28278 + Interview Questions in Maths in Class 12 Page 168 InterviewSolution

8351.	Let A=[{:(a,b,c),(p,q,r),(1,1,1):}]and B=A^(2) If (a-b)^(2) +(p-q)^(2) =25, (b-c) ^(2)+ (q-r)^(2)= 36 and (c-a)^(2) +(r-p)^(2)=49, then det B is
Answer» 192 864 2456 `25xx36xx47` ANSWER :B

Discussion

8352.	If Z=(i^i)^i" where "i=sqrt(-1) then
Answer» A) `\|Z\|=E^(-pi/2)` B) \|Z\|=1 C) Re(Z)=0 D) `Re(Z)=e^(-pi/2)` ANSWER :B

Discussion

8353.	One card is selecting from the pack of 52 playing cards if A and B denotes that card is an ace and it is of square then P(A\|B) = ………..
Answer» `(1)/(13)` `(12)/(13)` `(3)/(13)` None Answer :A

Discussion

8354.	divide is a binary operation on:
Answer» N R Z Q/(0) ANSWER :D

Discussion

8355.	If P(A) = (7)/(13) , P(B) = (9)/(13)and P(A cap B)= (4)/(13) then find P(A' \| B).
Answer» ANSWER :`(5)/(9)`

Discussion

8356.	Evaluate the following integrals. int(x^(2))/((x+1)(x+2)^(2))dx
Answer» ANSWER :`log\|x+1\|+(4)/(x+2)+C`

Discussion

8357.	int2x^3cosx^2dx
Answer» SOLUTION :`int2x^3cosx^2dx` [PUT `x^2=t Then 2xdx=dt] =`intx^2.cosx^2 .2xdx` =`intt.cost.dt` [1=1st cost=2nd] =`t.sint-int1sintdt` =tsint+cost+C =`x^2sinx^2+cosx^2+C`

Discussion

8358.	Find the area bounded by y=x^2,y=0,x=1
Answer» SOLUTION :AREA = `int_0^1x^2dx=[x^3/3]_0^1=1/3`

Discussion

8359.	Read the following passages and answer the following questions (4-6) Let n be positive integer such that l_(n)=intx^(n)sqrt(a^(2)-x^(2))dx, then answer the following questions: The value of l_(1) is
Answer» `(2)/(3)(a^(2)-X^(2))^(1//2)` `(1)/(3)(a^(2)-x^(2))^(3//2)` `-(2)/(3)(a^(2)-x^(2))^(3//2)` `-(1)/(3)(a^(2)-x^(2))^(3//2)` ANSWER :D

Discussion

8360.	The numerically greatest term in the expansion (2x - 3y)^12 when x = 1 and y = 5/2 is the
Answer» 11TH TERM 10th term 9TH term 6TH term ANSWER :A

Discussion

8361.	Find vec(a) * vec(b) if \|vec(a)\| = 6, \|vec(b)\| = 4 and \|vec(a) xx vec(b)\| = 12
Answer» Answer :`vec(a)*vec(B) = 12 sqrt(3)`

Discussion

8362.	Two fair dice are rolled at random. The probability that the difference between the numbers is (a) exactly 2 (b) atmost one
Answer» ANSWER :(a) `(2)/(9)` (B) `(4)/(9)`

Discussion

8363.	Evaluateint1/(sin^2xcos^2x)dx.
Answer» SOLUTION :`INTDX/(sin^2xcos^2x)=INT(sin^2x+cos^2x)/(sin^2xcos^2x)dx=int((sin^2x)/(sin^2xcos^2x)+(cos^2x)/(sin^2xcos^2x))dxint(sec^2x+cosec^2x)dx=tanx-cotx+C`

Discussion

8364.	Obtain reduction formula for I_(n) =int cosec ^(n) x dx, n being a positive integer, nge 2 and deduce the value of int cosec ^(5) x dx.
Answer» ANSWER :`-(COSEC^(3)xcotx)/(4)-(3cosec cot X)/(8)+(3)/(8)log\|cosec-cotx\|+c`

