28278 + Interview Questions in Maths in Class 12

1.	If the line (x-1)/(5)=(y-3)/(2)=(z-3)/(2) intersects the curve x^(2)-y^(2)=k^(2), z=0, then the value of 2k can be equal to
Answer» `-13` `-(13)/(2)` `(13)/(2)` `(13)/(4)` ANSWER :A

Discussion

2.	The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is .........
Answer» `""^(5)C_(4)(0.7)^(4) (0.3)` `""^(5)C_(1)(0.7)(0.3)^(4)` `""^(5)C_(4)(0.7)(0.3)^(4)` `(0.7)^(4)(0.3)` ANSWER :A

Discussion

3.	Find the sum of the infinite series (3)/(4.8)-(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)-......
Answer» SOLUTION :N/A

Discussion

4.	The points A(2, 3) and B(-7, -12) are conjugate points w.r.t to the circle x^2 + y^2 - 6x - 8y - 1 = 0. The centre of the circle passing through A and B and orthogonal to given circle is
Answer» (-5,-9) (-9,-15) `(-5//2.-9//2)` NONE Answer :C

Discussion

5.	int_(0)^(oo) (dx)/((x+sqrt(x^(2)+1))^(3))=
Answer» `3/8` `3/4` `3/2` `8/5` ANSWER :A

Discussion

6.	Find the value of "^nC_(r-1)//"^nC_r
Answer» SOLUTION :`"^nC_(R-1)//^nC_r = N!//(r-1)!(n-r+1)!//n!//r!(n-r)!` `r!(n-r)!//(r-1)!(n-r+1)!` = `r!(r-1)!(n-r)!//(r-1)!(n-r+1)(n-r)!` `r/n-r+1`

Discussion

7.	A(5,3) and B(3,-2) are 2 fixed points. Find the equation of locus of P, so that the area of trianglePAB is 9sq. Units.
Answer» ANSWER :`(5x-2y-37)(5x-2y-1)=0`

Discussion

8.	The value of \|vec(a)+hat(i)\|^(2)+\|vec(a)+vec(j)\|^(2)+\|vec(a)+vec(k)\|^(2)" if "absa=1 is ………….
Answer» 0 1 -1 3 Answer :B

Discussion

9.	If int(3tan(x-(pi)/(4)))/(cos^(2)xsqrt(tan^(3))+xtan^(2)x+tanx)=Ktan^(-1)(sqrt(tanx+1+cotx))+C, then the value of K is
Answer» 2 3 6 8 Solution :`I=int(3(tanx-1)SEC^(2)x)/((tanx+1)sqrt(tan^(2)x+tan^(2)x+tanx))dx` Put `tan x=t` `rArr""I=3int(1-(1)/(t^(2)))/((t+2+(1)/(t))sqrt(t+(1)/(t)+1))dt` `"Put"t+(1)/(t)+1=z^(2)` `rArr""I=3.2 tan^(-1)(sqrt(cosx+tanx+1))+C` `rArr""K=6`

Discussion

10.	For any integer n ge 1 , the sum sum_(k=1)^(n)k(k+2) is equal to
Answer» `(N(n+1)(n+2))/(6)` `(n(n+1)(2n+1))/(6)` `(n(n+1)(2n+7))/(6)` `(n(n+1)(2n+9))/(6)` ANSWER :C

Discussion

11.	The set of admissible value of x such that (2x+3)/(2x-9) lt 0 is
Answer» `(-OO , -3/2) UU (9/2 , oo)` `(-oo , 0) uu (9/2 , oo)` `(-3/2 , 0)` `(-3/2, 9/2)` ANSWER :D

Discussion

12.	A particle is thrown horizontally with velocity 10 m//s from an incline of inclination 30^(@) , it hits on the incline agin then displacement (in m) of the particle is:
Answer» ANSWER :`2.50`

Discussion

13.	Find int_(a)^(b)sqrt((x-a)(b-x)) dx
Answer» ANSWER :`(PI)/(8)(b-a)^(2)`

Discussion

14.	Write down negations of \|x\| is equal to either x or -x.
Answer» SOLUTION :\|X\| is NEITHER x nor -x

Discussion

15.	For the data {x,y}=(1,5),(3,7),(5,9),(6,12),(8,15), find (a) regression line of Y on X in the form y-y=b_(x) (x-y) (b) regression line of X on Y in the form x-x=b_(xy) (y-y) Estimate the value of y when x=4 and the value of x when y=11
Answer» ANSWER :(a) `y=9.6=1.445(x-4.6)" when x=4, y=8.733"` (B) `x-4.6=0.688 (y-9.6)" when y=11, x=5.5352"`

