28278 + Interview Questions in Maths in Class 12

1.	If the line px - qy = r intersects the co-ordinate axes at (a,0) and (0, b), then the value of a + b is equal to
Answer» `R((q+p)/(PQ))` `r((q-p)/(pq))` `r((p-q)/(pq))` `r((p+q)/(p-q))` ANSWER :B

Discussion

2.	Evaluate int_-1^1 sin^5x cos^4x dx
Answer» Solution :Let I = `int_-1^1 sin^5x cos^4x dx` Let f(x) = `sin^5x cox^4x`. Then `f(-x) = sin^5(-x) cos^4(-x)` =`-sin^5x cos^4x = -f(x)` i.e., f is an ODD FUNCTION. THEREFORE, by PROPERTY 8(II), I = 0.

Discussion

3.	If ""^(13)C_(r)=715, then find possible values of r.
Answer» ANSWER :4,9

Discussion

4.	Prove that : Find the 3^("rd") term from the end in the expansion of (x^(-2//3)-(3)/(x^(2)))^(8).
Answer» SOLUTION :N/A

Discussion

5.	LetA = {:\|(2,e^(ipi)),(i^(2),i^(2012))\|,C =(d)/(dx) ((1)/(x))\|_(x=1), D - int_(2i)(dx)/(x). if the sum of two roots of the equation Ax^(3) + Bx^(2) + Cx + D = 0is equal to zero. Then B =
Answer» `-1` 0 1 2 Answer :4

Discussion

6.	If cos theta - 4 sin theta -1 ,then sin theta + 4 cos theta i is equal to
Answer» `pm1` 0 `PM2` `PM4` ANSWER :D

Discussion

7.	Fill in the blank choosing correct answer from the brackets if the value of sin^(-1)x = pi/5 for some x in (-1,1 )then the value of cos^(-1) x is _____.((3pi)/10, (5pi)/10,(7pi)/10)
Answer» SOLUTION :`(3PI)/10`

Discussion

8.	Find the generalsolution : .(dy)/(dx) + 2y = sin x
Answer» Answer :`y = (1)/(5)(2 SIN X - cos x) + Ce^(-2x)`

Discussion

9.	Calculatethe areaunderthecurvey= 2 sqrt(x)includedbetweenthelinesx=0andx=1
Answer» ANSWER :`4/3` SEQ . UNIT

Discussion

10.	Evaluate : int(dx)/(sin^(2)cos^(2)x)
Answer» ANSWER :`tanx-cotx+C`

Discussion

11.	The period of cos (x+8x +27 x+...+n^(3) x) is
Answer» `(2 PI)/n` `(2 pi)/(n^(2) (n+1)^(2))` `(8 pi)/(n^(2) (n+1)^(2))` `(8 pi)/(n^(3)(n+1)^(2))` Answer :C

Discussion

12.	Solve the following system of equation by Gaussian elimination method.2x-y+3z=3 4x+2y-z=7x+3y+2z=9
Answer» ANSWER :X = 1, y = 2, Z = 1

Discussion

13.	One end of uniform wire of length Land of weight W is attached rigidly to a point in the roof and a weight W_(1) is suspended from its lower end. If S is the area if cross-section of the wire, the stress in the wire at a height (3L/4) from its lower end is
Answer» `W_(1)//S` `[W_(1)+(W//4)]//S` `[W_(1)+(3W//4)]//S` `(W_(1)+W)//S` ANSWER :C

Discussion

14.	The variance of 20 observations is 5. If each observations is multiplied by 2, then the new variance of the resulting observations is
Answer» ANSWER :20

Discussion

15.	If int(dx)/(x+x^(7))=p(x) then, int(x^(6))/(x+x^(7))dx is equal to:
Answer» In `\|X\|-p(x)+C` In `\|x\|+p(x)+c` `x-p(x)+c` `x+p(x)+c` ANSWER :1