Discussion

8365.	Consider the sequence of numbers 121, 12321, 1234321,... Each term in the sequence is
Answer» a PRIME number square of an ODD number divisible by 11 form a GP. Answer :B

Discussion

8366.	State which of the following statements are true (T) or false(F) The line(x+2)/-1=(y-3)/2=(z+4)/k and (x-4)/(-4)=(y-3)/k=(z+1)/2 are perpendicular at value of k=-1.
Answer» ANSWER :T

Discussion

8367.	Evaluate the determinant Delta = {:\|(1,2,4),(-1,3,0),( 4,1,0)\|:}
Answer» ANSWER :` -52`

Discussion

8368.	What is the value of 6t such that volume contained inside the planes sqrt(1-t^(2))x+tz=2sqrt(1-t^(2)) z=0,x=2+(tsqrt(4t^(2)-5t+2))/(sqrt(12)(1-t^(2))^((1)/(4))) and \|y\|=2 is maximum.
Answer» Solution :All the give planes are at rigt angles to `XZ` plane so a cross section PARALLEL to zx plane will be same every where. So, volume will be maximum when are of triangular cross section is maximum. When we cut these planes by the plane `y=0`, the Delta obtained is ABC, where `AB=(tsqrt(4t^(2)-5t+2))/(SQRT(12)(1-t^(2))^((1)/(4)))` Let `CAB=theta=` angle between first plane and `xy`- plane the `costheta=t` Area of `DeltaABC=Delta=(1)/(2)(AB)^(2)TANTHETA` `Delta=(1)/(2)(t^(2)(4t^(2)-5t+2))/(12(1-t^(2))^((1)/(2)))xx(sqrt(1-t^(2)))/(t)=(1)/(2)(4t^(3)-5t^(2)+2t)/(12)` For example `(dDelta)/(dt)=0implies12t^(2)-10t+2=0` `impliest=(10+-sqrt(100-96))/(24)=(1)/(2)` or `(1)/(3)` Now `(d^(2)Delta)/(dt^(2))=24t-10` So `Delta` is maximum at `t=(1)/(3)` and minimum at `t=(1)/(2)` `becauset=(1)/(3)`

Discussion

8369.	Let f(x) be a non-negative, continuous and even function such that area bounded by x-axis ,y-axis & y = f(x) is equal to (x^(2)+x^(3)) sq. unitsAax ge 0, then
Answer» `underset(r=1)OVERSET( N)sumf'(r )= 3n^(2)+5n AA n in N` ` underset(r=1)overset(n)sumf'(r ) = 6N^(2)+5n AA n in N` `f(x) = 3x^(2)+2x AA x le0` `f(x) = 3x^(2)-2x AAxle 0` SOLUTION :N//A

Discussion

8370.	The table above shows the distribution of age and gender for 25 people who entered a contest. If the contest winner will be selected at random, what is them probability that the winner will be either a female under age 40 or a male age 40 or older?
Answer» `4/25` `10/25` `11/25` `16/25` ANSWER :C

Discussion

8371.	Let f:[0, 1/2] rarr R be given by f(x)=x(x-1)(x-2). The value 'c', when Lagrange's mean-value theorem is applied for f(x), is
Answer» `SQRT(21)/6` `1/6` `1-sqrt(21)/6` `1 PM sqrt(21)/6` ANSWER :D

Discussion

8372.	The smallest positive value of x (in degrees) for which tan(x+100^(@))=tan(x+50^(@))tanxtan(x-50^(@)) is
Answer» `25^(@)` `82""1/2^(@)` `55^(@)` `30^(@)` ANSWER :D

Discussion

8373.	If x^(y) = y^(x) find (dy)/(dx)
Answer» ANSWER :`(y)/(X)((y-x LOGY)/(x-ylog x))`

Discussion

8374.	If f (x) + f (1 - x) is equal to 10 for all real numbers x then f ((1)/(100)) + f ((2)/(100)) + f ((3)/( 100))+...+f ((99)/(100)) equals
Answer» ANSWER :`495`

