28278 + Interview Questions in Maths in Class 12

1.	If x = 1/2 and if (1-2x)/ (1-x+ x^(2)) + (2x-4x^(3))/ (1-x^(2) + x^(4))+ (4x^(3)-8x^(7))/(1-x^(4)+x^(6))+...infty = k, then
Answer» `K = 8/7` k is a RATIONAL NUMBER `k = 4/7` `7/16` ANSWER :A::B

Discussion

2.	Find the real numbers x and y so that (xI+yA)^(2)=A, where A=[{:(0,1),(-1,0):}].
Answer» Answer :`X=(1)/(SQRT(2)),y=(1)/(sqrt(2))ORX=-(1)/(sqrt(2)),y=-(1)/(sqrt(2))`

Discussion

3.	Equation of circle passing through (1,sqrt(3)), (1,-sqrt(3)) and (3,-sqrt(3)) is
Answer» `(X-2)^(2)+y^(2)=4` `(x+2)^(2)+y^(2)=4` `(x-2)^(2)+y^(2)=2` `x^(2)+(y-2)^(2)=4` ANSWER :A

Discussion

4.	Solution set of the in equality log_(10^(2)) x-3(log_(10)x)( log_(10)(x-2))+2 log_(10^(2))(x-2) lt 0, is :
Answer» `(0,4)` `(-OO,1)` `(4,oo)` `(2, 4)` ANSWER :C

Discussion

5.	If a in [-20,0],then the probability that the graph of the function y=16x^(2)+8(a+5)x-7a-5 touches or above the x-aixs is
Answer» <P>`(3)/(20)` `(13)/(20)` `(7)/(20)` `(1)/(2)` SOLUTION :`a in [-20,0]` `because` Graph of the function `y=16x^(2)+8(a+5)x-7a-5`TOUCHES or above the x-axis `implies Dle0implies 64(a+5)^(2)+64(7a+5)le0impliesa^(2)+17a+30le0impliesa in [-10,-3]""therefore "Probability" P(7)/(20)`

Discussion

6.	Select the Correct Option f(x)={((sinkx)/(2x),x!=0),(3,(x=0) at (x=0)):} is continuous then k+2=
Answer» 6 8 (3/2) 4 Answer :B

Discussion

7.	Letz_(k) = cos ((2kpi)/(10)) + isin ((2kpi)/(10)), k = 1,2,,…,9.
Answer» <P>`{:(""P,Q,R,S),(""(i),(ii),(iv),(III)):}` `{:(""P,Q,R,S),(""(ii),(i),(iii),(iv)):}` `{:(""P,Q,R,S),(""(i),(ii),(iii),(iv)):}` `{:(""P,Q,R,S),(""(ii),(i),(iv),(iii)):}` ANSWER :D

Discussion

8.	The value of \|(cos.(2pi)/(63),cos.(3pi)/(70),cos.(4pi)/(77)),(cos.(pi)/(72),cos.(pi)/(40),cos.(3pi)/(88)),(1,cos.(pi)/(90),cos.(2pi)/(99))\| is equal to
Answer» 0 1 `2cos.(PI)/(9)` `COS.(pi)/(11)` Answer :A

Discussion

9.	If A,B,C are the minimum values of 2x^3-3x^2-12x+5,x^3-9x^2+24x-12,x^3-6x^2+9x+1 then the ascending order of A,B,C is
Answer» A,B,C B,C,A C,A,B A,C,B Answer :D

Discussion

10.	If the circle x^(2) + y^(2) + 4x - 6y + c = 0 bisects the circumference of the circle x^(2) + y^(2) - 6x + 4y - 12 = 0, then c is equal to
Answer» 16 24 `-42` `-62` SOLUTION :Given circle is , `S -= x^(2) + y^(2) + 4x - 6y + c - 0` and , `S^(1) -= x^(2) + y^(2) - 6x + 4y - 12 = 0` S = 0 bisects the CIRCUMFERENCE of `S^(1) = 0` `implies 2 g^(1) (g - g^(1)) + 2F^(1) (f - f^(1)) = c - c^(1)` `implies 2 (-3) (5) + 2 (-3, -2) - c + 12` `implies c = - 30 - 20 - 12` `:. c = - 62`

Discussion

11.	A) Area of the figure bounded by y^(2)=9x and y=3x B) Area bounded by y=x^(2)+3 between x=-1 and x = 2 C) Area of the figure bounded by y=x^(2) and y=4x D) Area bounded by one arc of y=sin2x and X-axis Arrange the above statements in the ascending order of areas.
Answer» A, D, C, B B, A, D, C C, A, B, D D, B, A, C Answer :A

