28278 + Interview Questions in Maths in Class 12 Page 204 InterviewSolution

10151.	if (m-1) a_(1)^(2)-2m a_(2) lt 0, then provethat x^(m-1) +a_(2)x^(m-2) +….+a_(m-1) x+a_(0) has at least onenon real root(a_(1),a_(2),……..a_(m) in R)
Answer»

Discussion

10152.	If the matrix A is both symmetric and skew symmetric, then
Answer» A is DIAGONAL matrix A is a zero matrix A is SCALAR matrix A is SQUARE matrix Answer :B

Discussion

10153.	The plane parallel to the lines (x+2)/(3) = (y-2)/(-1) = (z+1)/(2)and (x-2)/(1) = (y-3)/(1) = (y-3)/(2) = (z-4)/(3) and passing through the point (4,-1,2) is point also through...........
Answer» (1,1,1) (-1,-1,-1) (1,1,-1) (-1,-1,1) ANSWER :A

Discussion

10154.	If f : R rarr R be given by f(x) = (3 - x^3)^(1/3), then (f o f) (x) is
Answer» `X^(1/3)` `x^3` x (3 - x^3)` ANSWER :C

Discussion

10155.	Iine xsintheta+ycostheta=pintercepted between the coordinate axes .
Answer» <P> Answer :`(1)/(X^(2))+(1)/(y^(2))=(4)/(p^(2))`

Discussion

10156.	State which of thefollowingstatementis false
Answer» the most important feature of a LINEAR programming problem is the presenceof linearity in the problem the objective function may ASSUME its optimal VALUE ATMORE them ONE corner point of the feasible region multiple solutions of linear programming problem are solution each of which maximize orminimize the objective function an infeasible linear programming problem has no feasible solution Answer :C

Discussion

10157.	A : C_0-(C_1)/(2)+(C_2)/(3)+(C_2)/(3)-….+ (-1)^n (C_n)/(n+1)=(1)/(n+1) R :C_0 + (C_1)/(2)x. + (C_2)/(3) x^2 + (C_3)/(4) x^3 + ….+ (C_n)/ (n+1) .x^n = ((1+x)^(n+1)-1)/((n+1)x)
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

10158.	If f:NrarrZ defined as f(n)={{:((n-1)/(2),":"," if n is odd"),((-n)/(2),":", " if n is even"):} and g:NrarrN defined as g(n)=n-(-1)^(n), then fog is (where, N is the set of natural numbers and Z is the set of integers)
Answer» ONE - one and onto one - one and into many - one and onto many - one and into Answer :A

Discussion

10159.	The equation of the common tangent to x^(2)+y^(2)=2a^(2)"and" y^(2)=8axis
Answer» `y=+- (X+ a) ` ` y=+- (x+ 2A) ` ` y=+-(x-2a) ` ` y=+- (x-a) ` ANSWER :B

Discussion

10160.	Area bounded between the curve y = x^(2) and y = g(x) where g (x) g (x) = (2)/(f(x)) and x -axis is
Answer» `(pi)/(2) - (1)/(3)` `pi - (1)/(3)` `(pi)/(2) - (1)/(6)` `pi - (2)/(3)` ANSWER :D

Discussion

10161.	int(x^(3)+5x^(2)-4)/(x^(2))dx
Answer» ANSWER :`(X^(2))/2+5x+4/x+C`

Discussion

10162.	What is the surface area of a sphere when the volume is increasing at the same rate as its radius?
Answer» 1 `(1)/(2pi)` `4 PI` `(4 pi)/(3)` ANSWER :A::B::D

Discussion

10163.	A line passing through A(2,-1,5)andB(4,3,-10) meets the xy-plane at (x,y,z), then (x)/(y) = __________
Answer» ANSWER :8

Discussion

10164.	Find the second order derivatives of the functions given in Exercises 1 to 10. x^(20)
Answer» ANSWER :`380 X^(18)`

Discussion

10165.	If f(x) = underset(nrarroo)lim[2x+4x^(3)+...+2nx^(2n-1)] (0 lt x lt 1) then intf(x) dx is equal to
Answer» `-SQRT(1-X^(2))` `(1)/(sqrt(1-x^(2)))` `(1)/(x^(2)-1)` `(1)/(1-x^(2))` ANSWER :D

Discussion

10166.	Integrate the functions e^(2x)sinx
Answer» ANSWER :`(E^(2X))/5(2sinx-cosx)+C`

Discussion

10167.	Form the differential equation of the family of circles touching the x-axis at origin.
Answer» ANSWER :`(dy)/(dx) = (2XY)/(X^(2) - y^(2))`