Discussion

16.	Evaluate the following integrals int_(pi/4)^(pi/2)cotxdx
Answer» SOLUTION :`int_(pi/4)^(pi/2)cotxdx=[In SINX]_(pi/4)^(pi/2)` `Insin(pi/2)-In SIN(pi/4)=Insqrt2=(1/2)IN2`

Discussion

17.	A circle of constant radius 3k passes through (0,0) and cuts the axes in A and B then the locus of centroid of triangle OAB is
Answer» `X^(2)+y^(2)=K^(2)` `x^(2)+y^(2)=2K^(2)` `x^(2)+y^(2)=3k^(2)` `x^(2)+y^(2)=4K^(2)` Answer :D

Discussion

18.	A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probaility that it is actually a six.
Answer» Solution :In a throw of a die, LET `E_1` = EVENT of getting a SIX, `E_2`= event of not gettinga six, and E = event that the man reports that it is a six. Then, `P(E_1)=1/6, and P(E_2) =(1-1/6)=5/6`. `P(E//E_1)` = probability that the manreports that six occurs, when six has actually occurred = probability that the man speaks the TRUTH `=3/4`. `P(E//E_2)` = probability that the man reports that six occurs, when six has not actually occurred = probability that the man does not speak the truth `=(1-3/4)=1/4`. Probability of getting a six, GIVEN that the man reports it to be six `=P(E_1//E)` `=(P(E//E_1).P(PE_1))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2))`[by Bayes's theorem) `((3/4xx1/6))/((3/4xx1/6)+(1/4xx5/6))=(1/8xx3)=3/8`. Hence,the required probability is `3/8`.

Discussion

19.	Discuss the continuity of the following functions : f(x)= sin x - cos x
Answer» ANSWER :CONTINUOUS

Discussion

20.	Find the coordinates of the foot of the perpendicular drawn from the point (-1,2,3) thestraight linevecr=(hati-4hatj+3hatk)+t(2hati+3hatj+hatk)Also, find the shortest distance frompoint to the straight line.
Answer» ANSWER : ` SQRT(26) `

Discussion

21.	If f(x) = int_(0)^(x) sin^(8) t dt, then f(x+pi) equals
Answer» `(F(X))/( f(PI))` `f(x) f(pi)` `f(x) + f(pi)` `f(x) - f(pi)` ANSWER :C

Discussion

22.	Solve the following equation : (x^(2)-3.5 x + 1.5)/(x^(2)-x-6)=0
Answer» ANSWER :`1//2`

Discussion

23.	Evaluateint " sin "( sqrt(x)) dx
Answer» `2 [ sqrt(x)COS sqrt(x) - sin sqrt(x) ] + C ` `2 [ -sqrt(x)cos sqrt(x) - sin sqrt(x) ] + c ` `2 [ sqrt(x)cos sqrt(x) + sin sqrt(x) ] + c ` `2 [ -sqrt(x)cos sqrt(x) + sin sqrt(x) ] + c ` ANSWER :D

Discussion

24.	Prove that (ll_(1). l_(2)l_(3))/(sin A) =(ll_(2). l_(3)l _(1))/(sinB )
Answer» ANSWER :`LHS=RHS`

Discussion

25.	i.Write the inequality which represents the shaded half plane in the figure. ii. Solve (2x-1)/(5) le (7)/(2) , when x is a natural number.
Answer» Answer :The INEQUATION is `3x+2y GE 6` II. The solution is 9,8,7,6,5,4,3,2,1 , since x is a NATURAL number.

