28278 + Interview Questions in Maths in Class 12

1.	X= tan 1 , y= tan 2, Z= tan 3then the descending order is
Answer» X,Y,Z Z,Y,Z X,Z,Y Y,Z,X ANSWER :C

Discussion

2.	Find the range of x for which the binomial expansions of the following are valid .(a + bx)^r
Answer» ANSWER :`( - (\|a\|)/(\|B\|),(\|a\|)/(\|b\|) )`

Discussion

3.	A student obtained the two regression lines6x - 15y -21 =0 and 21x + 14y - 56 =0Is he found the equations correct ? Justify.
Answer» ANSWER :`b_(YX) and b_(xy)` Should have some SIGN, HENCE STUDENT obtained his equationwere incorrect

Discussion

4.	Lt_(n rarr oo)[(1)/(n+1) + (1)/(n+2)+..(1)/(2n)]
Answer» ANSWER :LOG 2

Discussion

5.	A triangle ABC of area Delta is inserted in the parabola y^(2) =4ax such that A is the vertex and BC is a focal chord of the parabola then find the difference of the ordinates of B and C.
Answer» ANSWER :`RARR DELTA = a^(2) \| t_1 -t_2\| rArr\| 2at_1 - 2 at_2\|= ( 2DELTA )/( a)`

Discussion

6.	Find the number of positive Integral solutions of x+y+z=20 if x ne y ne z :
Answer» 144 140 146 148 SOLUTION :GIVEN `x+y+z = 20` Required solution `PHI` Total POSITIVE Integral solution `-` (any two are equal) `-` (`x=y=z` not possible) `rArr .^(19)C_(2)-overset("lit (3 cases)")((x=y ne z))(z = 20-2y)` `rArr .^(19)C_(2)-3xx(y=1, 2, .....,0)` `rArr .^(19)C_(2)-3xx9 rArr 171 - 27 = 144`

Discussion

7.	If (2,0),(0,1),(4,5) and (0,c) are concyclic then find c.
Answer» ANSWER :`( 14)/(3) `

Discussion

8.	A fair coin and an unbiased die are tossed. Let A be the event 'head appears on the coin' and B be the event '3 on the die'. Check whether A and B are independent events or not.
Answer» ANSWER :A and B are INDEPENDENT

Discussion

9.	A circle passes through the points (3,4) and cuts the circle x^(2) + y^(2) = a^(2) orthogonally, the locus of its centre is a straight line. If the distance of this straight line from the origin is 25, then a^(2) is equal to
Answer» 250 225 100 25 Solution :GIVEN circle is ,`s -= x^(2) + y^(2) - a^(2) = 0` and point p (3,4) Let `C (x_(1), y_(1))` be the CENTRE of the circle Circle are orthogonal to each other `implies d^(2) = r_(1)^(2) + r_(2)^(2)` `implies x_(1)^(2) + y_(1)^(2) = a^(2) + (x_(1) - 3)^(2) (y_(1) - 4)^(2)` `implies x_(1)^(2) + y_(1)^(2) = a^(2) + x_(1)^(2) - 6x_(1) + 9 + y_(1)^(2) - 8y_(1) + 16` `:.` Locus of `C (X_(1),y_(1))` is, `6x + 8y = a^(2) + 25` Distance from (0,0) to EQUATION (1) is `(a^(2) + 25)/(sqrt(64 + 36)) = 25` `implies a^(2) + 25 = 250` `:. a^(2) = 225`

Discussion

10.	Write as a single matrix: ((-1,2,3))((-2,-1,5),(0,-1,4),(7,0,5))-2((4,-5,-7))
Answer» SOLUTION :N/A

Discussion

11.	If t_(r) = (r+2)/(r(r+)). 1/(2^(r+1))then sum_(r=1)^(n) is equal to
Answer» `(N2^(N)-1)/(n+1)` `(n+1)/(2^(n+1)(n+2))` `n/(2^(n))-1` `((n+1)2^(n)-1)/(2^(n+1)(n+1))` ANSWER :D

Discussion

12.	Brody's marbles have a red to yellow ratio of 2:1. If Brody has 22 red marbles, how many yellow marbles does Brody have?
Answer» ANSWER :11

