28278 + Interview Questions in Maths in Class 12

1.	Find the second order derivatives of the functions given in Exercises 1 to 10. sin (log x).
Answer» ANSWER :`-(SIN (LOG X)+COS (log x))/(x^2)`

Discussion

2.	Integrate the function in Exercise. x sec^(2)x
Answer» ANSWER :`X tanx+log\|cosx\|+c`

Discussion

3.	A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.
Answer» ANSWER :`(8)/(3)` CM /s

Discussion

4.	Evaluate the following integrals. int(x^(2))/(sqrt(1-x^(6)))dx
Answer» ANSWER :`(1)/(3)sin^(-1)(X^(3))+C`

Discussion

5.	The points (-4,6,10),(2,4,6) and (14,k,-2) are collinear then k is
Answer» A.0 B. 1 C. `-1` D. 2 Answer :A

Discussion

6.	If 12+6n is 20 percent bigger than k. what is k ?
Answer» `(12+6n)/5` 10+5n 2+n `(6(12+6n))/5` ANSWER :B

Discussion

7.	The wavelength of first member ofBalmer Series is 6563 Å. Calculate the wavelength of second member of Lyman series.
Answer» 1025.5Å 2050Å 6563Å none of these Answer :A

Discussion

8.	If a be the area bounded by y = (X^(2))/(1 + x^(4)) and y = (1)/(2) and A be the area bounded by y = (X^(2))/(1 + x^(4)) and y = (x^(2))/(2), then
Answer» `a + A = (2)/(3)` `a + A = (4)/(3)` `a + A = (1)/(3)` `a + A = 1` ANSWER :A

Discussion

9.	Choose the correct answer int(dx)/(x(x^(2)+1)) equals
Answer» `log\|x\|-(1)/(2)log(x^(2)+1)+C` `log\|x\|+(1)/(2)log(x^(2)+1)+c` `-log\|x\|+(1)/(2)log(x^(2)+1)+c` `(1)/(2)log\|x\|+loglog(x^(2)+1)+c` ANSWER :A

Discussion

10.	Simplify the following(cis(-3theta)cis2theta)/(cis4theta(cistheta)^6)
Answer» ANSWER :`CIS (11theta)`

Discussion

11.	Let R be the set of all real numbers. A relation R has been defined on R by aRb hArr \|a-b\| le 1, then R is
Answer» Symmetric and TRANSITIVE but not REFLEXIVE Reflexive and transitive but not symmetric Reflexive and symmetric but not transitive an equivalence RELATION ANSWER :C

Discussion

12.	Write the symmetric form of equation of the following lines : x-axis
Answer» Solution :D. CS. Of x-axis are `lt1,0,0gt`. X-axi passes through the origin. So the EQUATION of x-axis in symmetrical from is `(x-0)/1=(y-0)/0=(z-0)/0`

Discussion

13.	int_(pi//6)^(pi//3)(1)/(1+tan^(3)x)dx=
Answer» `pi/12` `pi/4` `pi/3` `pi/6` ANSWER :A

Discussion

14.	Evaluate the integrals :I = int_(1)^(sqrt(3)) (dx)/((1 + x^(2))^((3)/(2)))
Answer» ANSWER :`(SQRT(3) - sqrt(2))/( 2)`

Discussion

15.	If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. Then Prove thatcos2alpha+cos2beta+cos2gamma=0=sin2alpha+sin2beta+sin2gamma
Answer» 2 1 `1/2` 0 Answer :D

Discussion

16.	If the graph of a diffierentiable function y =f(x) meets the lines y = -1 and y = 1, then the graph
Answer» mects the LINE y =0 at LEAST once meets the line y=0 at least twice meets the line y= 0 at least thrice doest not MEET the line y = 0 Answer :A