Discussion

8375.	Find the coefficient of x^(n) in the expansion of (x)/((x-3)(x-2)) in powers of x specifying the interval in which the expansion is valid.
Answer» ANSWER :`(3^(N)-2^(n))/(3^(n).2^(n))`

Discussion

8376.	Let f (x) = sin ((pi)/(6) sin ((pi)/(2) sin x )) for all x in R and g(x) =(pi)/(2) sin x for allx in R . Let (fog) (x) denote f(g(x)) and (gof) (x) denote g (f(x)) . Then which of the following is (are ) true ?
Answer» F(x) is an odd FUNCTION f(x) is an one-one function f(x) is an ONTO function f(x) is an even function Answer :A::B::C

Discussion

8377.	If (3x^2+1)/((x^2+1)(x^2+2)^2)= (Ax+B)/(x^2+1)+ (Cx+D)/(x^2+2)+ (Ex+F)/(x^2 +2)^2, then A +C +E=
Answer» `0` `7/3` `1` `4/3` ANSWER :A

Discussion

8378.	p=(150)/(x^(2)+2)-4 represents the demand function for a product where p is the price per unit for x units. Determine the marginal revenue.
Answer» SOLUTION :N/A

Discussion

8379.	Find the numerically greatest terms in the expansion of(1 - 5x)^12 when x = 2/3
Answer» ANSWER :`T_10 = - ""^12C_9 . (10/3)^9, T_11= - ""^12C_10 (10/3)^10`

Discussion

8380.	Statement 1 In an ellipse the distance between foci is always less than the sum of focal distances of any point on it. Statement 2 If e be the eccentricity of the ellipse, then 0ltelt1.
Answer» STATEMENT I is TRUE, statement II is true: statement II is a correct explanation for statement I Statement I is true, statement II is true, statement II is not a correct explanation for statement I statement I is true, statement II is false statement I is false, statement II is true Answer :A

Discussion

8381.	If (2)/(sqrt(5)) is the length of the common chord of the circles x^(2)+y^(2)+2x+2y+1=0 andx^(2)+y^(2)+alphax+3y +2 = 0,alpha ne 0," then "alpha=
Answer» 4 3 2 1 Answer :A

Discussion

8382.	Find the slope of the tangent to curve y=x^(3)-x+1 at the point whose x- coordinate is 2.
Answer» ANSWER :11

Discussion

8383.	a, b, c are three mutually perpendicular unit vectors inthe right handed system. If the points P, Q, R with position vectors 2a+5b-4c, a+4b-3c " and "ka+7b-6c respectively lie on a line, then the ratio in which the point P divides QR is
Answer» `1:2` `-1:3` `3:1` `-1:2` ANSWER :A

Discussion

8384.	Probability distribhution of a random variable X is given by: Find k, hence find the mean and variance of the distributions.
Answer» Answer :` k = (1)/(3) ; ` Menu ` (MU) = (2)/(3) , " VARIANCE "= (4)/(9)`

Discussion

8385.	lim_(xto0)\|x\|/x
Answer» SOLUTION :L.H.L.`=lim_(xto0-)\|x\|/x` `=lim_(hto0)([0-h])/(0-h)=lim_(hto0)h/(-h)=-1` R.H.L.`=lim_(xto0+)([x])/x=lim_(hto0)([0+h])/(\|0+h\|)=1` As `L.H.L.neR.H.L.,` So the LIMIT does not EXIST.

Discussion

8386.	The solution set of the constraints 2x+3y le 6, x+4y le 4" and "x ge 0, y ge 0 includes the point ………. As corner point.
Answer» (1, 0) (1, 1) `(12/5, 2/5)` `(2/5, 12/5)` ANSWER :C

Discussion

8387.	Complex numbers z_1, z_2, z_3 are represented by the points of contact D, E, F of the incircle of triangle ABC, with the centre O of the incircle taken as the origin. If BO meets DE at G, find the complex number represented by G.
Answer» ANSWER :`Z=((z_1-z_2))/(z_2+z_3)` which is REPRESENTED by G.