Discussion

16.	Ifalpah , beta , gammaare therootsof the equationx^3 + qx +r=0 find thevalueof( beta + gamma)^(-1)+( gamma+ alpha)^(-1)+ ( alpha+ beta)^(-1)
Answer» ANSWER :`(Q)/(R )`

Discussion

17.	Number of common tangents of y=x^2" and " y=-x^2+4x-4 is
Answer» 1 2 3 4 Answer :B

Discussion

18.	If theareaof thetrianglewithvertices(-2,0) ( 0,4) (0,k)having4 sq. unitsthen K=
Answer» `+- 2` `+-3 ` `2,8` `0,8` ANSWER :D

Discussion

19.	Find the value of (1.02)^(3//2) - (0.98)^(3//2) correct to 6 decimals .
Answer» ANSWER :`0.059999`

Discussion

20.	A double-slit apparatus is set up and green light is used to form the interference pattern. The green light is then replaced by red light. Which of the following changes may allow the spacing of the bright bands on the screen to between to remain unaffected by the of light color ? (Given that the distance between the slits is d and that between the plane of the slite and the screen is D.)
Answer» Decrease D Increase d Increase d and decrease D Increase the brightness of the LIGHTNESS of the LIGHT source Solution :Fringe width `beta=(Dlamda)/(d)` `lamda` increases so to KEEP `brta` UNCHANGED either 'D' decreases or 'd' increases of both

Discussion

21.	Select the correct answer :sin(cos^-1x+tan^-1x) =
Answer» 1 `π` `0` `π/2` ANSWER :A

Discussion

22.	Consider f : R_(+) rarr [-5,oo) given by f(x) = 9x^(2) +6x-5. Show that f is invertible with f^(-1)(y) = ((sqrt(y+6)-1)/3)
Answer» SOLUTION :N/A

Discussion

23.	If u = (1)/(root 3 (x^(3) + y ^(2))) then x (del u)/(del x) + (del u )/( del y) is:
Answer» `3/2u` `2/3u` `(-2)/(3) U` `(-3)/(2)u` ANSWER :C

Discussion

24.	Evalute the following integrals int xe^(x) dx
Answer» ANSWER :`E^(X) (x - 1) + C`

Discussion

25.	A variable point P is on the circle x^2+y^2=1 on XY-plane.From point P perpendicular PN is drawn to the line L:x-2=y-2=-z, then minimumlength PN drawn is
Answer» `SQRT(9/2-2sqrt2)` `sqrt(3-4sqrt2)` `(2sqrt2-1)/SQRT3` `(2sqrt2-1)/3` ANSWER :C

Discussion

26.	If cos theta = ( cos alpha - cos beta )/(1- cos alpha cos beta ) " then " tan^(2)""((theta )/(2)) tan^(2)""((beta)/(2))=
Answer» `"tan"(ALPHA)/2` `"tan"^(2)(alpha)/2` `"COT"(alpha)/2` `"cot"^(2)(alpha)/2` ANSWER :B

Discussion

27.	Evaluate : (i) int_(0)^(oo) (dx)/(e^(x)+e^(-x)), (ii) int_(0)^(1) (x)/(1+sqrt(x))dx , (iii) int_(0)^(pi//2) (sinxcosx)/(cos^(2)x+3cosx+2) (iv) int_(0)^(pi/2) (sin2theta d theta)/(sin^(4)theta+cos^(4)theta), (v) int_(0)^(pi//4) (sinx+cosx)/(9+16 sin 2x)dx
Answer» SOLUTION :N//A

Discussion

28.	Expand (2X + 5Y)^(5)
Answer» Solution :By using BINOMIAL theorem, We have `(2X + 5Y)^(5)` = `.^(5)C_(0)(2X)^(5)(5Y)^(0)+^(5)C_(1)(2x)^(4)(5Y)+^(5)C_(2)(2X)^(3)(5y)^(2)+^(5)C_(3)(2x)^(2)(5Y)^(3)+^(5)c_(4)(2X)(5Y)^(4)+^(5)C_(5)(2X)^(0)(5Y)^(5)` = `32X^(5)+5.16X^(4).5Y+10.8X^(3).25Y^(2)+10.4X^(2) 125Y^(3) + 5.2X.625Y^(4)+3125Y^(5) ` `32X^(5)+400X^(4)Y+2000X^(3)Y^(2)+5000X^(2)Y^(3)+6250XY^(4)+3125Y^(5)`