Discussion

17.	If the unit bar(a),bar(b) and bar( c ) are coplanar then …………..
Answer» `bar(a).(bar(B)XX bar( c ))=1` `bar(a).(bar(b)xx bar( c ))=3` `(bar(a)xx bar(b)).bar( c )=0` `(bar( c )xx bar(a)).bar(b)=1` ANSWER :C

Discussion

18.	The locus of the points z satisfying the condition arg((z-1)/(z+1))=pi/3 is a
Answer» Parabola Circle Pair of STRAIGHT lines None of these Answer :B

Discussion

19.	Solve system of linear equations, using matrix method in examples 7 to 144x-3y=3 3x-5y=7
Answer» ANSWER :`x=-6/(11),y=-(19)/(11)`

Discussion

20.	Find the number of all onto functins from the set {1,2,3..,n} to itself.
Answer» ANSWER :`N !`

Discussion

21.	A student has to match three historical events Dandi March, Quit India movement and Mahatma Gandhi Assassinationwith the years 1948,1930 and 1942. The student has no knowledge ofthecorrect answers and decided to match theevents and years randomly. If x denotes the number of correctanswers he gets, then mean of x is
Answer» `0.5` 1 `1.5` 2 Answer :B

Discussion

22.	Solve (1= xy + x^(2)y^(2))dx + (x^(3)y - x^(2))dy = 0
Answer» Answer :`log X = xy - (1)/(2)x^(2)y^(2) = C`

Discussion

23.	A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and found to be all spades. Find the probability of the lost card being a spade.
Answer» ANSWER :`1049~~0.20`

Discussion

24.	If the straight line 2x+3y=1 intersects the circle x^2+y^2=4 at the points A and B then find the equation of the circle having AB as diameter.
Answer» ANSWER :`13(X^(2)+y^(2))-4x-6y-50=0`

Discussion

25.	If x^(2) + alpha y^(2) +B y = a^(2) represents a pair of perpendicular lines , then beta equals to ,
Answer» `4A` `a` `2A` `3A` ANSWER :B

Discussion

26.	(2x-1)/((x-1)(2x+3))=1/(5(x-1))-k/(5(2x+3)), then k =
Answer» 0 1 2 -8 Answer :D

Discussion

27.	Compute the indicated products:[(1),(2),(3)][(2,3,4)]
Answer» ANSWER :[(2,3,4),(4,6,8),(6,9,12)]

Discussion

28.	The solution of (1 + x^(2)) (dy)/(dx) + 2xy - 4x^(2) = 0 is
Answer» `3x(1+y^(2)) = 4Y^(3) + C` `3y(1+x^(2)) = 4y^(3) + c` `3x(1-y^(2)) = 4y^(3) + c` `3y(1+y^(2)) = 4x^(3) + c` Answer :B

Discussion

29.	Let S_(n)=sum_(r=1)^(n)((r^(4)_r^(3)n+r^(2)n^(2)+2n^(4))/(n^(5))) and T_(n)=sum_(r=0)^(n-1)((r^(4)+r^(3)n^(2)+2n^(4))/(n^(5))),n=1,2,3,……….then
Answer» `T_(n)gt167/60` `T_(n)lt167/60` `S_(n)gt167/60` `S_(n)lt167/60` SOLUTION :`T_(n)=1/n sum_(r=0)^(n-1) (r/n)` where `f(x)=x^(4)+x^(3)+x^(2)+2, f(x)` is an increasing function for `AA x gt 0`. `T_(n)=1/n[f(0)+f(1/n)…+f((n-1)/n)]` `T_(n)lt int_(0)^(1)(x^(4)+x^(3)+x^(2)+2)dx=167/60` `S_(n)=1/n sum_(r=1)^(n)(f (r/n)gt 1/n[f(1/n)+...+f(r/n)]=167/60`

Discussion

30.	Let t be a ral number satifying 2t ^(3) -9t ^(2) + 30 -lamda =0 where t =x + 1/xand lamda in R. If the cubic has four real and distinct solutions for x then exhustive set of values of lamda be :
Answer» `lamda in (3,10)` ` lamda in {3,10}` `lamda in (-oo, -22 ) UU (10, oo)` None of these ANSWER :A

