28278 + Interview Questions in Maths in Class 12 Page 13 InterviewSolution

601.	The value of lim_(xtooo) (cot^-1(x^-alog_ax))/(sec^-1(x^-alog_ax)),agt1, is equalto
Answer» 1 0 `(PI)/(2)` does not EXIST ANSWER :A

Discussion

602.	The sum of (1^(2)-1+1) (1!)+(2^(2)-2+1)(2!) +...+ (n^(2)-n+1) (n!) is -
Answer» `(N+2)!` `(n-1)((n+1)!)+1` `(n+2)!-1` `n((n+1)!)-1` SOLUTION :`T_(n)=(n^(2)-n+1)n!` `=(n^(2)-1)n!-(n-2)n!` `T_(n)=(n-1)(n+1)!-(n-1)n!` SUM `=1+(n-1) (n+1) !`

Discussion

603.	The logical statement [ ~ ( ~p vee q) vee (p ^^ r ) ^^ ( ~ q ^^ r ) ] is equivalent to
Answer» <P>`(p ^^ Q ) ^^ (~R) ` `(~p ^^ ~q) ^^ r` `~ p VEE r` `(p ^^ ~q) vee r` ANSWER :A

Discussion

604.	Evalute {:(" Lt"),(xrarr1):}(sin(x-1))/(x^(2)-1)
Answer» ANSWER :`(1)/(2)`

Discussion

605.	If A is a square matrix and \|A\| = 2 then \|A\|^n = ………. . Where n is positive integer.
Answer» 0 2n `2^n` `n^2` ANSWER :A

Discussion

606.	2 white balls and 3 blanks balls and 3 blank 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» `5:3:2` `4:1:2` `4:2:1` `3:2:5` ANSWER :A

Discussion

607.	State which of the following matrices is symmetric,slew symmetric, both or not either:[[0,1,2],[-1,y,3],[-2,-3,z]],(x,y,z) != (0,0,0)
Answer» SOLUTION :NEITHER SYMMETRIC nor SKEW symmetric

Discussion

608.	Show that the locus of P where the tangents drawn from P to the circle x^(2)+y^(2)=a^(2) include an angle alpha is x^(2)+y^(2)=a^(2)cosec^(2)(alpha)/2
Answer» ANSWER :`a^(2)COSEC C^(2)(ALPHA)/2`

Discussion

609.	Evaluate the following:lim_(xtoinfty) sinx/x
Answer» SOLUTION :`0lt\|sinx/x\|le1/\|x\|` `implies0lelim_(xtoinfty)\|sinx/x\|lelim_(xtoinfty)1/\|x\|` `0lelim_(xtoinfty)\|sinx/x\|le0` `implieslim_(xtoinfty)(sinx/x)=0`

Discussion

610.	Show that the tangents to the curve y=7x^(3)+11 at the point where x = 2 and x=-2 are parallel.
Answer» ANSWER :84

Discussion

611.	Removesecondterm( secondhigherpowerof x )fromthe equation x^4 +8x^3 +x-5=0
Answer» ANSWER :`X^4 -24 x^2 +65 x - 55=0`

Discussion

612.	There is a point inside an equilateral triangle ABC of side a whose distance from the vertices is 3,4,5 . Rotate the triangle and P through 60^@ about C. Let A go to A' and P to P'. The area of traingle PAP' is
Answer» 8 12 6 none of these Answer :C

Discussion

613.	If sin x = (2t)/(1+t^(2)), tan y = (2t)/(1-t^(2)), then (dy)/(dx) is equal to
Answer» 1)1 2)0 3)`-1` 4)2 Answer :A

Discussion

614.	int_(0)^(2pi) e^(x//2) sin (x/2 + pi/4) dx=
Answer» 1 `PI` 0 2 Answer :C

Discussion

615.	There are two factories located one at place P and the other at place Q.From these locations, a certain commodity is to be delivered to each of the three depots situated at A, B and C. The weekly requirments of the depots are respectively 5,5 and 4 units of the commodity while the production capacity of the factories at P and Q are respectively 8 and 6 units. The cost of transportation per unit is given below: How many units should be transported from each factory to each depot in order that the transportable cost is minimum? When will be the minimum transportation cost?
Answer» <P> ANSWER :0,5 and 3 from FACTORY P 5,0,1 from factory Q Min.cost = ₹ 1550.