Discussion

10168.	In the group (G,oplus_(15)) where G={3,6,9,12}, oplus_(15) is multiplication modulo 15, the identity element is
Answer» 3 6 12 9 Answer :B

Discussion

10169.	If from a packof 52 well shuffled cards,cards are drawn one by one without replacement andthe third card is found to be ACE. What is the probaility that first two cards are not ACES?
Answer» `260/329` `376/425` `161/329` None of these Solution :`=((.^(48)C_(2))/(.^(52)C_(2))xx4/50)/((.^(48)C_(2))/(.^(52)C_(2))xx4/50+(.^(48)C_(1).^(4)C_(1))/(.^(52)C_(2))xx3/50+(.^(4)C_(2))/(.^(52)C_(2))xx2/50)` `=(4.^(48)C_(2))/(4.^(48)C_(2)+12.^(48)C_(1)+12)`

Discussion

10170.	If G is the centroid of the triangleABC," then "overset(-)(GA)+overset(-)(BG)+overset(-)(GC)
Answer» `2overset(-)(GB)` `2 OVERSET(-)(GA)` `VEC0` `2 overset(-)(BG` Answer :D

Discussion

10171.	Evaluate int_(-pi//4)^(pi//4)x^(3)sin^(2)xdx
Answer» SOLUTION :`:'f(x)=x^(3)SIN^(2)x` Now, `f(-x)=(-x)^(3)sin^(2)(-x)=-x^(3)sin^(2)x=-f(x)` (odd function) `:. Int_(-pi//4)^(pi//4)x^(3)sin^(2)xdx=0`

Discussion

10172.	Equation of the line of shortest distance between the lines(x)/(1) =(y)/(-1)=(z)/(1) and(x-1)/(0)=(y+1)/(-2) =(z)/(1)is
Answer» ` (x)/(1) =(y)/(-1)=(z)/(2)` `( x-1)/(1) = ( y+1)/(-1) -(z)/(-2) ` ` (x-1)/(1) =(y+1)/(1) =(z)/(1) ` `(x)/(2) =(y)/(1) = (z)/(2) ` ANSWER :B

Discussion

10173.	If v(x,y) = log (e^(x) + e^(y)), then (del v)/(del x) + (del v)/(del y) is equal to
Answer» `E ^(X) + e ^(y)` `(1)/(e ^(x) + e ^(y))` `2` 1 Answer :D

Discussion

10174.	Find the coefficient of x^(n) in the expansion of (x-4)/(x^(2)-5x+6) in powers of x specifying the interval in which the expansion is valid.
Answer» ANSWER :`(1)/(3^(N+1))-(1)/(2^(n))`

Discussion

10175.	If the points A(-1, 3, 2), B(-4, 2, -2) and C(5, 5, lambda) are collinear then find the value of lambda.
Answer» ANSWER :`lambda=10`

Discussion

10176.	If S_(n) denote the sum to n terms of an A.P. whose first term is a and common differnece is d , then S_(n-3) - 3S_(n+1) - S_(n) is equal to
Answer» `-d` `-a` 0 2a Answer :3

Discussion

10177.	A fair coin is tossed n times, then what is the probability that H (Head) has appeared at least once ?
Answer» `(6^(n) - 5^(n))/(5)` `1- ((1)/(6))^(n)` `1- ((5)/(6))^(n)` `1- ((1)/(2))^(n)` Answer :D

Discussion

10178.	Find (dy)/(dx), if x= a t^(2), y= 2 a t
Answer» ANSWER :`(1)/(t)`

Discussion

10179.	If the straight lines (x-1)/(k)=(y-2)/(2)=(z-3)/(3) and (x-2)/(3)=(y-3)/(K)=(z-1)/(2) intersect at a point then the interger k is equal to
Answer» `-5` 5 2 `-2` ANSWER :A

Discussion

10180.	If the function f:RrarrR and g:R rarrR are such that f(x) is continuous at x=alpha and f(alpha)=a and g(x) is discontinuous at x = a but g(f(x)) is continuous at x=alpha, then (f(x) and g(x) are non - constant functions)
Answer» `X=alpha` is an extremum of f(x) and x = a is an extremum of g(x) `x=alpha` MAY not be an extremum of f(x) and x = a is an extremum of g(x) `x=alpha` is an extremum of f(x) and x= a may not be an extremum of g(x) none of these Answer :C