Discussion

29.	Determine whether a*b = a+ b-ab "on" R-{1}operations 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 R -{1}` ` ab =a+b -AB in R -{1}` `:. ` is a BINARY OPERATION on `R -{1}`

Discussion

30.	int_(1//2)^(1)(dx)/( sqrt(3x^(2) + 2x -1) ) is equal to (pi=3.14)
Answer» ANSWER :`0.52`

Discussion

31.	The angle between the curves y=x^2 and y=4-x^2 is
Answer» ANSWER :`(8)/(3)`

Discussion

32.	Selectthe Correct Option a*b=a+2b^2 then 32
Answer» 11 14 15 8 Answer :A

Discussion

33.	Find the maximum and minimum values of f, if any, of the function given by f(x)=\|x\|, x in R.
Answer» ANSWER :Maximum value of the FUNCTION F does not exists and minimum value is zero.

Discussion

34.	If [x] denotes the greatest integer not exceeding x andif the function f definedbyf (x) ={:{ ((a +2 cos x)/(x^(2)),x lt 0), ( btan "" pi/(x +4), x ge 0):}is continuous at x = 0,then the ordered pair(a,b) is equal to
Answer» (-2,1) (-2,-1) `(-1,SQRT3)` `(-2,-sqrt3)` ANSWER :B

Discussion

35.	If (1,2),(3,a) are conjugate points w.r.t x^(2)+y^(2)=16 then a=
Answer» 8 7.5 6.5 5.5 Answer :C

Discussion

36.	Evalute the following integrals int e^(x) ((x log x + 1)/(x ) )dx
Answer» ANSWER :`E^(X) ` SEC x + C

Discussion

37.	Let f be a function with domain X and range Y. Let A, B sube X and C, D subeY Which of the following is not true?
Answer» `f(AUUB)=f(A)uuf(B)` `f(ANNB)=f(A)NNF(B)` `f^(-1)(CuuD)=f^(-1)(C)uuf^(-1)(D)` `f^(-1)(CnnD)=f^(-1)(C)nnf^(-1)(D)` Answer :B

Discussion

38.	int_(0)^(1) sin^(-1) sqrt(x)dx=
Answer» ANSWER :`pi/4`

Discussion

39.	Let f (x) (cos ^(2) x)/(1+ cos +cos ^(2)x )and g (x) lamda tan x+1(1-lamda) sin x-x,where lamda in R and x in [0, pi//2]. The exhaustive seet of values of 'lamda' such that g '(x) ge 0 for any x in [0, pi//2):
Answer» `[1,OO)` `[0,oo)` `[(1)/(2), oo)` `[(1)/(3), oo)` ANSWER :D

Discussion

40.	Find the values of k so that the function f is continuous at the indicated pointf(x) = {((1- cos (kx))/(x^(2))",","if " x ne 0),((1)/(2)",","if " x= 0):} at x= 0
Answer» ANSWER :`+- 1`

Discussion

41.	Evaluate the definite integrals int_(-1)^(1)(x+1)dx
Answer» ANSWER :2

Discussion

42.	Evaluate the following integrals. int(1)/(1+cos^(2)x)dx
Answer» ANSWER :`-(1)/(1+tanx)+C`

Discussion

43.	(i) Find the other end of the diameter of the circle x^(2)+y^(2)-8x-8y+27=0 if one endof it (2,3). (ii) Snow that A(3,-1) lies on the circle x^(2)+y^(2)-2x+4y=0. Also find the other end of the diameter through A.
Answer» ANSWER :(i) (6,5) (II) (-1,-3)