Discussion

26.	For what values of x, the function f(x)=(x + 1)^3(x - 3)^3 is increasing on R.
Answer» `(OO,1)` `(1,oo)` `(-1,1)` (0,1) ANSWER :B

Discussion

27.	Solution of differential equation of (x+2y^3)dy = ydx is :
Answer» `x = y^3 = cy` `y = x^3 = cx ` `x^2 = y^2 =cxy` None of these Solution :The GIVEN differential equation can be WRITTEN as `(DX)/(DY) - 1/y. x = 2y^2` I.F. `e^(-int 1/y dy) = 1/y` So solution is `x. 1/y = int 1/y 2y^2 .""dy= y^2+c` So `x= y^3 + cy`

Discussion

28.	Ifcos alpha + cos beta + cos gamma = 0= sin alpha + sin beta + sin gammathen show thatsin 3 alpha + sin 3 beta + sin 3 gamma = 3 sin( alpha + beta + gamma)
Answer»

Discussion

29.	If the sum of p terms of an A.P is equal to sum of q terms (p != q) then the sum of (p + q) terms is
Answer» 1 2 0 `-1` ANSWER :C

Discussion

30.	By using the properties of definite integrals, evaluate the integrals int_(2)^(8)abs(x-5)dx
Answer» ANSWER :9

Discussion

31.	Find x and y if sqrt(x^(2)+3x+8)+(h+4)i=y(2+i)
Answer» ANSWER :`X=-7`, `y=3` , `x=-(8)/(3)`, `y=(4)/(3)`

Discussion

32.	If a=hati+2hatj+3hatk,b=2hati+3hatj+2hatk, and c is a vector perpendicular to b, then \|{(a(bxxc))/(\|bxxc\|^(2))}(bxxc)+{(ab)/(\|b\|^(2))}b+{(a*c)/(\|c\|^(2))}\|=
Answer» `SQRT14` 14 13 `SQRT17` ANSWER :A

Discussion

33.	int_(0)^(1) (1)/(sqrt(2+3x))dx=
Answer» `2/3 (SQRT(5)+sqrt(2))` `2/3 (sqrt(5)-sqrt(2))` `3/5 (sqrt(5)+sqrt(2))` `2sqrt(5)` ANSWER :B

Discussion

34.	If p is a prime integer, the set G={1,2, . . . . P-1} will form an abelion group with respect to the binary composition defined as
Answer» addition of integers MULTIPLICATION of integers addition MODULO p multiplication modulo p. ANSWER :D

Discussion

35.	The molar mass of a substance , each molecule of which contains 9 C atoms, 13 H-atoms and 3.32xx10^(-23) g of other component is (N_A=6.022xx10^23)
Answer» ANSWER :140.50 to 141.50

Discussion

36.	((d^(2)y)/(dx^(2)))^(2) + cos ((dy)/(dx)) = 0
Answer» ANSWER :ORDER 2; DEGREE not DEFINED

Discussion

37.	Let triangle ABC is right triangle right angled at C such that A lt B and r=8, R=41 . Q."tan"(A)/(2)=
Answer» `(1)/(18)` `(1)/(3)` `(1)/(6)` `(1)/(9)` ANSWER :D

Discussion

38.	If the line OP of length r makes an angle alpha with the X - axis , and lies in the ZX - plane , then the co - ordinates of P are
Answer» `(r.cos ALPHA,0,r.sin alpha)` `(r.cos alpha,0,r.sin alpha)` `(0,0,r.cos alpha)` `(0,r.cos alpha , 0)` ANSWER :a

Discussion

39.	4 moles of ..................
Answer» SOLUTION :`TV^(GAMMA-1) =C` `gamma-1 =n` `n=6/13` `gamma=(4xx7/2 R+2xx5/2 R)/(4xx5/2 R+2xx3/2 R)=19/13`

Discussion

40.	Consider the number N=2012. Find the number of cyphers at the end of ""^(N)C_(N//2).
Answer» SOLUTION :`""^(N)C_(N//2)=""^(2012)C_(1006)=((2012)!)/((1006)!(1006)!)` NUMBER of 5's in numerator =402+80+16+3=501 number of 5's in denominator`=2[201+40+8+1]=500` `:.` number of cyphers in `""^(N)C_(N//2)` is 1

Discussion

41.	Evaluate the following integrals. int(1)/(3sin^(2)x+4cos^(2)x)dx
Answer» ANSWER :`(1)/(10)KG\|(2tanx+1)/(2-tanx)\|+C`

