28278 + Interview Questions in Maths in Class 12

1.	Find the points where the following function are not differentiable.\|x^2-4\|
Answer» SOLUTION :`\|x^2-4\|`is not DIFFERENTIABLE at the PINTS where `x^2-4=0`i.e,`x=+-2.`

Discussion

2.	Find the area of the region enclosed by the curves y= 6x -x^(2) and y= 3x
Answer» ANSWER :`((9)/(2))`

Discussion

3.	If x=a (cos t+ t sin t) and y= a (sin t - t cos t), find (d^(2)y)/(dx^(2)).
Answer» ANSWER :`(sec^(3)t)/(a t), 0 lt t lt (pi)/(2)`

Discussion

4.	A is one of 6 horses entered for a race and is to be ridden by one of two jockeys P and Q. It is 2 to 1 that P rides A, in which case all the horses are likely to win. If Q rides A, his chace is tribled . The odds favour of his winning are
Answer» `3//13` `2//11` `5//17` `5//18` ANSWER :D

Discussion

5.	In thre throws of a dice, the events A and B are defined as follows: A: 4 appears on 3rd throw B: 3 appears on 1st throw and 5 appears on 2nd throw. Find the probability of the occurrence of event A if it is known that event B is already occur.
Answer» SOLUTION :NA

Discussion

6.	If sum_(n=3)^(oo) (""^nC_3)/(n!) =a.e^(b) +c then descending orderof a, b, c is
Answer» a,B,C a,c ,b b,c,a b,a,c Answer :D

Discussion

7.	Ifalpha,beta, gammaarerootsof x^3+ ax^2 + bx + ab =0findthe equationwhoseroots arealpha^3, beta^3 , gamma ^3
Answer» ANSWER :`X^3 +a^3 x^2 +b^3 x +a^3 b^3 =0`

Discussion

8.	If (a+b). (a-b) = 8 and \|a\| = 8 \|b\|, then the values of \|a\| and \|b\| are
Answer» `(16)/(3)sqrt((2)/(7)), (2)/(3)sqrt((2)/(7))` `(4)/(3)sqrt((2)/(7)),(2)/(3)sqrt((3)/(7))` `(12)/(5)sqrt((2)/(7)),(4)/(3)sqrt((2)/(7))` None of these Solution :GIVEN,`(a+b).(a-b)=8 and \|a\|=8 \|b\|` `implies a.a-a.b+b.a-b.b=8` `implies \|a\|^(2)-\|b\|^(2)=8[ :' a.a=\|a\|^(2)and a.b=b.a]` `implies (8\|b\|)^(2)-\|b\|^(2)=8` `= 63\|b\|^(2)=8` `implies \|b\|= sqrt((8)/(63))=(2)/(3) sqrt((2)/(7))` Also ,`\|a\|=8\|b\|=8((2)/(3)sqrt((2)/(7)))=(16)/(3)sqrt((2)/(7))`

Discussion

9.	If (21.4)^(a) = (0.00214)_(b) = 100, then the value of (1)/(a)-(1)/(b) is
Answer» is a RATIONAL number prime irrational composite Answer :D

Discussion

10.	The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is actually 110. Then the true mean and median are
Answer» 50.1, 52 51, 52 50, 52 50, 51 Answer :A

Discussion

11.	If the Boolean expression (p oplusq)wedge (~p Theta q) is equivalent to p wedge q, where oplus, Theta in {vee, wedge}, then the ordered pair (oplus, Theta) is
Answer» `( WEDGE, VEE)` `( vee, vee)` `( wedge, wedge)` `(vee, wedge)` ANSWER :A

Discussion

12.	A randdom variable X takes the values 1, 2, 3 and 4 such that 2P(X=1)=3P (X=2)=P(X=3)=5P(X=4). If sigma^(2) is the variance and mu is the mean of X. Then, sigma^(2)+mu^(2)=
Answer» `(421)/(61)` `(570)/(61)` `(149)/(61)` `(3480)/(3721)` ANSWER :A