Discussion

616.	Differntiate the following functions by proper substitution.sin^(-1)2xsqrt(1-x^2)
Answer» SOLUTION :`y=sin^(-1)2xsqrt(1-X^2)`[Putx=`sin thet `sin^(-1)(2 sin THETA.cos theta)` `sin^(-1)sin2theta=2theta=2 sin^(-1)x.` `dy/dx=2/sqrt(1-x^2)`

Discussion

617.	The negation of 'For every natural number x, x +5 gt 4' is
Answer» `AA x in N, x + 5 lt 4` `AA x in N, x - 5 lt 4` For every integer x, x + 5 lt 4 There exists a natural NUMBER x, for which ` x+ 5 lt = 4` ANSWER :D

Discussion

618.	If S.D of x_(1), x_(2), x_(3),….x_(n),…x-(n) is sigma, then find S.D of -x_(1), -x_(2), -x_(3),….-x_(n) ?
Answer» ANSWER :`SIGMA`

Discussion

619.	int_0^2 x[2x]dx, where [.] denotes greatest integer function, equals: -
Answer» 540 544 `17/4` `33/44` SOLUTION :`I=int_0^(1//2)0.dx+int_(1//2)^1 xdx+int_1^(3//2) 2xdx + int_(3//2)^(2)3xdx` `=0+(x^2/2)_(1//2)+(x^2)_(1)^(3//2) + ((3x^2)/2)_(3//2)^(2) =17/4`

Discussion

620.	There are 2 white and 3 red balls in box A and 4 white, 5 red balls in box B One box is selected at random and one ball is drawn from it. Then ......... is the probability that selected ball is of red colour.
Answer» `(5)/(14)` `(5)/(16)` `(5)/(18)` `(26)/(45)` Answer :D

Discussion

621.	If the boundary of figure is represented by parametric equations i.e. x = x (t), y = y (t), then the area of the figure is evaluated by one of the three formulas S = - underset(alpha)overset(beta)(int)y(t) x' (t) dt,S = underset(alpha)overset(beta)(int) x(t). y'(t) dt S = (1)/(2) underset(alpha)overset(beta)(int) (xy' - yx') dt where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of of the traversal of the curve corresponding to increasing t The area enclose by the asteroid ((x)/(a))^(z//3) + ((y)/(a))^(2//3) = 1 is
Answer» `(3)/(4) a^(2) pi` `(3)/(18) pi a^(2)` `(3)/(8) pi a^(2)` `(3)/(4) a pi` ANSWER :C

Discussion

622.	f:R-{q} rarrR -{1},f(x) = (x-p)/(x-q), p ne q ,then f is .........
Answer» ONE - one and ONTO . MANY - one and not onto . one - one and not onto . many - one and onto . SOLUTION :N/A

Discussion

623.	If ((1)/(2),2) is one extermity of a focalchord of the parabola y^(2)=8x. Find the co-ordinates of the other extremity.
Answer» ANSWER :`(8,8)`

Discussion

624.	Integrate the following functions w.r.t.x cosx/sqrt(4-sin^2x)
Answer» SOLUTION :Put t = SINX. Then dt = cosx DX therefore `INT cosx/sqrt(4-sin^2x) dx = int (dt)/sqrt(4-t^2)` =`int dt/sqrt(2^2 -t^2) = sin^-1(t/2) +c` =`sin^-1(sinx/2) +c`

Discussion

625.	Prove that the following functions do not have maxima or minima f(x)=e^x
Answer» SOLUTION :`F(x)=e^xne0` for any REAL x `thereforef(x)` does .t have MAXIMA or minima

Discussion

626.	Consider the vectors "" oversetrarra=2overset^^i-3overset^^j+overset^^k"and"oversetrarrb = overset^^i+overset^^j-2overset^^k. ""Find \|3 oversetrarra+oversetrarrb \|
Answer» SOLUTION :`3veca+vecb=6overset^^i-9overset^^j3overset^^k)+(overset^^i+overset^^j-2overset^^k)` `7overset^^i-8overset^^j+overset^^k` `implies\|3veca+vecb\|=SQRT(49+64+1)=sqrt(114)`

Discussion

627.	Intergrate the following: intsin6x sin3xdx
Answer» SOLUTION :`INTSIN6X sin3xdx` =`1/2int(-cos9x+cos3x)DX` = -1/18sin9x+1/6sin3x+C =1/6sin3x-1/18sin9x+C

Discussion

628.	Let A and B be independent events with P(A)=0.2,P(B)=0.5. Let us find (i) P(A//B) (ii) P(B//A) (iii) P(AnnB)(iv) P(AuuB) (v) P(A^(c )nnB^(c ))
Answer» ANSWER :`(i) 0.2` `(II) 0.5` `(III) 0.1` `(IV) 0.6` `(V) 0.4`