Discussion

31.	If R={(x,y)//x,y in Z, x^(2)+y^(2)le4} is a relation in Z, then domain of R si
Answer» {0, 1, 2} `{0,-1,-2}` `{-2,-1,0,1,2}` `{0,1,2,3}` ANSWER :C

Discussion

32.	If vec(a)=3hat(i)-5hat(j),vec(b)=6hat(i)+3hat(j)andvec(c)=vec(a)xxvec(b), then \|vec(a)\|":"\|vec(b)\|":"\|vec(c)\|=
Answer» `SQRT(34):sqrt(45):sqrt(39)` `sqrt(34):sqrt(45):sqrt(39)` `34:39:45` `39:35:34` ANSWER :B

Discussion

33.	By using the properties of definite integrals, evaluate the integrals int_(0)^(2)xsqrt(2-x)dx
Answer» ANSWER :`(16 SQRT(2))/(15)`

Discussion

34.	Two matrices A and B equivalent. Find which is correct :
Answer» A and B are of the same ORDER `RHO(A) = rho(B)` A and B are of the same order and `rho(A)=rho(B)` `\|A\|=\|B\|` ANSWER :C

Discussion

35.	Integrate the function is exercise. sqrt(1-4x^(2))
Answer» Answer :`(X)/(2)SQRT(1-4x^(2))+(1)/(8)SIN^(-1)(2x)+C`

Discussion

36.	(18^3+7^3+3.18. 7. 25)/(3^6 +6.243.2+15.81.4+20.27.8+15.9.16+6.3.32+64)=
Answer» 4 3 2 1 Answer :D

Discussion

37.	Find the area of the parabola y^(2)=4ax bounded by its latus rectum.
Answer» ANSWER :`(8)/(3)a^(2)`

Discussion

38.	If a=hati+hatj,b=hatj+hatk,c=hati+hatk, then ([(bxxc)xx(cxxa)(cxxa)xx(axxb)(axxb)xx(bxxc)])/([b+c" "c+a" "a+b][bxxc" "cxxa" "axxb])
Answer» 0 1 `SQRT3` `SQRT2` ANSWER :B

Discussion

39.	If a card is drawn from pack, find the probability that the card is Ace or spade.
Answer» ANSWER :`(4)/(13)`

Discussion

40.	A vector bara has components a_1,a_2,a_3 in the right handed rectangular Cartesian system OXYZ. The co-ordinate system is rotated about the x-axis through an angle pi/4 in the anticlock wise direction. The components of bara in the new system are
Answer» `a_1,(a_2+a_3)((a_3-a_2)/SQRT2)` `a_1((a_2+a_3)/sqrt2),((a_3-a_2)/sqrt2)` `a_1,((a_2+a_3)/sqrt2),a_3-a_2` NONE of these Answer :B

Discussion

41.	If x^(2)+y^(2)=c^(2) and x/a+y/b=1 intersect at A and B, then find AB. Hence deduce the condition that the line touches the circle.
Answer» ANSWER :This is the REQUIRED CONDITIONS.

Discussion

42.	Let(log a)/( b-c) = (logb)/(c-a) = (log c)/(a-b) STATEMENT-1 : a^(a) b^(b) c^(c)= 1and STATEMENT-2 :a^(b+c) b^(c +a) c^(a + b) = 1 .
Answer» Statemant-1 is True , STATEMENT-2 is True, Statement -2 is a CORRECT explanation for Statement-1 Statemant-1 is True , Statement-2 is True, Statement -2 is NOTA correct explanation for Statement-1 Statement-1 is True, Stetement-2 is FALSE. Statement-1 is False, Statement-2 is True ANSWER :2