Discussion

42.	Two tangents are drawn from (- 2, -1) to y^(2) = 4x. If theta is the acute angle between two tangents then Tan theta equal to
Answer» 3 `(1)/(3)` 2 `(1)/(2)` ANSWER :A

Discussion

43.	If the quadratic equation 2x(2) - px + q = 0where p and q are real, then the orderedpair (p,q) is equal to
Answer» `-3` `-2` `-1` 0 Answer :B

Discussion

44.	If the probability that two queens, placed at random on a class-board, do not take on each other, is (23K)/(6), then 12 K equals______
Answer» ANSWER :2

Discussion

45.	Eighteen rupee coins are distributed among 6 children at random in such a way that each child receives atleast one coins. Find the probability that the total number of coins received by first five children is atleast 8 and atmost 12.
Answer» ANSWER :`(771)/(6188)`

Discussion

46.	If I_(n)= int_(1)^(e) (log x)^(n) dx then I_(8) + 8I_(7)=
Answer» 1 e 2 2e Answer :B

Discussion

47.	int_(0)^(pi) (sin^(3)x)/(1+cos^(2)x)dx=
Answer» `pi-1` `pi+2` `pi-2` `2-pi` ANSWER :C

Discussion

48.	Let A=NxxN be the Cartesian product of N and N. Let S={(m,n),(p,q)epsilonAxxA:m+q=n+p} Consider the following statements: I.If ((m,n)),(p,q))epsilonS and ((p,q),(r,s))epsilon then ((r,s),(m,n))epsilonS II. There exists at least one element ((m,n),(p,q))epsilonS such that ((p,q),(m,n))!inS Which of the statements given above is /are correct?
Answer» I only II only Both I and II Neither I nor II Solution :NA

Discussion

49.	If x = 1 + 3a + 6a^2 + 10 a^3 + ……" to " oo terms \|a\| lt 1, y = 1+4a+10a^2 + 20a^3 + ….." to " oo terms, \|a\| lt 1, then x:y
Answer» `(1 - a):1` `1:(1 - a)` `(1+a):1` `1:(1+a)` ANSWER :A

Discussion

50.	Three friends whose ages form a G.P ivide a certain sum of money in in proportional to theirages . If theyo that three years later , when the youngest is half the age of the youngest friend will get Rs. 15 more than now , then the ageof the youngest friend is
Answer» 27 18 14 12 Answer :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the line (x-1)/(5)=(y-3)/(2)=(z-3)/(2) intersects the curve x^(2)-y^(2)=k^(2), z=0, then the value of 2k can be equal to

The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is .........

Find the sum of the infinite series (3)/(4.8)-(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)-......

The points A(2, 3) and B(-7, -12) are conjugate points w.r.t to the circle x^2 + y^2 - 6x - 8y - 1 = 0. The centre of the circle passing through A and B and orthogonal to given circle is

int_(0)^(oo) (dx)/((x+sqrt(x^(2)+1))^(3))=

Find the value of "^nC_(r-1)//"^nC_r

A(5,3) and B(3,-2) are 2 fixed points. Find the equation of locus of P, so that the area of trianglePAB is 9sq. Units.

The value of |vec(a)+hat(i)|^(2)+|vec(a)+vec(j)|^(2)+|vec(a)+vec(k)|^(2)" if "absa=1 is ………….

If int(3tan(x-(pi)/(4)))/(cos^(2)xsqrt(tan^(3))+xtan^(2)x+tanx)=Ktan^(-1)(sqrt(tanx+1+cotx))+C, then the value of K is

For any integer n ge 1 , the sum sum_(k=1)^(n)k(k+2) is equal to

The set of admissible value of x such that (2x+3)/(2x-9) lt 0 is

A particle is thrown horizontally with velocity 10 m//s from an incline of inclination 30^(@) , it hits on the incline agin then displacement (in m) of the particle is:

Find int_(a)^(b)sqrt((x-a)(b-x)) dx

Write down negations of |x| is equal to either x or -x.

For the data {x,y}=(1,5),(3,7),(5,9),(6,12),(8,15), find (a) regression line of Y on X in the form y-y=b_(x) (x-y) (b) regression line of X on Y in the form x-x=b_(xy) (y-y) Estimate the value of y when x=4 and the value of x when y=11

Evaluate the following integrals int_(pi/4)^(pi/2)cotxdx

A circle of constant radius 3k passes through (0,0) and cuts the axes in A and B then the locus of centroid of triangle OAB is

A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probaility that it is actually a six.