Discussion

629.	Find the value of c in [-2,2] inLagranges Mean value theorem for the functionf(x)=x^(2)-2x+3.
Answer» a) `0` B) `-1` c) `1` d) NONE of these Answer :D

Discussion

630.	Differentiate the following w.r.t.x log(cose^x)
Answer» SOLUTION :`d/dxlog(cose^X)-1/(COS(x^2))d/dxcos(e^x)=(-SIN(e^x))/(cos(e^x)x)xxd/dxe^x=-tan(e^x)xxe^x`

Discussion

631.	The numerically greatest term in the expansion (5x - 6y)^14 when x = 2/5, y = 1/2 is
Answer» `""^14C_(6)2^(8) 3^6` `""^14C_(7) 2^(6)3^8` `""^14C_(6) 2^(6) 3^8` `""^14C_(7)2^(8)3^6` Answer :C

Discussion

632.	If hati+2hatj+3hatk, 3hati+2hatj+hatk are the sides of a parallelogram, then a unit vector is prallel to one of the diagonals of the parallelogram, is
Answer» `(hati+hatk+hatk)/(SQRT3)` `(hati-hatj+hatk)/(sqrt3)` `(hati+hatj-hatk)/(sqrt3)` `(-hati+hatk+hatk)/(sqrt3)` ANSWER :A

Discussion

633.	if f(x) is differentiable function such that f(1) = sin 1, f (2)= sin 4 and f(3) = sin 9, then the minimum number of distinct roots of f'(x) = 2x cosx^(2) in (1,3) is "_______"
Answer» ANSWER :2

Discussion

634.	int_(0)^(pi//2) ln (tan x+ cot x)dx=
Answer» `PI/2 LN 2` 1 `pi ln 2` `2 pi ln 2` ANSWER :C

Discussion

635.	The solution of y'' + y' = 1 is
Answer» `y = X - AC^(-x) + B` `y = x + ac^(x) + b` `y + x = ac^(-x) + b` `y + x = ac^(x) + b` ANSWER :A

Discussion

636.	Find area bounded by y = f^(-1)(x), x = 10, x = 4 and x-axis. Given thatarea bounded by y = f(x) , x = 2, x = 6 and x -axis is 30 sq. units, where f(2) = 4 and f(6) = 10. (given f(x)is an invertiablefunction).
Answer» SOLUTION :N//A

Discussion

637.	If Eand F are two evetns such that P(E) = (1)/(4) , P(F) =(1)/(2) and P(E and F) = (1)/(8) . Find P(not E and not F)
Answer» ANSWER :`(3)/(8)`

Discussion

638.	How many integral solutions are there to the systems of equations x_(1)+x_(2)+x_(3)+x_(4)+x_(5)=20andx_(1)+x_(2)=15 where x_(k)ge0.
Answer» ANSWER :336

Discussion

639.	Solve the following : [[4,x+1],[3,x]]=5
Answer» SOLUTION :`[[4,X+1],[3,x]]`=5 or, 4x-3x-3=5 or, x=8

Discussion

640.	If : R - {(3)/(7) rarr R - {(3)/(7)} is given by f(x) = (3x + 5)/(7x - 3), then the statement which is not true, is
Answer» `f^(-1) (X) = f(x)` (FOF)(x) = x (FOFOF)(x) = x (fofofof)(x) = x Answer :C

Discussion

641.	Let vec(alpha),vec(beta),vec(gamma) be three unit vectors such that vec(alpha).vec(beta)=vec(alpha).vec(gamma)=0 and the angle between vec(beta)andvec(gamma) is 30^(@)." Then "vec(alpha) is
Answer» `2(VEC(BETA)xxvec(gamma))` `-2(vec(beta)xxvec(gamma))` `+-2(vec(beta)xxvec(gamma))` `(vec(beta)xxvec(gamma))` Answer :C

Discussion

642.	Assertion (A) If alpha =12 ^(@),beta = 15^(@),gamma = 18^(@),then tan 2 alpha tan 2beta + tan 2betatan 2gamma+tan2gamma tan 2alpha=1Reason ( R ) In DeltaABC, " tan "(A)/(2) " tan " (B)/(2)+ " tan " (B)/(2) " tan " (C)/(2) + " tan "(C)/(2) " tan "(A)/(2)=1 Which of the following is true?
Answer» Both (A) and ( R ) are TRUE and ( R ) is the CORRECT EXPLANATION of (A) Both (A) and ( R ) are true, but ( R ) is not the correct explanation of (A) (A) is true, but ( R ) is FALSE (A) is false, but ( R ) is true Answer :A