Discussion

13.	If ln 2=x and ln 3=y find the value of ln 18 in terms of x and y.
Answer» SOLUTION :`ln18=ln(3^(2)*2)=ln2+2ln3=x+2y`

Discussion

14.	The solution of (1)/(x)(dy)/(dx) + y e^(x) = e^((1-x)^(e^(x))) is
Answer» `y E^(e^(x(x-1))) = (x^(2))/(2) + c` `y e^(e^(x(x+1))) = (x^(2))/(2) + c` `y e^(e^(x(x-1))) = (x^(3))/(3) + c` `y e^(e^(x(x-1))) = (x^(4))/(4) + c` Answer :A

Discussion

15.	Determine P(E/F) Two coins are tossed once, where i. E: tail appears on one coin, F: one coin shows head ii E: no tail appears, F: no head appears
Answer» ANSWER :(i) 1, (II) 0

Discussion

16.	int_(0)^(a)f(x)dx=lambda and int_(0)^(a)f(2a-x)dx=mu then int_(0)^(2a)f(x) dx is equal to
Answer» `LAMBDA +MU` `lambda-mu` `2lambda-mu` `lambda-2mu` ANSWER :1

Discussion

17.	If x and y are positive integers and xdivy has a remainder of 5, what is the smallest. Possible value of xy?
Answer» ANSWER :30

Discussion

18.	For a function f:AtoB such that n(A)=a,n(B)=b(a,b in N) then which of the following statements must be CORRECT?
Answer» if function is one - one, onto then `agtb` if function is one - one into, then `agtb` iif function si MANY - one, onto then `agtb` if function is many - one into, then `altb` Solution :(A). If function is one-one & onto then `a=b` SINCE every element of seb should have exactly one preimage in A. (B). For one-one, into function every element of SET B should have either one pre-image or no preimage in set A `IMPLIES` no of elementsin set `Bge` no. of elements in A `becauseBgea` (C) for many one onto function every element of set B should have one or more tha one pre-images in A. `impliesn(B)len(A)impliesblea` or `AGEB` (D). for many- one into function `a in N` & `b in N`.

Discussion

19.	10C_0=
Answer»

Discussion

20.	Prove that vecR+([vecR.(vecbetaxx(vecbetaxxvecalpha))]vecalpha)/(\|vecalphaxxvecbeta\|^(2))+([vecR.(vecalphaxx(vecalphaxxvecbeta))]vecbeta)/(\|vecalphaxxvecbeta\|^(2))=([vecRvecalphavecbeta](vecalphaxx vecbeta))/(\|vecalphaxx vecbeta\|^(2))
Answer» Solution :`vecalpha , vecbeta and vecalpha xx vecbeta` are THREE non-coplanar vectors. Any vector `vecR` can be respresented as a linear combination of these vectors. Thus , `vecR=k_(1)vecalpha+k_(2)vecbeta+k_(3)(vecalphaxxvecbeta)` Take dot PRODUCT of (i) with `(vecalpha xx vec BETA)` . we have `vecR.(vecalphaxxvecbeta)=k_(3)(vecalpha xxvecbeta)=k_(3)\|vecalphaxxvecbeta\|^(2)` `k_(3)=(vecR.(vecalphaxxvecbeta))/(\|vecalphaxxvecbeta\|^(2))=([vecRvecalphavecbeta])/(\|vecalphaxxvecbeta\|^(2))` Take dot product of (i) with `vecalphaxx(vecalphaxxvecbeta)` we have `vecR.(vecalphaxx(vecalphaxxvecbeta))=k_(2)(vecalphaxx(vecalphaxxvecbeta)).vecbeta` `= k_(2)[(vecalpha.vecbeta)vecalpha-(vecalpha.vecalpha)vecbeta].vecbeta=k_(2)[(vecalpha.vecbeta)^(2)-\|vecalpha\|^(2)\|vecbeta\|^(2)]` `=-k_(2)\|vecalphaxxvecbeta\|^(2)` `k_(2)=(-[vecR.(vecalphaxx(vecalphaxxvecbeta))])/(\|vecalphaxxvecbeta\|^(2)) " simiarly "k_(1)=-([vecR.(vecbetaxx(vecbetaxxvecalpha))])/(\|vecalphaxx vecbeta\|^(2))` `RIGHTARROW vecR=(-[vecR.[vecbetaxx(vecbetaxxvecalpha))]vecalpha)/(\|vecalphaxxvecbeta\|^(2))-([vecR.(vecalphaxx(vecalphaxxvecbeta))]vecbeta)/(\|vecalphaxxvecbeta\|^(2))+(([vecR.(vecalphaxxvecbeta))](vecalphaxxvecbeta))/(\|vecalpha xx vecbeta\|^(2))` `Rightarrow vecR=(-[vecR.[vecbetaxx(vecbetaxxvecalpha))]vecalpha)/(\|vecalphaxxvecbeta\|^(2))-([vecR.(vecalphaxx(vecalphaxxvecbeta))]vecbeta)/(\|vecalphaxxvecbeta\|^(2))+(([vecR.(vecalphaxxvecbeta))](vecalphaxxvecbeta))/(\|vecalpha xx vecbeta\|^(2))`