Discussion

10181.	ABCD is a regular tetrahedron P & Q are the mid -points of the edges AC and AB respectively, G is the cenroid of the face BCD and theta is the angle between the vectors vec(PG) and vec(DQ), then
Answer» The angle between `vec(AB)` and `vec(CD)` is `90^(@)` The angle `theta` is `pi-cos^(-1)(5/(3sqrt(3)))` The angle `theta` is `pi-cos^(-1)(5/(6sqrt(3)))` The angle between `vec(AB)` and `vec(CD)` is `120^(@)` Solution :`vec(DA)=veca,vec(DB),VECB, vec(DC)=vecc` `vec(AD).vec(BC)=(-veca).(vecc-vecb)` `=-veca.vecc+veca.vecb` `=0` Hence `vec(AD)_\|_^(r) vec(BC)impliesvec(AB)_\|_vec(CD)` Now, `vec(PG)=-1/6(3veca-2vecb+vecc)` & `vec(DQ)=1/2(veca+vecb)` Let `\|veca\|=\|vecb\|=\|vecc\|=K` `implies\|vec(PG)\|=K/2` & `\|vec(DQ)\|=(sqrt(3))/2K` `impliesvec(PG).vec(DQ)=-1/6(3veca-2vecb+vecc).1/2(veca+vecb)` `costheta=-5/(6sqrt(3))impliestheta-pi-cos^(-1)(5/(6sqrt(3)))`

Discussion

10182.	If one side of a triangle , inscribed in a semi-circle of radius r,is the bounding diameter, then ist maximum aera is
Answer» `(PI r ^(2))/(2)` `(pi r^(2))/(4)` `(r^(2))/(2)` `r^(2)` ANSWER :B

Discussion

10183.	The sum of two numbers is 20. If the product of the square of one number and cube of the other is maximum, then the numbers are
Answer» 12, 8 3, 4 9, 12 15, 18 Answer :A

Discussion

10184.	Which of the followingis logically equivalent to ~~(~~p rarrq)
Answer» <P>` p ^^ Q` `p^^ ~~ q` ` ~~p ^^ q` `~~p ^^ ~~ q` ANSWER :D

Discussion

10185.	Roots of the equations2x^(2)-5x+1 =0and x^(2)+5x+2=0 are
Answer» Reciprocal and of the same sign Reciprocal and of OPPOSITE sign Equal in MAGNITUDE None of these Answer :B

Discussion

10186.	Area of the region bounded by the curves y = sqrt(5 - x^(2)) and y = \|x-1\| is
Answer» `(5PI -2)/(4)` `(5pi + 2)/(4)` `(3PI -2)/(4)` `(3pi +2)/(4)` ANSWER :A

Discussion

10187.	bar(a),bar(b) and bar( c ) are unit vectors. The value of \|bar(a)-bar(b)\|^(2)+\|bar(b)-bar( c )\|^(2)+\|bar( c )-bar(a)\|^(2) is not expected ………………
Answer» 4 9 8 6 Answer :B

Discussion

10188.	The volume of the paralleloP1ped whose co-terminous edges are overline(a), overline(b), overline(c), where overline(a), overline(b), overline(c) are non-coplanar units vectors each inclined with other at an angle of 60^(@) is
Answer» 2CU. UNITS `sqrt(2)`CU. Units `(1)/(2)`cu. Units `(1)/(sqrt(2))`cu. Units Answer :D

Discussion

10189.	Find underset(-a)overset(a)int x^(2) (a^(2)-x^(2))^(3//2)dx
Answer» ANSWER :`(PI a^(6))/(16)`

Discussion

10190.	If f (x) = (1+sqrt(2cosx))/(1-sqrt(2)cosx)andg(x)=tan""(x)/(2)andh(x)=log\|x\| "then" int(dx)/(sinx(2cos^(2)x-1)) is equal to
Answer» `(1//sqrt(2))log\|f(X)\|+G o h (x) + C` `sqrt(2)` h o f (x) + h o g (x) + C h o (f + g) (x) + C `(1//sqrt(2))` f o (g + h) (x) + C` Answer :B

Discussion

10191.	Integrate the function is Exercise. sqrt((1-sqrt(x))/(1+sqrt(x)))
Answer» ANSWER :`-2sqrt(1-X)+COS^(-1)(sqrt(x))+sqrt(x-x^(2))+c`

Discussion

10192.	There are fifteen players for a cricket match In how many ways the 11 players can be selected?
Answer» ANSWER :1365

Discussion

10193.	Evaluate the following integrals int(2x-5)/(3x^(2)+4x+5)dx
Answer» Answer :`(1)/(3)LOG\|3x^(2)+4x+5\|-(19)/(6sqrt(11))log\|(3x+1-sqrt(1))/(3x+1+sqrt(1))\|+c`