Discussion

13.	Prove that : log_em-log_en=(m-n)/m+1/2((m-n)/m)^2..........m,n>0
Answer» SOLUTION :R.H.S=`(m-n)/m+1/2((m-n)/m)^(2)1/3((m-n)/m)^3+...=-[log(1-(m-n)/n)]=-[log((m-m+n)/m)]=-[logn-logm]=logm-logn=L.H.S`

Discussion

14.	Integration by partial fraction : int(x^(2))/((x^(2)+2)(x^(2)+3))dx=....
Answer» `-sqrt(2)tan^(-1)x+sqrt(3)tan^(-1)x+c` `-sqrt(2)tan^(-1)(x)/(sqrt(2))+sqrt(3)tan^(-1)x+c` `sqrt(2)tan^(-1)(x)/(sqrt(2))+sqrt(3)tan^(-1)x+c` None of these Answer :B

Discussion

15.	Let f(x)=x[1/x] for all x (ne 0) in R , where for each t in R, [t] denotes the greatest integer less than or equal to t. Then
Answer» `lim_(X to 1//3+) F(x)=1` `lim_( xto 1//2-) f(x)=1` `lim_( xto 2-)f(x)=1` `lim_( xto 0+) f(x)=0` Answer :B

Discussion

16.	(d)/(dx). ((1)/(log\|x\|))= …….
Answer» `(1)/(\|x\|)` `(1)/((LOG x)^(2))` `(-1)/(x(log \|x\|)^(2))` `E^(x)` ANSWER :C

Discussion

17.	Find all the points for discontinuity of the function f(x) =[x^2] on [1,2], where [x] denotes the greatest integer function.
Answer» ANSWER :`[1,2]`

Discussion

18.	Resolve into partial fractions the expression ((1+x)(1+2x)(1+3x))/((1-x)(1-2x)(1-3x)).
Answer» ANSWER :`-1 + (12)/(1-x)-(30)/(1-2x)+(20)/(1-3x)`

Discussion

19.	Let a tangent be drawn at a point on the focus f(x,y) = 0 and it meets the positive X and Y- axes at point P and Q. Let A and G be respectively the arithmetic and geometric means of the segments OP and OQ. Now, If G = 1 then, the locus f(x, y)= 0, is
Answer» `kx^(2)-2XY + KY^(2) +1 = 0` (where 'k' is a parameter) `(1-k)X^(2)-2xy + ky^(2) +1 = 0` (where 'k' is a parameter) `kx^(2)-2xy +1/ ky^(2) +1 = 0 `(where 'k' is a parameter) `(1-k)x^(2)-2xy + 1/ky^(2) +1 = 0` (where 'k' is a parameter) Answer :C

Discussion

20.	For each operation defined below, determine , whether is binary , commutative or associative. On Z^(+), define a "*" b =ab
Answer» SOLUTION :N/A

Discussion

21.	Find (dy)/(dx) given x^(2) + xy + y^(2) = 100.
Answer» ANSWER :`-((2x+y))/((x+2y))`

Discussion

22.	Let f : N rarr N be a function defined as f(x) = 4x^(2) + 12x + 15 is invertible (where S is range of f). Find the inverse of f and hence find f^(-1)(31).
Answer» ANSWER :`f^(-1) : S RARR N`, such that `f^(-1)(x) = (sqrt(x-6) - 3)/(2); f^(-1)(31) = 1`

Discussion

23.	Consider the curve y=tan^(-1)x and a point A(1,(pi)/4) on ti if the variable pont P_(i)(x_(i),y_(i)) moves on the curve for i=1,2,3,.n(n epsilonN) such that y_(r)=sum_(m=1)^(r)tan^(-1)(1/(2m^(2))) and B(x,y) be the limiting position of variable point P_(n) as ntooo, the value of reciprocal of the slope of AB will be.
Answer» ANSWER :B

