

50.	The value of c in Lagrange's mean value theorem for the function f(x) = x^(2) + 2x -1 in (0, 1) is
Answer» `-1` 1 0 `(1)/(2)` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If A is matrix of order m xx n and B is a matrix such that AB' and B'A are both defined, the order of the matrix B is

x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy

Differentiate the following functions with respect to x: (x^(2))/(4)- (y^(2))/(9)=1

The locus of the poles of chords of the parabolay^(2) = 4pxwhich touch the hyperbolax^(2)//a^(2)-y^(2)//b^(2)= 1 is

The value ofunderset0overset(pi//2)int[cosx]dx=________

Integrate the following : int((x+sqrtx)(2x+1))/x^2dx

From any point M two normals are drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 where a gt b which are at right angles and their corresponding tangents meet at N. Find the locus of the mid point of MN.

The sum of series 1/2! + 1/4! + 1/6! + …….. is

Find the equation of a line parallel to x-axis and passing through the origin

int(1)/(sin^(2)x+2sin x cos x +5 cos^(2)x)dx=

A=[{:(0,1,2),(1,2,3),(3,a,1):}]and A^(-1)=[{:(1/2,-1/2,1/2),(-4,3,c),(5/2,-3/2,1/2):}] then a=...... and c= .........

If A = [(a,b),(c,d)] such that A satisfies the relation A^(2)-(a+d) A=O then inverse of A is

If x=a (cos t +t sin t)" and "y= a (sin t -t cos t), find (d^(2)y)/(dx^(2)).

Vectors a and b are such that |a|=1,|b|=4 and a.b=2." If " c=2axxb-3b, then the angle between b and c is

Maximum number of +1/2 spin electrons in Cr which have |l x m| =2

int (2 + cos x//2)/(x + sin x//2)dx =

The tengent line at (a/sqrt(8),a/sqrt(8)) to the curve x^(2//3)+y^(2//3)=a^(2//3) is parallel to the line

If f(x) = (x-1) (x-2) (x-3) " for ' x in [0,4] then the value of c in (0,4) satisfying Lagrange's mean value theorem, is

Determine whethera ** b = "GCD" {a,b} "on" Noperations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

y"' + 2y'' + y' = 0

A car moving with a speed of 40 km/h can be stopped by applying brakes after at least 2m. If the same car is moving with a speed of 80 km/h., what is the minimum stopping distance ?

On using elementary column operations C_(2)toC_(2)-2C_(1) in the following matrix equation [{:(1,-3),(2,4):}]=[{:(1,-1),(0,1):}]*[{:(3,1),(2,4):}] we have :

A family of curves is such that the slope of normal at any point (x, y) is 2(1-y). The area bounded by the curve y = f(x) of question number 1 and the line x+2y = 0 is

Let f:N rarr Ybe a function defined as f(x) = 4x + 3, where, Y = { y in N:y = 4x + 3for some x in N}. Show that f is invertible. Find the inverse.

IF T_(n)dentoesthe numberof triangleformedwithn pointsin planenothreeof whichare collinearand If T_(n+1) - T_(n)= 36 then n=

vec(a)=2hati-10hatj+2hatk,vec(b)=3hati+hatj+2hatk and vec( c )=2hati+hatj+3hatk then find vec(a)xx(vec(b)xxvec( c )).

Find the probability that a non leap year contains exactly (i) 53 Sundays (ii) 52 Sundays ?

If A and B are events such that P(A' cup B') = (2)/(3) and P(A cup B) = (5)/(9) , then P(A') + P(B') = ……….

Using elementary transformations, find the inverseof the matrices [(3,-1),(-4,2)]

Letf be a function defined by - f(x)={underset(1"",""x=0)((tanx)/(1) "", ""x ne 0). Statement -1 : x=0 is pointof minima of f Statement -2 : f'(0)=0.

Integrate the functions (sin^(8)-cos^(8)x)/(1-2sin^(2)xcos^(2)x)

lim_(ntooo)(sin^(n)1+cos^(n)1)^(n) is equal to

Six balls are drawn successively from an urn containing 7 red and 9 black﻿ balls. Tell whether or not the trials of drawing balls are Bernoulli trials when after each﻿ draw the ball drawn is﻿ (i) replaced﻿ (ii) not replaced in the urn.

Charge Q is given a displacement vec(r)=ahat(i)+bhat(j)in an electric field vec(E)=E_(1)+E_(2)hat(j). The work done

Solve y(xy +1)dx+x(1+xy+x^(2)y^(2))dy = 0

The mod-amplitude form of sin theta + icos theta is

Construct a 3xx4 matrix, whose elements are given by: (i) a_(ij)=(1)/(2)|-3i+j| (ii) a_(ij)=2i-j

The solution of the differential equation (dy)/(dx)=(y)/(x)+(phi(y//x))/(phi'(y//x)) is

Find the equation of normal to the hyperobla3x^(2) - 2y^(2) = 30 at (4, -3)

Solve: (dy)/(dx)=(x-y+5)/(2(x-y)+7)

A tangent to the parabola y^2=4bx=0meets the parabola y^2=4ax in P and Q. Then the locus of the middle points of PQ is:

One amu is equal to :-

Let A = { a,b,c }, absB = {1,2} Determine all the relation from B to A .

The value of c in Lagrange's mean value theorem for the function f(x) = x^(2) + 2x -1 in (0, 1) is

Six balls are drawn successively from an urn containing 7 red and 9 black balls. Tell whether or not the trials of drawing balls are Bernoulli trials when after each draw the ball drawn is (i) replaced (ii) not replaced in the urn.