Discussion

10194.	Let L = 4x- 5y, L_(i) = (x)/(10) - (i)/(n), L_(i) = x/10 +y/8 + i/n, andE = (x^(2))/(50) + (y^(2))/(32) - 1.LetA_(i) repersents the area of regioncommon between L_(i-1) gt 0, L_(i) lt 0, E lt 0 and L lt 0,A'_(i)represents the area of region common between L'_(i-1) lt 0, L'_(i) gt 0, E lt 0 and L lt 0.B_(i) repersents the area of region common between L_(i-1) gt 0, L_(i) lt 0, E lt 0 and L gt 0,B'_(i) repersents the area of region common between L'_(i - 1) lt , L'_(i) gt 0, E lt 0 and L gt 0, then value of (A_(1) + A'_(2) + A_(3) + A'_(4) + ".......") + (B_(1) + B'_(2) + B'_(4) + ".......") is equalto .
Answer» SOLUTION :N//A

Discussion

10195.	The number of values of (costheta+isintheta)^(p//q) where p and q are non zero integers prime to each other is :
Answer» <P>`p` `Q` `p+q` `p-q` ANSWER :B

Discussion

10196.	If xgt0 then (x-1)/(x+1)+(1)/(2)(x^(2)-1)/((x+1)^(2))+(1)/(3)(x^(3)-1)/((x+1)^(3))+....=
Answer» `log_(E )X ` `log_(e )(1//x)` `log_(e )(1+x)` `log_(e )(1-x)` ANSWER :A

Discussion

10197.	If Delta=\|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}\| and C_(ij)=(-1)^(i+j) M_(ij), "where " M_(ij) is a determinant obtained by deleting ith row and jth column then then \|{:(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33)):}\|=Delta^(2). If \|{:(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x):}\| =5 and Delta =\|{:(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1):}\| then sum of digits of Delta^(2) is
Answer» 7 8 13 11 Answer :C

Discussion

10198.	Find the angle between x-axis and the vector hat(i) + hat(j) + hat(k)
Answer» Answer :`theta = cos^(-1)((1)/(sqrt(3)))`

Discussion

10199.	If (x-a)^(2) + (y-b)^(2) = c^(2), for some c gt 0, prove that ([1 + ((dy)/(dx))^(2)]^((3)/(2)))/((d^(2)y)/(dx^(2))) is a constant independent of a and b.
Answer» ANSWER :`-C`

Discussion

10200.	Which of the following numbers are non positive?
Answer» `5^(log_(11)7) - 7^(log_(11)5)` `log_(3) (sqrt(7)-2)` `log_(7)((1)/(2))^(-1//2)` `log_(sqrt(2)-1).(sqrt(2)+1)/(sqrt(2)-1)` Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

if (m-1) a_(1)^(2)-2m a_(2) lt 0, then provethat x^(m-1) +a_(2)x^(m-2) +….+a_(m-1) x+a_(0) has at least onenon real root(a_(1),a_(2),……..a_(m) in R)

If the matrix A is both symmetric and skew symmetric, then

The plane parallel to the lines (x+2)/(3) = (y-2)/(-1) = (z+1)/(2)and (x-2)/(1) = (y-3)/(1) = (y-3)/(2) = (z-4)/(3) and passing through the point (4,-1,2) is point also through...........

If f : R rarr R be given by f(x) = (3 - x^3)^(1/3), then (f o f) (x) is

Iine xsintheta+ycostheta=pintercepted between the coordinate axes .

State which of thefollowingstatementis false

A : C_0-(C_1)/(2)+(C_2)/(3)+(C_2)/(3)-….+ (-1)^n (C_n)/(n+1)=(1)/(n+1) R :C_0 + (C_1)/(2)x. + (C_2)/(3) x^2 + (C_3)/(4) x^3 + ….+ (C_n)/ (n+1) .x^n = ((1+x)^(n+1)-1)/((n+1)x)

If f:NrarrZ defined as f(n)={{:((n-1)/(2),":"," if n is odd"),((-n)/(2),":", " if n is even"):} and g:NrarrN defined as g(n)=n-(-1)^(n), then fog is (where, N is the set of natural numbers and Z is the set of integers)

The equation of the common tangent to x^(2)+y^(2)=2a^(2)"and" y^(2)=8axis

Area bounded between the curve y = x^(2) and y = g(x) where g (x) g (x) = (2)/(f(x)) and x -axis is

int(x^(3)+5x^(2)-4)/(x^(2))dx

What is the surface area of a sphere when the volume is increasing at the same rate as its radius?