Discussion

643.	If z=2+i, then (z-1) (barz-5)+(barz+1) (z-5) is equal to
Answer» 2 7 `-1` `-4` ANSWER :D

Discussion

644.	From each of 3 married couples one partner is selected at random then the probability of the chosen ones being all of the same sex is
Answer» `(1)/(8)` `(1)/(6)` `(1)/(4)` `(4)/(19)` ANSWER :C

Discussion

645.	Let S=1 + (1)/(sqrt2) + (1)/(sqrt3) + (1)/(sqrt99) + (1)/(sqrt100). Find [S] You may use the fact that (sqrtn lt (1)/(2) ) ( sqrtn + sqrt ( n +1)) lt sqrt ( n +1) for all integers n ge 1.
Answer» ANSWER :18

Discussion

646.	int_0^pisin^8thetad theta
Answer» SOLUTION :`I=int_0^pisin^8thetad THETA` =`2int_0^(pi/2)sin^8thetad theta (becausesin(2cdotpi/2-theta)=SINTHETA)` =`2cdot7/8cdot5/6cdot3/4cdot1/2cdotpi/2=(210pi)/768`

Discussion

647.	Integrate the function 1/(sqrt(1+4x^(2)))
Answer» ANSWER :`1/2logabs(2x+sqrt(1+4x^(2)))+C`

Discussion

648.	Evaluate the following integrals. int(32)/((x-1)(x+2)(x-3))dx
Answer» Answer :`-(1)/(6)log\|x-1\|-(8)/(15)log\|x+2\|+(7)/(10)log\|x-3\|+c`

Discussion

649.	Evalute the following integrals int (1)/(x^(2) + 2x + 5)dx
Answer» ANSWER :`(1)/(2)TAN^(-1)((x+1)/(2))+C`

Discussion

650.	Statement-I At least two of the lines L_1, l_2 and L_3 are non parallel Statement-II The three planes do not have a common point.
Answer» STATEMENT-I is TRUE, Statement II is also true, Statement-II is the CORRECT explanation of Statement-I. Statement-I is true, Statement-II is also true, Statement-II is not the correct explanation of Statement-I. Statement-I is true, Statement-II is FALSE. Statement-I is false, Statement -II is true. Answer :(a)

Discussion

Explore topic-wise InterviewSolutions in .

The value of lim_(xtooo) (cot^-1(x^-alog_ax))/(sec^-1(x^-alog_ax)),agt1, is equalto

The sum of (1^(2)-1+1) (1!)+(2^(2)-2+1)(2!) +...+ (n^(2)-n+1) (n!) is -

The logical statement [ ~ ( ~p vee q) vee (p ^^ r ) ^^ ( ~ q ^^ r ) ] is equivalent to

Evalute {:(" Lt"),(xrarr1):}(sin(x-1))/(x^(2)-1)

If A is a square matrix and |A| = 2 then |A|^n = ………. . Where n is positive integer.

2 white balls and 3 blanks balls and 3 blank 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

State which of the following matrices is symmetric,slew symmetric, both or not either:[[0,1,2],[-1,y,3],[-2,-3,z]],(x,y,z) != (0,0,0)

Show that the locus of P where the tangents drawn from P to the circle x^(2)+y^(2)=a^(2) include an angle alpha is x^(2)+y^(2)=a^(2)cosec^(2)(alpha)/2

Evaluate the following:lim_(xtoinfty) sinx/x

Show that the tangents to the curve y=7x^(3)+11 at the point where x = 2 and x=-2 are parallel.

Removesecondterm( secondhigherpowerof x )fromthe equation x^4 +8x^3 +x-5=0

There is a point inside an equilateral triangle ABC of side a whose distance from the vertices is 3,4,5 . Rotate the triangle and P through 60^@ about C. Let A go to A' and P to P'. The area of traingle PAP' is

If sin x = (2t)/(1+t^(2)), tan y = (2t)/(1-t^(2)), then (dy)/(dx) is equal to

int_(0)^(2pi) e^(x//2) sin (x/2 + pi/4) dx=

Differntiate the following functions by proper substitution.sin^(-1)2xsqrt(1-x^2)

The negation of 'For every natural number x, x +5 gt 4' is

If S.D of x_(1), x_(2), x_(3),….x_(n),…x-(n) is sigma, then find S.D of -x_(1), -x_(2), -x_(3),….-x_(n) ?

int_0^2 x[2x]dx, where [.] denotes greatest integer function, equals: -

There are 2 white and 3 red balls in box A and 4 white, 5 red balls in box B One box is selected at random and one ball is drawn from it. Then ......... is the probability that selected ball is of red colour.

f:R-{q} rarrR -{1},f(x) = (x-p)/(x-q), p ne q ,then f is .........