Discussion

43.	Find the points where the following function are not differentiable.\|x-1\|+\|x-2\|
Answer» SOLUTION :`\|x-1\|+\|x-2\|`is not DIFFERENTIABLE at x=1and x=2

Discussion

44.	Find maximum value of y=2x^(3)-24x+107 in [1, 3].
Answer» ANSWER :89

Discussion

45.	A player tosses 3 fair coins and wins Rs. 8 if three heads occur, Rs. 3 if 2 heads occur and Rs. 1 if one head occurs. If the game as to be fair (i.e., expected value is zero) how must should he lose, if no head occur ?
Answer» ANSWER :`a=-20`

Discussion

46.	X is nearly normally distributed, with a mean of 6 and a standard deviation of 2. Would the answers to questions #12-14, be the same if variable X were ul("not") nearly normally distributed ?
Answer» ANSWER :No, not NECESSARILY.

Discussion

47.	IF the equation of the hyperbola whose focus is ( 2,4) eccentricity is 5 and directrix is4x-3y + 1 =0" is " 15x ^(2) -24xy + 8y^(2) +ax+ by + c= 0then the ascending orderof a,b,c is
Answer» a,b,C b,c,a c,a,b c,b,a Answer :D

Discussion

48.	A matrix which is both symmetric and skew-symmetric is a
Answer» UNIT MATRIX Null matrix Non-singular matrix NONE of these ANSWER :B

Discussion

49.	Evaluate the following integrals (viii) int_(0)^(3) (x dx)/(sqrt(x^(2)+16))
Answer» ANSWER :1

Discussion

50.	Aline makesa postitiveX - interceptanda negativeY - interceptand hasa slopeequalof (4)/(3). If thecoordinates of the pointswherethe lineintersects theX and Y axesare integers,what is the angleformed bythe linewith the X and Y axes ?
Answer» ANSWER :`0.67`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

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

Integrate the function in Exercise. x sec^(2)x

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.

Evaluate the following integrals. int(x^(2))/(sqrt(1-x^(6)))dx

The points (-4,6,10),(2,4,6) and (14,k,-2) are collinear then k is

If 12+6n is 20 percent bigger than k. what is k ?

The wavelength of first member ofBalmer Series is 6563 Å. Calculate the wavelength of second member of Lyman series.

If a be the area bounded by y = (X^(2))/(1 + x^(4)) and y = (1)/(2) and A be the area bounded by y = (X^(2))/(1 + x^(4)) and y = (x^(2))/(2), then

Choose the correct answer int(dx)/(x(x^(2)+1)) equals

Simplify the following(cis(-3theta)cis2theta)/(cis4theta(cistheta)^6)

Let R be the set of all real numbers. A relation R has been defined on R by aRb hArr |a-b| le 1, then R is

Write the symmetric form of equation of the following lines : x-axis

int_(pi//6)^(pi//3)(1)/(1+tan^(3)x)dx=

Evaluate the integrals :I = int_(1)^(sqrt(3)) (dx)/((1 + x^(2))^((3)/(2)))

If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. Then Prove thatcos2alpha+cos2beta+cos2gamma=0=sin2alpha+sin2beta+sin2gamma

If the graph of a diffierentiable function y =f(x) meets the lines y = -1 and y = 1, then the graph

If the unit bar(a),bar(b) and bar( c ) are coplanar then …………..

The locus of the points z satisfying the condition arg((z-1)/(z+1))=pi/3 is a

Solve system of linear equations, using matrix method in examples 7 to 144x-3y=3 3x-5y=7

Find the number of all onto functins from the set {1,2,3..,n} to itself.

Solve (1= xy + x^(2)y^(2))dx + (x^(3)y - x^(2))dy = 0

A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and found to be all spades. Find the probability of the lost card being a spade.

If the straight line 2x+3y=1 intersects the circle x^2+y^2=4 at the points A and B then find the equation of the circle having AB as diameter.