Discussion

12.	In a bank, principal increases continuously at the rate of r% per year.Find thevalue of r if Rs 100 double itself in 10 years (log_(e)2 = 0.6931).
Answer» ANSWER :`6.93%`

Discussion

13.	If p=a^2cos^2theta+b^2 sin^2 theta, where a^2+b^2+c^2,then 4p+(d^2p)/(d theta^2) is equal to
Answer» `c^2` `2c^2` `4c^2` `8c^2` ANSWER :B

Discussion

14.	If lines (x+l)/(3)=(y+3)/(5)=(z+5)/(7) and (x-2)/(1)=(y-4)/(3)=(z-6)/(5) are coplanar, thenl is equal to
Answer» 0 1 2 3 Answer :B

Discussion

15.	int sin^(-1)(cos x)dx=....
Answer» `(pix)/(2)` `(PI)/(12)` `(pix-x^(2))/(2)` `(pix+x^(2))/(2)` ANSWER :C

Discussion

16.	If 1+sin x+sin^(2)x+…………… upto oo=4+2sqrt(3),0ltxltpi and x!=(pi)/2, then x=
Answer» 1)`pi//6` 2)`pi//4` 3)`pi//3` 4)`3pi//4` ANSWER :C

Discussion

17.	If omega is a imaginary cube root of unity , then 225 + (3 omega + 8 omega^(2))^(2) + (3 omega^(2) + 8 omega)^(2) =
Answer» `72` 192 200 248 Answer :D

Discussion

18.	int_(-pi//2)^(pi//2) sin^(4)x.cos^(6) x dx=
Answer» `(3PI)/(128)` `(3pi)/(256)` `(3pi)/(572)` `(3pi)/(64)` ANSWER :B

Discussion

19.	Using elementary transformations, find the inverseof the matrices
Answer» ANSWER :`[(4,-1),(-7,2)]`

Discussion

20.	If α, β are the eccentric angles of the extremeties of a focal chord of the ellipse (i) e cos (alpha+beta)/(2)=cos (alpha-beta)/(2) (ii) tan (alpha/2)tan (beta/2)=(e-1)/(e+1)
Answer»

Discussion

21.	If f(x)=(x+2)/(2x+3), then intsqrt((f(x))/(x^2))dxequals : (1)/(sqrt(2))g((1+sqrt(2f(x)))/(1-sqrt(2f(x))))-sqrt((2)/(3))h((sqrt(3f(x))+sqrt(2))/(sqrt(3f(x))-sqrt(2)))+c, where :
Answer» `G(X)=log\|x\|,H(x)=tan^(-1)x` `g(x)=h(x)=tan^(-1)` `g(x)=tan^(-1)x,h(x)=log\|x\|` `g(x)=log\|x\|,h(x)=log\|x\|`. ANSWER :D

Discussion

22.	Find the locus of the point of intersection of tangents to the ellipse x^2/a^2+y^2/b^2=1 at the points the sum of whose ordinates are constant.
Answer» ANSWER :`(2Y)/LAMDA`

Discussion

23.	If alpha, beta , gammaare the roots of x^(3) + 3x + 4 = 0 then the equation whose roots (beta)/(gamma) + (gamma)/(beta) , (gamma)/(alpha) + (alpha)/(gamma), (alpha)/(beta) + (beta)/(alpha)is
Answer» `16x^(3) + 48X^(2) + 75X + 70 = 0` `16x^(3) - 48x^(2) + 75x + 70 = 0 ` `16x^(3) + 48x^(2) - 75x + 70 = 0 ` `16x^(2) - 48x^(2) + 75x - 70= 0` Answer :1

Discussion

24.	Determine all pairs (a,b) real numbers such that 10 ,a , b, ab are in arithmetic progression.
Answer» ANSWER :`(4,2), ((5)/(2),-5)`

Discussion

25.	I : The foot of the perpendicular of (3, -5) in y-axis is (-5, 3). II. If (2, -3) is the foot of the perpendicular from (-4, 5) on a line then the equation of the line is 3x-4y=18.
Answer» only I is TRUE only II is true both I and II are true NEITHER I nor II are true ANSWER :B

Discussion

26.	Let x be any real number, then [x+y]=[x]+[y] holds for :
Answer» `YINR,y!INQ` `yinQ` `yinR` `yinI` ANSWER :D

Discussion

27.	ABCisa rightangledtriangle withangleB = 90 ^@, a=6cm if theradiusof the circumcircleis 5 cmthen theareaofDeltaABC is
Answer» 25CM `""^2` 30cm `""^2` 36CM `""^2` 24cm `""^2` ANSWER :D