Discussion

44.	if p is true and q is false, then
Answer» `~(pvv~q)` is true `~(~p^^~q)` is false `(p^^q)VV(p^^~q)` is true `(PVVQ)^^(qvv~q)` is false Answer :C

Discussion

45.	int e^(x)secx(1+tanx)dx=
Answer» ANSWER :`E^(X) SEC x + C`

Discussion

46.	Evaluate the integrals by using substitution int_(0)^(pi/2)(sinx)/(1+cos^(2)x)dx
Answer» ANSWER :`pi/4`

Discussion

47.	Lt_(n rarr oo)[(sqrt(n))/(sqrt(n^(3)))+(sqrt(n))/(sqrt((n+4)^(3)))+....+(sqrt(n))/(sqrt([n+4(n-1)]^(3)))]
Answer» ANSWER :`(1)/(10)(5-sqrt(5))`

Discussion

48.	The region shaded horizontally is represented by the inequations
Answer» `yge0,3x+2yge12,x+2yle8` `yge0,3x+2yle12,x+2yle8` `yge0,3x+2yle12,x+2yge8` NONE of these ANSWER :A

Discussion

49.	Evaluate the following integrals intsqrt((1+x)/(1-x))dx
Answer» ANSWER :`SIN^(-1)x-sqrt(1-x^(2))+C`

Discussion

50.	Write each of the statements in the form "if p, then q". i. p: It is necessary to have a password to log on to the server. ii. q: There is traffic jam whenever it rains. iii. r: You can access the website only if you pay a subscription fee.
Answer» ANSWER :If you can ACCESS the WEBSITE,then you PAY a sibscription FEE.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the line px - qy = r intersects the﻿ co-ordinate axes at (a,0) and (0, b), then﻿ the value of a + b is equal to

Evaluate int_-1^1 sin^5x cos^4x dx

If ""^(13)C_(r)=715, then find possible values of r.

Prove that : Find the 3^("rd") term from the end in the expansion of (x^(-2//3)-(3)/(x^(2)))^(8).

LetA = {:|(2,e^(ipi)),(i^(2),i^(2012))|,C =(d)/(dx) ((1)/(x))|_(x=1), D - int_(2i)(dx)/(x). if the sum of two roots of the equation Ax^(3) + Bx^(2) + Cx + D = 0is equal to zero. Then B =

If cos theta - 4 sin theta -1 ,then sin theta + 4 cos theta i is equal to

Fill in the blank choosing correct answer from the brackets if the value of sin^(-1)x = pi/5 for some x in (-1,1 )then the value of cos^(-1) x is _____.((3pi)/10, (5pi)/10,(7pi)/10)

Find the generalsolution : .(dy)/(dx) + 2y = sin x

Calculatethe areaunderthecurvey= 2 sqrt(x)includedbetweenthelinesx=0andx=1

Evaluate : int(dx)/(sin^(2)cos^(2)x)

The period of cos (x+8x +27 x+...+n^(3) x) is

Solve the following system of equation by Gaussian elimination method.2x-y+3z=3 4x+2y-z=7x+3y+2z=9

One end of uniform wire of length Land of weight W is attached rigidly to a point in the roof and a weight W_(1) is suspended from its lower end. If S is the area if cross-section of the wire, the stress in the wire at a height (3L/4) from its lower end is

The variance of 20 observations is 5. If each observations is multiplied by 2, then the new variance of the resulting observations is

If int(dx)/(x+x^(7))=p(x) then, int(x^(6))/(x+x^(7))dx is equal to:

Ifalpah , beta , gammaare therootsof the equationx^3 + qx +r=0 find thevalueof( beta + gamma)^(-1)+( gamma+ alpha)^(-1)+ ( alpha+ beta)^(-1)

Number of common tangents of y=x^2" and " y=-x^2+4x-4 is

If theareaof thetrianglewithvertices(-2,0) ( 0,4) (0,k)having4 sq. unitsthen K=

Find the value of (1.02)^(3//2) - (0.98)^(3//2) correct to 6 decimals .