If ((1)/(2),2) is one extermity of a focalchord of the parabola y^(2)=8x. Find the co-ordinates of the other extremity.

Integrate the following functions w.r.t.x cosx/sqrt(4-sin^2x)

Prove that the following functions do not have maxima or minima f(x)=e^x

Consider the vectors "" oversetrarra=2overset^^i-3overset^^j+overset^^k"and"oversetrarrb = overset^^i+overset^^j-2overset^^k. ""Find |3 oversetrarra+oversetrarrb |

Intergrate the following: intsin6x sin3xdx

Let A and B be independent events with P(A)=0.2,P(B)=0.5. Let us find (i) P(A//B) (ii) P(B//A) (iii) P(AnnB)(iv) P(AuuB) (v) P(A^(c )nnB^(c ))

Find the value of c in [-2,2] inLagranges Mean value theorem for the functionf(x)=x^(2)-2x+3.

Differentiate the following w.r.t.x log(cose^x)

The numerically greatest term in the expansion (5x - 6y)^14 when x = 2/5, y = 1/2 is

If hati+2hatj+3hatk, 3hati+2hatj+hatk are the sides of a parallelogram, then a unit vector is prallel to one of the diagonals of the parallelogram, is

if f(x) is differentiable function such that f(1) = sin 1, f (2)= sin 4 and f(3) = sin 9, then the minimum number of distinct roots of f'(x) = 2x cosx^(2) in (1,3) is "_______"

int_(0)^(pi//2) ln (tan x+ cot x)dx=

The solution of y'' + y' = 1 is

Find area bounded by y = f^(-1)(x), x = 10, x = 4 and x-axis. Given thatarea bounded by y = f(x) , x = 2, x = 6 and x -axis is 30 sq. units, where f(2) = 4 and f(6) = 10. (given f(x)is an invertiablefunction).

If Eand F are two evetns such that P(E) = (1)/(4) , P(F) =(1)/(2) and P(E and F) = (1)/(8) . Find P(not E and not F)

How many integral solutions are there to the systems of equations x_(1)+x_(2)+x_(3)+x_(4)+x_(5)=20andx_(1)+x_(2)=15 where x_(k)ge0.

Solve the following : [[4,x+1],[3,x]]=5

If : R - {(3)/(7) rarr R - {(3)/(7)} is given by f(x) = (3x + 5)/(7x - 3), then the statement which is not true, is

Let vec(alpha),vec(beta),vec(gamma) be three unit vectors such that vec(alpha).vec(beta)=vec(alpha).vec(gamma)=0 and the angle between vec(beta)andvec(gamma) is 30^(@)." Then "vec(alpha) is

Assertion (A) If alpha =12 ^(@),beta = 15^(@),gamma = 18^(@),then tan 2 alpha tan 2beta + tan 2betatan 2gamma+tan2gamma tan 2alpha=1Reason ( R ) In DeltaABC, " tan "(A)/(2) " tan " (B)/(2)+ " tan " (B)/(2) " tan " (C)/(2) + " tan "(C)/(2) " tan "(A)/(2)=1 Which of the following is true?

If z=2+i, then (z-1) (barz-5)+(barz+1) (z-5) is equal to

From each of 3 married couples one partner is selected at random then the probability of the chosen ones being all of the same sex is

Let S=1 + (1)/(sqrt2) + (1)/(sqrt3) + (1)/(sqrt99) + (1)/(sqrt100). Find [S] You may use the fact that (sqrtn lt (1)/(2) ) ( sqrtn + sqrt ( n +1)) lt sqrt ( n +1) for all integers n ge 1.

int_0^pisin^8thetad theta

Integrate the function 1/(sqrt(1+4x^(2)))

Evaluate the following integrals. int(32)/((x-1)(x+2)(x-3))dx

Evalute the following integrals int (1)/(x^(2) + 2x + 5)dx

Statement-I At least two of the lines L_1, l_2 and L_3 are non parallel Statement-II The three planes do not have a common point.