A line passing through A(2,-1,5)andB(4,3,-10) meets the xy-plane at (x,y,z), then (x)/(y) = __________

Find the second order derivatives of the functions given in Exercises 1 to 10. x^(20)

If f(x) = underset(nrarroo)lim[2x+4x^(3)+...+2nx^(2n-1)] (0 lt x lt 1) then intf(x) dx is equal to

Integrate the functions e^(2x)sinx

Form the differential equation of the family of circles touching the x-axis at origin.

In the group (G,oplus_(15)) where G={3,6,9,12}, oplus_(15) is multiplication modulo 15, the identity element is

If from a packof 52 well shuffled cards,cards are drawn one by one without replacement andthe third card is found to be ACE. What is the probaility that first two cards are not ACES?

If G is the centroid of the triangleABC," then "overset(-)(GA)+overset(-)(BG)+overset(-)(GC)

Evaluate int_(-pi//4)^(pi//4)x^(3)sin^(2)xdx

Equation of the line of shortest distance between the lines(x)/(1) =(y)/(-1)=(z)/(1) and(x-1)/(0)=(y+1)/(-2) =(z)/(1)is

If v(x,y) = log (e^(x) + e^(y)), then (del v)/(del x) + (del v)/(del y) is equal to

Find the coefficient of x^(n) in the expansion of (x-4)/(x^(2)-5x+6) in powers of x specifying the interval in which the expansion is valid.

If the points A(-1, 3, 2), B(-4, 2, -2) and C(5, 5, lambda) are collinear then find the value of lambda.

If S_(n) denote the sum to n terms of an A.P. whose first term is a and common differnece is d , then S_(n-3) - 3S_(n+1) - S_(n) is equal to

A fair coin is tossed n times, then what is the probability that H (Head) has appeared at least once ?

Find (dy)/(dx), if x= a t^(2), y= 2 a t

If the straight lines (x-1)/(k)=(y-2)/(2)=(z-3)/(3) and (x-2)/(3)=(y-3)/(K)=(z-1)/(2) intersect at a point then the interger k is equal to

If the function f:RrarrR and g:R rarrR are such that f(x) is continuous at x=alpha and f(alpha)=a and g(x) is discontinuous at x = a but g(f(x)) is continuous at x=alpha, then (f(x) and g(x) are non - constant functions)

ABCD is a regular tetrahedron P & Q are the mid -points of the edges AC and AB respectively, G is the cenroid of the face BCD and theta is the angle between the vectors vec(PG) and vec(DQ), then

If one side of a triangle , inscribed in a semi-circle of radius r,is the bounding diameter, then ist maximum aera is

The sum of two numbers is 20. If the product of the square of one number and cube of the other is maximum, then the numbers are

Which of the followingis logically equivalent to ~~(~~p rarrq)

Roots of the equations2x^(2)-5x+1 =0and x^(2)+5x+2=0 are

Area of the region bounded by the curves y = sqrt(5 - x^(2)) and y = |x-1| is

bar(a),bar(b) and bar( c ) are unit vectors. The value of |bar(a)-bar(b)|^(2)+|bar(b)-bar( c )|^(2)+|bar( c )-bar(a)|^(2) is not expected ………………

The volume of the paralleloP1ped whose co-terminous edges are overline(a), overline(b), overline(c), where overline(a), overline(b), overline(c) are non-coplanar units vectors each inclined with other at an angle of 60^(@) is

Find underset(-a)overset(a)int x^(2) (a^(2)-x^(2))^(3//2)dx

If f (x) = (1+sqrt(2cosx))/(1-sqrt(2)cosx)andg(x)=tan""(x)/(2)andh(x)=log|x| "then" int(dx)/(sinx(2cos^(2)x-1)) is equal to

Integrate the function is Exercise. sqrt((1-sqrt(x))/(1+sqrt(x)))

There are fifteen players for a cricket match In how many ways the 11 players can be selected?

Evaluate the following integrals int(2x-5)/(3x^(2)+4x+5)dx

The number of values of (costheta+isintheta)^(p//q) where p and q are non zero integers prime to each other is :

If xgt0 then (x-1)/(x+1)+(1)/(2)(x^(2)-1)/((x+1)^(2))+(1)/(3)(x^(3)-1)/((x+1)^(3))+....=

Find the angle between x-axis and the vector hat(i) + hat(j) + hat(k)

If (x-a)^(2) + (y-b)^(2) = c^(2), for some c gt 0, prove that ([1 + ((dy)/(dx))^(2)]^((3)/(2)))/((d^(2)y)/(dx^(2))) is a constant independent of a and b.

Which of the following numbers are non positive?

Which of the followingis logically equivalent to (p rarrq)