Discussion

24.	Resolve the following into partial fractions. (x^(3))/((x-1)(x+2))
Answer» ANSWER :`x-1 + (1)/(3(x-1))+(8)/(3(x+2))`

Discussion

25.	Let a tangent be drawn at a point on the focus f(x,y) = 0 and it meets the positive X and Y- axes at point P and Q. Let A and G be respectively the arithmetic and geometric means of the segments OP and OQ. Now, If A=1 then the locus f(x, y) = 0, is (A) x = Y/k +2/(1-K), (where 'k' is a parameter)
Answer» `X = y/k + 2/1-k, `(where 'k' is a PARAMETER) `x/k + y/1-k, = 2` (where 'k' is a parameter) `y = x/k^(2) + 1/1-k` (where 'k' is a parameter) `x /k^(2) + y/1-k = 1` (where 'k' is a parameter) ANSWER :A

Discussion

26.	If the vertex of the parabola y = x^(2)-8x+c lies on x-axis then the value of c is
Answer» (2,0) (4,0) (6,0) (8,0) ANSWER :B

Discussion

27.	Choose the correct answerfrom the bracket. ifd/(dx) (f(x)) = 4x^3-3/x^4 such that f(2) = 0, then f(x) is
Answer» `x^4+1/x^3 - (129)/8` `x^3 + 1/x^4 + (129)/8` `x^4+1/x^3 + (129)/8` `x^3+1/x^4 - (129)/8` ANSWER :A

Discussion

28.	Is there any tangent to the curve y=\|2x-1\| at (1/2,0)?
Answer» SOLUTION :As y=\|2x -1 \| is not DIFFERENTIABLE at `(1/2,0)` there is no TANGENT there.

Discussion

29.	Integrate the following functions (e^(2x) - 1)/(e^(2x) +1
Answer» Solution :`(e^(2X)-1)/(e^(2x)+1) = (e^x(e^x-e^-x))/(e^x(e^x-e^+x)) = (e^x-e^-x)/(e^x+e^-x)` Let `t = e^x+e^-x`. Then dt = `(e^x-e^-x) dx` therefore `INT (e^(2x) -1)/(e^(2x)+1) dx = int(e^x-e^-x)/e^x+e^-x)dx` `int (dt)/t = LOG \|t\|+c` = `log\|e^x+e^-x\|+c`

Discussion

30.	Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1andg(x) be a function that satisfies f(x)+g(x)=x^(2). Then the value of the integral int_(0)^(1)f(x)g(x)dx, is
Answer» `E + (e^(2))/(2) + 5/2` `e - (e^(2))/(2) - 3/2` `e - (e^(2))/(2) - 5/2` `e + (e^(2))/(2)-3/2` ANSWER :B

Discussion

31.	LetS _(n ) = sum _( k =0) ^(n) (1)/( sqrt ( k +1) + sqrt k) What is the value ofsum _( n -1) ^( 90) (1)/( S _(n ) + S _( n -1)) ?=
Answer» ANSWER :9

Discussion

32.	Three white balls and five blacks balls are placed in a bag and three men draw a ball in succession (the balls drawn not being replaced) until a white ball is drawn. The ratio of their respective chances is
Answer» `27:18:11` `11:18:27` `18:11:27` `18:27:11` ANSWER :A

Discussion

33.	If the ellipse x^(2)+lambda^(2)y^(2)=lambda^(2)a^(2) , lambda^(2) gt1 is confocal with the hyperbola x^(2)-y^(2)=a^(2), then
Answer» ratio of eccentricities of ellipse and HYPERBOLA is `1:SQRT(3)` ratio of major AXIS of ellipse and transverse axis of hyperbola is `sqrt(3):1` `Theellipse and hyperbola cuts each other orthogonally ratio of length of latusrectumof ellipse and hyperbola is `1:3` ANSWER :A::B::C

Discussion

34.	If the angle between the circle x^2+y^2-2x-4y+c=0 and x^2+y^2-4x-2y+4=0 is 60^@, then C is equal to
Answer» `(3pmsqrt5)/2` `(6pmsqrt5)/2` `(9pmsqrt5)/2` `(7pmsqrt5)/2` ANSWER :D

Discussion

35.	Find of the total number of words which are formed by using the all the letters of the word "SUCCESS" such the no two alike letters are together.
Answer» ANSWER :96