Discussion

8388.	The tworegression lines intersect at unique point, then it should be
Answer» `( VEC X, vec y ) ` ` (0,0) ` ` (-OVERSET(-) x, -overset( -)y)` NONE of these ANSWER :A

Discussion

8389.	Find the number of solutions of the equations (sin x - 1)^(3) + (cos x - 1)^(3) + ( sin x)^(3) = ( 2 sin x + cos x - 2)^(3)in ( 0, 2 pi) .
Answer» ANSWER :4

Discussion

8390.	Differentiate sqrtx+1/sqrtx-root(3)(x^2)
Answer» SOLUTION :`y=sqrtx+1/sqrtx-root(3)(X^2)` `x^(1/2)+x^(-1/2)-x^(2/3)` `IMPLIES dy/dx=1/2x^(-1/2)-1/2x^(-3/2)-2/3x^(-1/3)`

Discussion

8391.	The point of intersection of lines is (alpha, beta) , then the equation whose roots are alpha, beta, is
Answer» `4x^2+x-8=0` `6x^2+x-12=0` `4x^2-x-8=0` `6x^2-x-12=0` ANSWER :B

Discussion

8392.	Determine the pointwhere the line 2y+x=3, is normal to the curve y=x^(2).
Answer» (-1, -1) (1, -1) (-1, 1) NONE of these SOLUTION :N/A

Discussion

8393.	A : 3. C_0 + 7.C_1 + 11. C_2 + ….+(4n + 3). C_n = (2n +3) 2^n. R : a. C_0 + (a+d). C_1 + (a+2d). C_2 + …..+ (a+nd). C_n - (2a+nd). 2^(n-1).
Answer» Both A and R are TRUE and R is the correct EXPLANATION of A Both A and R true but R is not correct explanation of A A is true but R is false A is false but R is true Answer :A

Discussion

8394.	Solve [[x+a,0,0],[a,x+b,0],[a,0,x+c]]=0
Answer» SOLUTION :`[[x+a,0,0],[a,x+b,0],[a,0,x+c]]=0` or, `(x+a)[[x+b,0],[0,x+c]]=0` or, (x+a)(x+b)(x+c)=0 `THEREFORE` x=-a, x=-b, x=-c

Discussion

8395.	If theequation x^5 -3x^4 -5x^3 +27x^2- 32 x+12=0hasrepeatedroots, then theprimenumberthatdividesthe nonrepeatedrootof thisequationis
Answer» 7 5 3 2 Answer :C

Discussion

8396.	If the direction ratios of the lines L_(1)andL_(2) are 2, -1, 1 and 3, -3, 4 respectively, then the direction cosines of a line that is perpendicular to both L_(1)andL_(2) are
Answer» `pm2/sqrt6,pm1/sqrt6,pm1/sqrt6` `pm1/sqrt35,pm5/sqrt35,pm3/sqrt35` `pm3/sqrt34,pm3/sqrt34,pm4/sqrt34` `pm1/sqrt14,pm2/sqrt14,pm3/sqrt14` ANSWER :B

Discussion

8397.	A real valued function f(x) is given as f(x) = {{:(int_(0)^(x) 2{x}dx",",x + {x} in I),(x^(2) - x + (1)/(2)",",(1)/(2) lt x lt (3)/(2) and x ne "1, where" []),(x^(2) - x + (1)/(6)",","otherwise"):} denotes greatest integer less than or equals to x and {} denotes fractional part function of x. Then,
Answer» F(X) is continuous and differentiable in `x in [-(1)/(2),(1)/(2)]` f(x) is continuous and differentiable in `x in [-(1)/(2),(1)/(2)]` f(x) is continuous and differentiable in `x in [(1)/(2),(3)/(2)]` f(x) is continuous but not differentiable in `x in (0, 1)` ANSWER :D

Discussion

8398.	x^(2)-2x +2 cos^(2)theta + sin^(2)theta=0, then maximum number of ordered pair (x, 0) such that x ∈ R, theta∈ [0,2pi].
Answer» ANSWER :5