Discuss the continuity of the following functions : f(x)= sin x - cos x

Find the coordinates of the foot of the perpendicular drawn from the point (-1,2,3) thestraight linevecr=(hati-4hatj+3hatk)+t(2hati+3hatj+hatk)Also, find the shortest distance frompoint to the straight line.

If f(x) = int_(0)^(x) sin^(8) t dt, then f(x+pi) equals

Solve the following equation : (x^(2)-3.5 x + 1.5)/(x^(2)-x-6)=0

Evaluateint " sin "( sqrt(x)) dx

Prove that (ll_(1). l_(2)l_(3))/(sin A) =(ll_(2). l_(3)l _(1))/(sinB )

i.Write the inequality which represents the shaded half plane in the figure. ii. Solve (2x-1)/(5) le (7)/(2) , when x is a natural number.

For what values of x, the function f(x)=(x + 1)^3(x - 3)^3 is increasing on R.

Solution of differential equation of (x+2y^3)dy = ydx is :

Ifcos alpha + cos beta + cos gamma = 0= sin alpha + sin beta + sin gammathen show thatsin 3 alpha + sin 3 beta + sin 3 gamma = 3 sin( alpha + beta + gamma)

If the sum of p terms of an A.P is equal to sum of q terms (p != q) then the sum of (p + q) terms is

By using the properties of definite integrals, evaluate the integrals int_(2)^(8)abs(x-5)dx

Find x and y if sqrt(x^(2)+3x+8)+(h+4)i=y(2+i)

If a=hati+2hatj+3hatk,b=2hati+3hatj+2hatk, and c is a vector perpendicular to b, then |{(a*(bxxc))/(|bxxc|^(2))}(bxxc)+{(a*b)/(|b|^(2))}b+{(a*c)/(|c|^(2))}|=

int_(0)^(1) (1)/(sqrt(2+3x))dx=

If p is a prime integer, the set G={1,2, . . . . P-1} will form an abelion group with respect to the binary composition defined as

The molar mass of a substance , each molecule of which contains 9 C atoms, 13 H-atoms and 3.32xx10^(-23) g of other component is (N_A=6.022xx10^23)

((d^(2)y)/(dx^(2)))^(2) + cos ((dy)/(dx)) = 0

Let triangle ABC is right triangle right angled at C such that A lt B and r=8, R=41 . Q."tan"(A)/(2)=

If the line OP of length r makes an angle alpha with the X - axis , and lies in the ZX - plane , then the co - ordinates of P are

4 moles of ..................

Consider the number N=2012. Find the number of cyphers at the end of ""^(N)C_(N//2).

Evaluate the following integrals. int(1)/(3sin^(2)x+4cos^(2)x)dx

Two tangents are drawn from (- 2, -1) to y^(2) = 4x. If theta is the acute angle between two tangents then Tan theta equal to

If the quadratic equation 2x(2) - px + q = 0where p and q are real, then the orderedpair (p,q) is equal to

If the probability that two queens, placed at random on a class-board, do not take on each other, is (23K)/(6), then 12 K equals______

Eighteen rupee coins are distributed among 6 children at random in such a way that each child receives atleast one coins. Find the probability that the total number of coins received by first five children is atleast 8 and atmost 12.

If I_(n)= int_(1)^(e) (log x)^(n) dx then I_(8) + 8I_(7)=

int_(0)^(pi) (sin^(3)x)/(1+cos^(2)x)dx=

If x = 1 + 3a + 6a^2 + 10 a^3 + ……" to " oo terms |a| lt 1, y = 1+4a+10a^2 + 20a^3 + ….." to " oo terms, |a| lt 1, then x:y

Three friends whose ages form a G.P ivide a certain sum of money in in proportional to theirages . If theyo that three years later , when the youngest is half the age of the youngest friend will get Rs. 15 more than now , then the ageof the youngest friend is

If a=hati+2hatj+3hatk,b=2hati+3hatj+2hatk, and c is a vector perpendicular to b, then |{(a(bxxc))/(|bxxc|^(2))}(bxxc)+{(ab)/(|b|^(2))}b+{(a*c)/(|c|^(2))}|=