Discussion

36.	A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is nonzero is
Answer» `5//8` `3//8` `1//16` `3//16` ANSWER :D

Discussion

37.	If a, b and c in N then which one of the following is not true ?
Answer» `a\|b` and `a\|C RARR a\|3b+2c` `a\|b` and `b\|c rArr a\|c` `a\|b+c rArr a\|b` and `a\|c` `a\|b` and `a\|c rArr a\|b+c` ANSWER :C

Discussion

38.	Express the 3i points geometrically in the Argrand plane.
Answer» SOLUTION :`3i=0+3i=(0,3)`

Discussion

39.	A square piece of tin of side 18 cm is to be made into a box without top, by cutting off square from each corner and foling up the flaps of the box. What should be the side of the square to be cut off so that the volume of the box is maximum possible.
Answer» ANSWER :3 CM

Discussion

40.	The vector equation of the plane which is at distance of (3)/(sqrt(14)) form the origin and the normal form the origin is 2hati-3hatj+hatk is
Answer» `BARR.(hati+hatj+hatk)=9` `barr.(2hati+hatk)=3` `barr.(2hati-3hatj+hatk)=3` `barr.(hati+2hatj)=3` ANSWER :C

Discussion

41.	Integrate the functions ((x+1)(x+logx)^(2))/x
Answer» ANSWER :`((X LOGX)^(3))/(3)+C`

Discussion

42.	Express the value of "cosec"("cos"^(-1) 3/5 +"cos"^(-1) 4/5) in simplest form.
Answer» SOLUTION :`"COSEC"("COS"^(-1) 3/5 +"cos"^(-1) 4/5)` `"cosec"("SIN"^(-1) 4/5 +"cos"^(-1) 4/5)` ` ="cosec" (pi/2)=1`

Discussion

43.	If there is a possible error of 0.01 cm in the measurement of side of a cube, the possible error in its surface area when the side is 10 cm is
Answer» 1.2 sq.cm 1.4 sq.cm 2.4 sq.cm 3.6 sq.cm Answer :A

Discussion

44.	Find the points of inflection of y = x^(4) - 6x^(2) + 8x -1
Answer» ANSWER :(1,2) and `(-1, -14)`

Discussion

45.	If A = [{:(1,2),(4,2):}] then show that [2A] = 4[A]
Answer» ANSWER :-24

Discussion

46.	Evaluate: int cos^(-1)sqrt(x)dx
Answer» Answer :`XCOS^(-1)""(-SQRT(x-x^(2)))/2-1/2sin^(-1)sqrt(x)+C`

Discussion

47.	Let x_(1),x_(2),x_(3)…..,x_(n) be a sequence of integers such that -1 le x_(i) le 2 AA I = 1 , 2, 3 …. n x_(1)+x_(2)+x_(3) +…..+x_(n)=19andx_(1)^(2)+x_(2)^(2)+x_(3)^(2)+….+x_(n)^(2) = 99
Answer» ANSWER :`M/m = 133/19 = 7`

Discussion

48.	Let lceiling denote a curve y=y(x) which is in the first quadrant and let the point (1,0) lie on it . Let the tangant ot lceiling at a point P intersect the y-axis at Y_P. If PY_P has length l for each point P on lceiling, then which of the following options is/ are correct ?
Answer» `xy'+sqrt(1-x^2)=0` `xy'-sqrt(1-x^2)=0` `y=log_(e)((1+sqrt(1-x^2))/(x))-sqrt(1-x^2)` `y=-log_e((1+sqrt(1-x^2))/(x))+sqrt(1-x^2)` Solution :Let a point P(h,k)on the CURVE `y=y(x)`, so equation of tangent to the curve at point P is `y-k=((dy)/(dx))_(h,k) (x-h)` ....(i) Now, the tangent (i) intersect the Y-axis at `Y_p` , so coordinates `Y_(p)` is `(0,k-h(dy)/(dx))`, where `(dy)/(dx) =((dy)/(dx))_(h,k)` So, `PY_p=1`(given) `rArr sqrt(h^2+h^2((dy)/(dx))^2)=1` `rArr (dy)/(dx)=+-(sqrt(1-x_1^2))/(x)""["on replacing h by x"]` `rArr dy= +-sqrt(1-x^2)/(x)dx` On PUTTING `x=sintheta, dx =cos thetad theta`,we get `dy =+-sqrt(1-sin^2)/(sin theta)cos theta d theta =+-(cos^2 theta)/(sin theta)d theta` `=+-(cosec theta -sintheta )d theta` `rArr y=+-[In (cosec theta -cot theta )+cos theta]+C` ` y=+-[-In ((1+sqrt((1-x^2)))/(x))+sqrt(1-sin^2)]+C` `rArr y+-[In ((1-costheta)/(sin theta))+cos theta]+C` `rArr y=+-[In (1-sqrt(1-x^2)/(x))+sqrt(1-x^2)]+C ""[because x=sintheta]` ` =+-[-In (1+sqrt(1-x^2))/(x)+sqrt(1-x^2)]+C` [On ratioalization] `because` The curve is in the first QUADRANT so y MUST be positive, so `y=In(1+sqrt((1-x^2))/(x))-sqrt(1-x^2)+C` As curve passes through `(1,0)`, so `0=0-0+c rArr c=0`, so required curve is `y=In (1+sqrt(1-x^2))/(x)=sqrt(1-x^2)` and required differential equation is `(dy)/(dx)=-(sqrt(1-x^2))/(x)` `rArr xy'+sqrt(1-x^2)=0` Hence, options (a) and (c) are CORRECT.