If x^(2) + alpha y^(2) +B y = a^(2) represents a pair of perpendicular lines , then beta equals to ,

(2x-1)/((x-1)(2x+3))=1/(5(x-1))-k/(5(2x+3)), then k =

Compute the indicated products:[(1),(2),(3)][(2,3,4)]

The solution of (1 + x^(2)) (dy)/(dx) + 2xy - 4x^(2) = 0 is

Let S_(n)=sum_(r=1)^(n)((r^(4)_r^(3)n+r^(2)n^(2)+2n^(4))/(n^(5))) and T_(n)=sum_(r=0)^(n-1)((r^(4)+r^(3)n^(2)+2n^(4))/(n^(5))),n=1,2,3,……….then

Let t be a ral number satifying 2t ^(3) -9t ^(2) + 30 -lamda =0 where t =x + 1/xand lamda in R. If the cubic has four real and distinct solutions for x then exhustive set of values of lamda be :

If R={(x,y)//x,y in Z, x^(2)+y^(2)le4} is a relation in Z, then domain of R si

If vec(a)=3hat(i)-5hat(j),vec(b)=6hat(i)+3hat(j)andvec(c)=vec(a)xxvec(b), then |vec(a)|":"|vec(b)|":"|vec(c)|=

By using the properties of definite integrals, evaluate the integrals int_(0)^(2)xsqrt(2-x)dx

Two matrices A and B equivalent. Find which is correct :

Integrate the function is exercise. sqrt(1-4x^(2))

(18^3+7^3+3.18. 7. 25)/(3^6 +6.243.2+15.81.4+20.27.8+15.9.16+6.3.32+64)=

Find the area of the parabola y^(2)=4ax bounded by its latus rectum.

If a=hati+hatj,b=hatj+hatk,c=hati+hatk, then ([(bxxc)xx(cxxa)(cxxa)xx(axxb)(axxb)xx(bxxc)])/([b+c" "c+a" "a+b][bxxc" "cxxa" "axxb])

If a card is drawn from pack, find the probability that the card is Ace or spade.

A vector bara has components a_1,a_2,a_3 in the right handed rectangular Cartesian system OXYZ. The co-ordinate system is rotated about the x-axis through an angle pi/4 in the anticlock wise direction. The components of bara in the new system are

If x^(2)+y^(2)=c^(2) and x/a+y/b=1 intersect at A and B, then find AB. Hence deduce the condition that the line touches the circle.

Let(log a)/( b-c) = (logb)/(c-a) = (log c)/(a-b) STATEMENT-1 : a^(a) b^(b) c^(c)= 1and STATEMENT-2 :a^(b+c) b^(c +a) c^(a + b) = 1 .

Find the points where the following function are not differentiable.|x-1|+|x-2|

Find maximum value of y=2x^(3)-24x+107 in [1, 3].

A player tosses 3 fair coins and wins Rs. 8 if three heads occur, Rs. 3 if 2 heads occur and Rs. 1 if one head occurs. If the game as to be fair (i.e., expected value is zero) how must should he lose, if no head occur ?

X is nearly normally distributed, with a mean of 6 and a standard deviation of 2. Would the answers to questions #12-14, be the same if variable X were ul("not") nearly normally distributed ?

IF the equation of the hyperbola whose focus is ( 2,4) eccentricity is 5 and directrix is4x-3y + 1 =0" is " 15x ^(2) -24xy + 8y^(2) +ax+ by + c= 0then the ascending orderof a,b,c is

A matrix which is both symmetric and skew-symmetric is a

Evaluate the following integrals (viii) int_(0)^(3) (x dx)/(sqrt(x^(2)+16))

Aline makesa postitiveX - interceptanda negativeY - interceptand hasa slopeequalof (4)/(3). If thecoordinates of the pointswherethe lineintersects theX and Y axesare integers,what is the angleformed bythe linewith the X and Y axes ?