Discussion

28.	If a straight line perpendicular to 2x-3y+7=0 forms a triangle with the coordinates axes whose area is 3 sq unit, then the equation of the straight line is
Answer» `3x+2y=pm2` `3x+2y=pm6` `3x+2y=pm4` `3x+2y=pm8` ANSWER :B

Discussion

29.	Determine if the set A=x:xisa prime number }is a proper subset of the set B={2n-1:n=1,2,3…..}
Answer» SOLUTION :A `={2,3,5,7,11……..}` B `={1,3,5,7……}:.A CANCEL SUB B`, Because `2 in A `but 2 but `2 in B`.

Discussion

30.	The number of vectors of unit length perpendicular to the vectors a = (1,1,0) and b = (0,1,1) is
Answer» one two three infinite Answer :B

Discussion

31.	If A+B=(pi)/(4)," then "(d)/(dx){[1+tan(A-x)][1+tan(B+x)]}=
Answer» `-1` 1 `TANATANB` 0 Answer :D

Discussion

32.	Integrate the function (1)/(sqrt(x^(2)-1))
Answer»

Discussion

33.	The measure of two sides of a triangle is 10 m and 15 m. The angle between them is increasing at the rate of 0.01 radi./sec. when the angle between them is (pi)/(3), find the rate of change of increase in third side.
Answer» ANSWER :`(3)/(20)SQRT((3)/(7))m//s`

Discussion

34.	int_(0)^(1)e^(x)(x^(x)+1)^(3)dx=
Answer» `((E+1)^(4))/(4)` `1/4((e+1)^(4)-2^(4))` `1/4 ((e+1)^(4)-1)` `(e^(4))/(4)` ANSWER :B

Discussion

35.	Who is the author of this chapter?
Answer» Shakespeare Leo Tolstoy Ramaswami lyer Krishnamurthy None of the above Answer :C

Discussion

36.	Integrate the following intsin^(-1)x/(sqrt(1-x^2))dx
Answer» Solution :`int(SIN^(-1)X)/sqrt(1-x^2)DX` [put `sin^(-1)x=t then `dx/(sqrt(1-x^2)=DT` `inttdt` `(1/2)t^2+C=(1/2)(sin^(-1)x)^2+C`

Discussion

37.	The slope of the line, which is drawn through the point (1, 2) so that its point of intersection with the line x+y+3=0 is at a distance 3sqrt(2) is :
Answer» `(1)/(SQRT(3))` `sqrt(3) ` 1 `(sqrt(3)-1)/(2)` ANSWER :C

Discussion

38.	6 balanced dice are tossed 729 times. At least how many times 3 dice shows number 5 or 6 ?
Answer» ANSWER :233

Discussion

39.	intsqrt(1+cos2x)dx
Answer» SOLUTION :`intsqrt(1+cos2x)dx=intsqrt2 cosxdx` =sqrt2sinx+C

Discussion

40.	intsqrt(1-cos2x)dx
Answer» SOLUTION :`intsqrt(1-cos2x)DX=intsqrt(2sin^2x)dx` =`sqrt2intsinxdx=-sqrt2cosx+C`

Discussion

41.	Obtain the following integrals : int(e^(6logx)-e^(5logx))/(e^(4 logx)-e^(3logx))dx
Answer» ANSWER :`:.I=(X^(3))/(3)+C`

Discussion

42.	observethefollowinglists:(##VMC_MAT_WOR_BOK_05_C16_E02_022_Q01.png" width="80%">
Answer» ANSWER :`A- 4 ; b-2; c-2;d-1`

Discussion

43.	Let f(x)=f_(1)(x)-2f_(2)(x), where where f(x)={(min{x^(2)","\|x\|}",",\|x\| le 1),(max{x^(2)","\|x\|}",",\|x\| gt 1):} andf_(2)(x)={(min{x^(2)","\|x\|}",",\|x\| gt 1),(max{x^(2)","\|x\|}",",\|x\| le 1):} and let g(x)={(min{f(t):-3 le t le x", "-3 le x lt 0}),(max{f(t): 0let le x"," 0 le x le 3}):} Forx in (-1,0), f(x)+g(x) is
Answer» `X^(2)-2x+1` `x^(2)+2x-1` `x^(2)+2x+1` `x^(2)-2x-1` SOLUTION :For `x in (-1,0),F(x)+G(x)=x^(2)+2x-1.`