Discussion

49.	Integrate the function xcos^(-1)x
Answer» ANSWER :`(2X^(2)-1)(cos^(-1)x)/4-x/4sqrt(1-x^(2))+C`

Discussion

50.	if the function f (x) = ax^(3) + bx^(2) + 11 x - 6satisfies the conditions of Rolle's theorem in [1, 3]and f(2 + 1 /sqrt(3)) = 0then a + b =
Answer» `-5` `-3` 4 7 Answer :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

X= tan 1 , y= tan 2, Z= tan 3then the descending order is

Find the range of x for which the binomial expansions of the following are valid .(a + bx)^r

A student obtained the two regression lines6x - 15y -21 =0 and 21x + 14y - 56 =0Is he found the equations correct ? Justify.

Lt_(n rarr oo)[(1)/(n+1) + (1)/(n+2)+..(1)/(2n)]

A triangle ABC of area Delta is inserted in the parabola y^(2) =4ax such that A is the vertex and BC is a focal chord of the parabola then find the difference of the ordinates of B and C.

Find the number of positive Integral solutions of x+y+z=20 if x ne y ne z :

If (2,0),(0,1),(4,5) and (0,c) are concyclic then find c.

A fair coin and an unbiased die are tossed. Let A be the event 'head appears on﻿ the coin' and B be the event '3 on the die'. Check whether A and B are﻿ independent events or not.﻿

A circle passes through the points (3,4) and cuts the circle x^(2) + y^(2) = a^(2) orthogonally, the locus of its centre is a straight line. If the distance of this straight line from the origin is 25, then a^(2) is equal to

Write as a single matrix: ((-1,2,3))((-2,-1,5),(0,-1,4),(7,0,5))-2((4,-5,-7))

If t_(r) = (r+2)/(r(r+)). 1/(2^(r+1))then sum_(r=1)^(n) is equal to

Brody's marbles have a red to yellow ratio of 2:1. If Brody has 22 red marbles, how many yellow marbles does Brody have?

Prove that : log_em-log_en=(m-n)/m+1/2((m-n)/m)^2..........m,n>0

Integration by partial fraction : int(x^(2))/((x^(2)+2)(x^(2)+3))dx=....

Let f(x)=x[1/x] for all x (ne 0) in R , where for each t in R, [t] denotes the greatest integer less than or equal to t. Then

(d)/(dx). ((1)/(log|x|))= …….

Find all the points for discontinuity of the function f(x) =[x^2] on [1,2], where [x] denotes the greatest integer function.

Resolve into partial fractions the expression ((1+x)(1+2x)(1+3x))/((1-x)(1-2x)(1-3x)).

Let a tangent be drawn at a point on the focus f(x,y) = 0 and it meets the positive X and Y- axes at point P and Q. Let A and G be respectively the arithmetic and geometric means of the segments OP and OQ. Now, If G = 1 then, the locus f(x, y)= 0, is

For each operation ** defined below, determine , whether **is binary , commutative or associative. On Z^(+), define a "*" b =ab

Find (dy)/(dx) given x^(2) + xy + y^(2) = 100.