Select the correct answer :sin(cos^-1x+tan^-1x) =

Consider f : R_(+) rarr [-5,oo) given by f(x) = 9x^(2) +6x-5. Show that f is invertible with f^(-1)(y) = ((sqrt(y+6)-1)/3)

If u = (1)/(root 3 (x^(3) + y ^(2))) then x (del u)/(del x) + (del u )/( del y) is:

Evalute the following integrals int xe^(x) dx

A variable point P is on the circle x^2+y^2=1 on XY-plane.From point P perpendicular PN is drawn to the line L:x-2=y-2=-z, then minimumlength PN drawn is

If cos theta = ( cos alpha - cos beta )/(1- cos alpha cos beta ) " then " tan^(2)""((theta )/(2)) tan^(2)""((beta)/(2))=

Evaluate : (i) int_(0)^(oo) (dx)/(e^(x)+e^(-x)), (ii) int_(0)^(1) (x)/(1+sqrt(x))dx , (iii) int_(0)^(pi//2) (sinxcosx)/(cos^(2)x+3cosx+2) (iv) int_(0)^(pi/2) (sin2theta d theta)/(sin^(4)theta+cos^(4)theta), (v) int_(0)^(pi//4) (sinx+cosx)/(9+16 sin 2x)dx

Expand (2X + 5Y)^(5)

Determine whether a**b = a+ b-ab "on" R-{1}operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

int_(1//2)^(1)(dx)/( sqrt(3x^(2) + 2x -1) ) is equal to (pi=3.14)

The angle between the curves y=x^2 and y=4-x^2 is

Selectthe Correct Option a**b=a+2b^2 then 3*2

Find the maximum and minimum values of f, if any, of the function given by f(x)=|x|, x in R.

If [x] denotes the greatest integer not exceeding x andif the function f definedbyf (x) ={:{ ((a +2 cos x)/(x^(2)),x lt 0), ( btan "" pi/(x +4), x ge 0):}is continuous at x = 0,then the ordered pair(a,b) is equal to

If (1,2),(3,a) are conjugate points w.r.t x^(2)+y^(2)=16 then a=

Evalute the following integrals int e^(x) ((x log x + 1)/(x ) )dx

Let f be a function with domain X and range Y. Let A, B sube X and C, D subeY Which of the following is not true?

int_(0)^(1) sin^(-1) sqrt(x)dx=

Let f (x) (cos ^(2) x)/(1+ cos +cos ^(2)x )and g (x) lamda tan x+1(1-lamda) sin x-x,where lamda in R and x in [0, pi//2]. The exhaustive seet of values of 'lamda' such that g '(x) ge 0 for any x in [0, pi//2):

Find the values of k so that the function f is continuous at the indicated pointf(x) = {((1- cos (kx))/(x^(2))",","if " x ne 0),((1)/(2)",","if " x= 0):} at x= 0

Evaluate the definite integrals int_(-1)^(1)(x+1)dx

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

(i) Find the other end of the diameter of the circle x^(2)+y^(2)-8x-8y+27=0 if one endof it (2,3). (ii) Snow that A(3,-1) lies on the circle x^(2)+y^(2)-2x+4y=0. Also find the other end of the diameter through A.

if p is true and q is false, then

int e^(x)secx(1+tanx)dx=

Evaluate the integrals by using substitution int_(0)^(pi/2)(sinx)/(1+cos^(2)x)dx

Lt_(n rarr oo)[(sqrt(n))/(sqrt(n^(3)))+(sqrt(n))/(sqrt((n+4)^(3)))+....+(sqrt(n))/(sqrt([n+4(n-1)]^(3)))]

The region shaded horizontally is represented by the inequations

Evaluate the following integrals intsqrt((1+x)/(1-x))dx

Write each of the statements in the form "if p, then q". i. p: It is necessary to have a password to log on to the server. ii. q: There is traffic jam whenever it rains. iii. r: You can access the website only if you pay a subscription fee.

If the line px - qy = r intersects the co-ordinate axes at (a,0) and (0, b), then the value of a + b is equal to