Discussion

44.	int(dx)/(a^2 sin^2x+b^2cos^2x)=
Answer» `(-1)/(ab)TAN^(-1)((btanx)/(a))+C` `(1)/(ab)tan^(-1)((btanx)/(a))+c` `(-1)/(ab)tan^(-1)((ATANX)/(b))+c` `(1)/(ab)tan^(-1)((atanx)/(b))+c` ANSWER :D

Discussion

45.	IF r.a = 0, r. b = 0 and r. c= 0 for some non-zero vector r. Then, the value of [a b c] is
Answer» 0 `(1)/(2)` 1 2 Solution :The given condition MEAN their that R is a PERPENDICULAR to all three vectors a,b and c, This is possible only if they are coplanar. `[abc]=0`

Discussion

46.	Distance between the pair of lines represented by the equation x^(2)– 6xy +9y^(2)+ 3x - 9y -4 = 0 is
Answer» `(15)/(sqrt(10))` `(1)/(2)` `sqrt((5)/(2))` `(1)/(sqrt(10))` Answer :C

Discussion

47.	If z satisfies the inequality \|-1\|lt\|z+1\|, then one has
Answer» `\|z-2-i\|lt\|z+2-i\|,i=sqrt(-1)` `\|arg(z+i)\|lt(PI)/(2),i=sqrt(-1)` `Re(z)lt0` `Im(ibarz)gt0,isqrt(-1)` Answer :a,B,d

Discussion

48.	Let f:R to R be a continuous function and f(x)=f(2x) is true AA x in R. If f(1) = 3 then the value of int_(-1)^(1) f(f(x))dx=
Answer» 6 or 2F(0) 0 3f(X) 3f(0) Answer :1

Discussion

49.	Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each of the folowing A+B , A-B
Answer» SOLUTION :`A-B=[[2-1,4-3],[3+2,2-5]]=[[1,1],[5,-3]]`

Discussion

50.	Find the value of x and y from the following equation: 2[(x,5),(7,y-3)]+[(3,-4),(1,2)]=[(7,6),(15,14)]
Answer» ANSWER :x=2 and y=9

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If x = 1/2 and if (1-2x)/ (1-x+ x^(2)) + (2x-4x^(3))/ (1-x^(2) + x^(4))+ (4x^(3)-8x^(7))/(1-x^(4)+x^(6))+...infty = k, then

Find the real numbers x and y so that (xI+yA)^(2)=A, where A=[{:(0,1),(-1,0):}].

Equation of circle passing through (1,sqrt(3)), (1,-sqrt(3)) and (3,-sqrt(3)) is

Solution set of the in equality log_(10^(2)) x-3(log_(10)x)( log_(10)(x-2))+2 log_(10^(2))(x-2) lt 0, is :

If a in [-20,0],then the probability that the graph of the function y=16x^(2)+8(a+5)x-7a-5 touches or above the x-aixs is

Select the Correct Option f(x)={((sinkx)/(2x),x!=0),(3,(x=0) at (x=0)):} is continuous then k+2=

Letz_(k) = cos ((2kpi)/(10)) + isin ((2kpi)/(10)), k = 1,2,,…,9.

The value of |(cos.(2pi)/(63),cos.(3pi)/(70),cos.(4pi)/(77)),(cos.(pi)/(72),cos.(pi)/(40),cos.(3pi)/(88)),(1,cos.(pi)/(90),cos.(2pi)/(99))| is equal to

If A,B,C are the minimum values of 2x^3-3x^2-12x+5,x^3-9x^2+24x-12,x^3-6x^2+9x+1 then the ascending order of A,B,C is

If the circle x^(2) + y^(2) + 4x - 6y + c = 0 bisects the circumference of the circle x^(2) + y^(2) - 6x + 4y - 12 = 0, then c is equal to

A) Area of the figure bounded by y^(2)=9x and y=3x B) Area bounded by y=x^(2)+3 between x=-1 and x = 2 C) Area of the figure bounded by y=x^(2) and y=4x D) Area bounded by one arc of y=sin2x and X-axis Arrange the above statements in the ascending order of areas.

In a bank, principal increases continuously at the rate of r% per year.Find thevalue of r if Rs 100 double itself in 10 years (log_(e)2 = 0.6931).

If p=a^2cos^2theta+b^2 sin^2 theta, where a^2+b^2+c^2,then 4p+(d^2p)/(d theta^2) is equal to

If lines (x+l)/(3)=(y+3)/(5)=(z+5)/(7) and (x-2)/(1)=(y-4)/(3)=(z-6)/(5) are coplanar, thenl is equal to

int sin^(-1)(cos x)dx=....