Let f : N rarr N be a function defined as f(x) = 4x^(2) + 12x + 15 is invertible (where S is range of f). Find the inverse of f and hence find f^(-1)(31).

Resolve the following into partial fractions. (x^(3))/((x-1)(x+2))

Let a tangent be drawn at a point on the focus f(x,y) = 0 and it meets the positive X and Y- axes at point P and Q. Let A and G be respectively the arithmetic and geometric means of the segments OP and OQ. Now, If A=1 then the locus f(x, y) = 0, is (A) x = Y/k +2/(1-K), (where 'k' is a parameter)

If the vertex of the parabola y = x^(2)-8x+c lies on x-axis then the value of c is

Choose the correct answerfrom the bracket. ifd/(dx) (f(x)) = 4x^3-3/x^4 such that f(2) = 0, then f(x) is

Is there any tangent to the curve y=|2x-1| at (1/2,0)?

Integrate the following functions (e^(2x) - 1)/(e^(2x) +1

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1andg(x) be a function that satisfies f(x)+g(x)=x^(2). Then the value of the integral int_(0)^(1)f(x)g(x)dx, is

LetS _(n ) = sum _( k =0) ^(n) (1)/( sqrt ( k +1) + sqrt k) What is the value ofsum _( n -1) ^( 90) (1)/( S _(n ) + S _( n -1)) ?=

Three white balls and five blacks balls are placed in a bag and three men draw a ball in succession (the balls drawn not being replaced) until a white ball is drawn. The ratio of their respective chances is

If the ellipse x^(2)+lambda^(2)y^(2)=lambda^(2)a^(2) , lambda^(2) gt1 is confocal with the hyperbola x^(2)-y^(2)=a^(2), then

If the angle between the circle x^2+y^2-2x-4y+c=0 and x^2+y^2-4x-2y+4=0 is 60^@, then C is equal to

Find of the total number of words which are formed by using the all the letters of the word "SUCCESS" such the no two alike letters are together.

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is nonzero is

If a, b and c in N then which one of the following is not true ?

Express the 3i points geometrically in the Argrand plane.

A square piece of tin of side 18 cm is to be made into a box without top, by cutting off square from each corner and foling up the flaps of the box. What should be the side of the square to be cut off so that the volume of the box is maximum possible.

The vector equation of the plane which is at distance of (3)/(sqrt(14)) form the origin and the normal form the origin is 2hati-3hatj+hatk is

Integrate the functions ((x+1)(x+logx)^(2))/x

Express the value of "cosec"("cos"^(-1) 3/5 +"cos"^(-1) 4/5) in simplest form.

If there is a possible error of 0.01 cm in the measurement of side of a cube, the possible error in its surface area when the side is 10 cm is

Find the points of inflection of y = x^(4) - 6x^(2) + 8x -1

If A = [{:(1,2),(4,2):}] then show that [2A] = 4[A]

Evaluate: int cos^(-1)sqrt(x)dx

Let x_(1),x_(2),x_(3)…..,x_(n) be a sequence of integers such that -1 le x_(i) le 2 AA I = 1 , 2, 3 …. n x_(1)+x_(2)+x_(3) +…..+x_(n)=19andx_(1)^(2)+x_(2)^(2)+x_(3)^(2)+….+x_(n)^(2) = 99

Let lceiling denote a curve y=y(x) which is in the first quadrant and let the point (1,0) lie on it . Let the tangant ot lceiling at a point P intersect the y-axis at Y_P. If PY_P has length l for each point P on lceiling, then which of the following options is/ are correct ?

Integrate the function xcos^(-1)x

if the function f (x) = ax^(3) + bx^(2) + 11 x - 6satisfies the conditions of Rolle's theorem in [1, 3]and f(2 + 1 /sqrt(3)) = 0then a + b =

A fair coin and an unbiased die are tossed. Let A be the event 'head appears on the coin' and B be the event '3 on the die'. Check whether A and B are independent events or not.

For each operation defined below, determine , whether is binary , commutative or associative. On Z^(+), define a "*" b =ab