Discussion

8399.	A particle is projected horizontally from tower of height 79 m with speed v_0 (in m/sec) . Due to air blow, it gets constant horizontal acceleration of 2m//s^2 in the direction of projection and it lands perpendicularly on inclined plane, then the value of v_0 is ?
Answer» ANSWER :15.40 to 15.70

Discussion

8400.	The value of (dy)/(dx) at x = i/2, where y is given by y =x ^(sin x) + sqrtx is
Answer» `1 + (1)/(SQRT(2PI))` `1` `(1)/( sqrt (2pi))` `1- (1)/(sqrt (2pi ))` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

Let A=[{:(a,b,c),(p,q,r),(1,1,1):}]and B=A^(2) If (a-b)^(2) +(p-q)^(2) =25, (b-c) ^(2)+ (q-r)^(2)= 36 and (c-a)^(2) +(r-p)^(2)=49, then det B is

If Z=(i^i)^i" where "i=sqrt(-1) then

One card is selecting from the pack of 52 playing cards if A and B denotes that card is an ace and it is of square then P(A|B) = ………..

divide is a binary operation on:

If P(A) = (7)/(13) , P(B) = (9)/(13)and P(A cap B)= (4)/(13) then find P(A' | B).

Evaluate the following integrals. int(x^(2))/((x+1)(x+2)^(2))dx

int2x^3cosx^2dx

Find the area bounded by y=x^2,y=0,x=1

Read the following passages and answer the following questions (4-6) Let n be positive integer such that l_(n)=intx^(n)sqrt(a^(2)-x^(2))dx, then answer the following questions: The value of l_(1) is

The numerically greatest term in the expansion (2x - 3y)^12 when x = 1 and y = 5/2 is the

Find vec(a) * vec(b) if |vec(a)| = 6, |vec(b)| = 4 and |vec(a) xx vec(b)| = 12

Two fair dice are rolled at random. The probability that the difference between the numbers is (a) exactly 2 (b) atmost one

Evaluateint1/(sin^2xcos^2x)dx.

Obtain reduction formula for I_(n) =int cosec ^(n) x dx, n being a positive integer, nge 2 and deduce the value of int cosec ^(5) x dx.

Consider the sequence of numbers 121, 12321, 1234321,... Each term in the sequence is

State which of the following statements are true (T) or false(F) The line(x+2)/-1=(y-3)/2=(z+4)/k and (x-4)/(-4)=(y-3)/k=(z+1)/2 are perpendicular at value of k=-1.

Evaluate the determinant Delta = {:|(1,2,4),(-1,3,0),( 4,1,0)|:}

What is the value of 6t such that volume contained inside the planes sqrt(1-t^(2))x+tz=2sqrt(1-t^(2)) z=0,x=2+(tsqrt(4t^(2)-5t+2))/(sqrt(12)(1-t^(2))^((1)/(4))) and |y|=2 is maximum.

Let f(x) be a non-negative, continuous and even function such that area bounded by x-axis ,y-axis & y = f(x) is equal to (x^(2)+x^(3)) sq. unitsAax ge 0, then

The table above shows the distribution of age and gender for 25 people who entered a contest. If the contest winner will be selected at random, what is them probability that the winner will be either a female under age 40 or a male age 40 or older?

Let f:[0, 1/2] rarr R be given by f(x)=x(x-1)(x-2). The value 'c', when Lagrange's mean-value theorem is applied for f(x), is

The smallest positive value of x (in degrees) for which tan(x+100^(@))=tan(x+50^(@))*tanx*tan(x-50^(@)) is

If x^(y) = y^(x) find (dy)/(dx)

If f (x) + f (1 - x) is equal to 10 for all real numbers x then f ((1)/(100)) + f ((2)/(100)) + f ((3)/( 100))+...+f ((99)/(100)) equals

Find the coefficient of x^(n) in the expansion of (x)/((x-3)(x-2)) in powers of x specifying the interval in which the expansion is valid.

Let f (x) = sin ((pi)/(6) sin ((pi)/(2) sin x )) for all x in R and g(x) =(pi)/(2) sin x for allx in R . Let (fog) (x) denote f(g(x)) and (gof) (x) denote g (f(x)) . Then which of the following is (are ) true ?