If 1+sin x+sin^(2)x+…………… upto oo=4+2sqrt(3),0ltxltpi and x!=(pi)/2, then x=

If omega is a imaginary cube root of unity , then 225 + (3 omega + 8 omega^(2))^(2) + (3 omega^(2) + 8 omega)^(2) =

int_(-pi//2)^(pi//2) sin^(4)x.cos^(6) x dx=

Using elementary transformations, find the inverseof the matrices

If α, β are the eccentric angles of the extremeties of a focal chord of the ellipse (i) e cos (alpha+beta)/(2)=cos (alpha-beta)/(2) (ii) tan (alpha/2)tan (beta/2)=(e-1)/(e+1)

If f(x)=(x+2)/(2x+3), then intsqrt((f(x))/(x^2))dxequals : (1)/(sqrt(2))g((1+sqrt(2f(x)))/(1-sqrt(2f(x))))-sqrt((2)/(3))h((sqrt(3f(x))+sqrt(2))/(sqrt(3f(x))-sqrt(2)))+c, where :

Find the locus of the point of intersection of tangents to the ellipse x^2/a^2+y^2/b^2=1 at the points the sum of whose ordinates are constant.

If alpha, beta , gammaare the roots of x^(3) + 3x + 4 = 0 then the equation whose roots (beta)/(gamma) + (gamma)/(beta) , (gamma)/(alpha) + (alpha)/(gamma), (alpha)/(beta) + (beta)/(alpha)is

Determine all pairs (a,b) real numbers such that 10 ,a , b, ab are in arithmetic progression.

I : The foot of the perpendicular of (3, -5) in y-axis is (-5, 3). II. If (2, -3) is the foot of the perpendicular from (-4, 5) on a line then the equation of the line is 3x-4y=18.

Let x be any real number, then [x+y]=[x]+[y] holds for :

ABCisa rightangledtriangle withangleB = 90 ^@, a=6cm if theradiusof the circumcircleis 5 cmthen theareaofDeltaABC is

If a straight line perpendicular to 2x-3y+7=0 forms a triangle with the coordinates axes whose area is 3 sq unit, then the equation of the straight line is

Determine if the set A=x:xisa prime number }is a proper subset of the set B={2n-1:n=1,2,3…..}

The number of vectors of unit length perpendicular to the vectors a = (1,1,0) and b = (0,1,1) is

If A+B=(pi)/(4)," then "(d)/(dx){[1+tan(A-x)][1+tan(B+x)]}=

Integrate the function (1)/(sqrt(x^(2)-1))

The measure of two sides of a triangle is 10 m and 15 m. The angle between them is increasing at the rate of 0.01 radi./sec. when the angle between them is (pi)/(3), find the rate of change of increase in third side.

int_(0)^(1)e^(x)(x^(x)+1)^(3)dx=

Who is the author of this chapter?

Integrate the following intsin^(-1)x/(sqrt(1-x^2))dx

The slope of the line, which is drawn through the point (1, 2) so that its point of intersection with the line x+y+3=0 is at a distance 3sqrt(2) is :

6 balanced dice are tossed 729 times. At least how many times 3 dice shows number 5 or 6 ?

intsqrt(1+cos2x)dx

intsqrt(1-cos2x)dx

Obtain the following integrals : int(e^(6logx)-e^(5logx))/(e^(4 logx)-e^(3logx))dx

observethefollowinglists:(##VMC_MAT_WOR_BOK_05_C16_E02_022_Q01.png" width="80%">

int(dx)/(a^2 sin^2x+b^2cos^2x)=

IF r.a = 0, r. b = 0 and r. c= 0 for some non-zero vector r. Then, the value of [a b c] is

Distance between the pair of lines﻿ represented by the equation x^(2)– 6xy +9y^(2﻿)+ 3x - 9y -4 = 0 is

If z satisfies the inequality |-1|lt|z+1|, then one has

Let f:R to R be a continuous function and f(x)=f(2x) is true AA x in R. If f(1) = 3 then the value of int_(-1)^(1) f(f(x))dx=

Let A=[[2,4],[3,2]] , B=[[1,3],[-2,5]] , C=[[-2,5],[3,4]] Find each of the folowing A+B , A-B

Find the value of x and y from the following equation: 2[(x,5),(7,y-3)]+[(3,-4),(1,2)]=[(7,6),(15,14)]

Distance between the pair of lines represented by the equation x^(2)– 6xy +9y^(2)+ 3x - 9y -4 = 0 is