If (3x^2+1)/((x^2+1)(x^2+2)^2)= (Ax+B)/(x^2+1)+ (Cx+D)/(x^2+2)+ (Ex+F)/(x^2 +2)^2, then A +C +E=

p=(150)/(x^(2)+2)-4 represents the demand function for a product where p is the price per unit for x units. Determine the marginal revenue.

Find the numerically greatest terms in the expansion of(1 - 5x)^12 when x = 2/3

Statement 1 In an ellipse the distance between foci is always less than the sum of focal distances of any point on it. Statement 2 If e be the eccentricity of the ellipse, then 0ltelt1.

If (2)/(sqrt(5)) is the length of the common chord of the circles x^(2)+y^(2)+2x+2y+1=0 andx^(2)+y^(2)+alphax+3y +2 = 0,alpha ne 0," then "alpha=

Find the slope of the tangent to curve y=x^(3)-x+1 at the point whose x- coordinate is 2.

a, b, c are three mutually perpendicular unit vectors inthe right handed system. If the points P, Q, R with position vectors 2a+5b-4c, a+4b-3c " and "ka+7b-6c respectively lie on a line, then the ratio in which the point P divides QR is

Probability distribhution of a random variable X is given by: Find k, hence find the mean and variance of the distributions.

lim_(xto0)|x|/x

The solution set of the constraints 2x+3y le 6, x+4y le 4" and "x ge 0, y ge 0 includes the point ………. As corner point.

Complex numbers z_1, z_2, z_3 are represented by the points of contact D, E, F of the incircle of triangle ABC, with the centre O of the incircle taken as the origin. If BO meets DE at G, find the complex number represented by G.

The tworegression lines intersect at unique point, then it should be

Find the number of solutions of the equations (sin x - 1)^(3) + (cos x - 1)^(3) + ( sin x)^(3) = ( 2 sin x + cos x - 2)^(3)in ( 0, 2 pi) .

Differentiate sqrtx+1/sqrtx-root(3)(x^2)

The point of intersection of lines is (alpha, beta) , then the equation whose roots are alpha, beta, is

Determine the pointwhere the line 2y+x=3, is normal to the curve y=x^(2).

A : 3. C_0 + 7.C_1 + 11. C_2 + ….+(4n + 3). C_n = (2n +3) 2^n. R : a. C_0 + (a+d). C_1 + (a+2d). C_2 + …..+ (a+nd). C_n - (2a+nd). 2^(n-1).

Solve [[x+a,0,0],[a,x+b,0],[a,0,x+c]]=0

If theequation x^5 -3x^4 -5x^3 +27x^2- 32 x+12=0hasrepeatedroots, then theprimenumberthatdividesthe nonrepeatedrootof thisequationis

If the direction ratios of the lines L_(1)andL_(2) are 2, -1, 1 and 3, -3, 4 respectively, then the direction cosines of a line that is perpendicular to both L_(1)andL_(2) are

A real valued function f(x) is given as f(x) = {{:(int_(0)^(x) 2{x}dx",",x + {x} in I),(x^(2) - x + (1)/(2)",",(1)/(2) lt x lt (3)/(2) and x ne "1, where" []),(x^(2) - x + (1)/(6)",","otherwise"):} denotes greatest integer less than or equals to x and {} denotes fractional part function of x. Then,

x^(2)-2x +2 cos^(2)theta + sin^(2)theta=0, then maximum number of ordered pair (x, 0) such that x ∈ R, theta∈ [0,2pi].

A particle is projected horizontally from tower of height 79 m with speed v_0 (in m/sec) . Due to air blow, it gets constant horizontal acceleration of 2m//s^2 in the direction of projection and it lands perpendicularly on inclined plane, then the value of v_0 is ?

The value of (dy)/(dx) at x = i/2, where y is given by y =x ^(sin x) + sqrtx is

The smallest positive value of x (in degrees) for which tan(x+100^(@))=tan(x+50^(@))tanxtan(x-50^(@)) is