Discussion

21.	If the circles x^(2)+y^(2)-4x+6y+8=0, x^(2)+y^(2)-10x-6y+14=0 touch each other, then the point of contact is
Answer» (3,-1) (3,1) (7,5) (-7,-5) ANSWER :A

Discussion

22.	If f(x)=\|x\| then show that f(3) =1
Answer»

Discussion

23.	Prove that the function f:R to R defined by f(x) = 4x + 3 is invertible and find the inverse of 'f'.
Answer» ANSWER :`therefore F^(-1) (X) = (x-3)/( 4)`

Discussion

24.	A plane which passes through the point (3,2,0) and the line (x-3)/(1)=(y-6)/(5)=(z-4)/(4) is
Answer» x-y+z=1 x-y+z=5 x+2y-z=1 2x-y+z=5 Answer :A

Discussion

25.	int_(0)^(a)x^(3)(ax-x^(2))^(3//2)dx=
Answer» `( 9 PI a^(7))/(2048)` `(7 pi a^(7))/(2048)` `(pi a^(7))/(1024)` `(5 pi a^(7))/(2048)` ANSWER :A

Discussion

26.	If Delta is the area of the triangle formed by the positive x-axis and the normal and tangent to the circle x^2+y^2=4 (1,root()3), then Delta is equal to
Answer» `ROOT()3/2` `root()3` `2ROOT()3` 6 Answer :C

Discussion

27.	Maximum number of electrons in a subshell can be calculated by following formula ?
Answer» (2l+1) 2(2l+1) `2n^2` `n^2`

Discussion

28.	Integrate the following functions: sin 3x cos4x
Answer» SOLUTION :`sin 3X cos 4x = cos 4x sin 3x =1/2[sin(4x+3x)-sin(4x-3x)] =1/2[sin7x-sinx] therefore `int SIN3X cos4x dx` =1/2[-cos(7X)/7+cosx]+C

Discussion

29.	Using calculus prove that Hmle GM le AM forpositiverealnumbers.
Answer»

Discussion

30.	Find least non negative integer r such that 6xx18xx27xx(-225) -= r "(mod 8)"
Answer» SOLUTION :`6xx18xx27xx -225 -= R("mod8")` `"Now" 6xx18=108 -=4 "MOD"8` `27 -= 3 "mod" 8` `-225-=7 "mod" 8` `implies6xx18xx27xx-225 -= 4xx3xx7 "mod"8` `-=84 "mod"8 -= 4 "mod" 8` `:. r=4`

Discussion

31.	Find the domain and range of those relations in a which are functions. {(a,1),(b,1),(c,1)}
Answer» SOLUTION :RANGE of the FUNCTION is {1}

Discussion

32.	Integrate the following functions xsqrt(1+2x^2)
Answer» Solution :PUT `1+2x^2 = t`. Then dt = 4x dx `gt xdx = 1/4 dt` therefore `INT x SQRT(1+2x^2) dx = int sqrtt 1/4 dt` =`1/4 int sqrtt dt = 1/4 t^(1/2+1)/(1/2+1) +C` =`1/6 t^(3/2) +c = 1/6 (1+2x^2)^(3/2) +c`

Discussion

33.	Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%.
Answer» ANSWER :`-0.12x^(2)m^(2)`

Discussion

34.	Write down and simplify 7th term in ((4)/(x^3) + (x^2)/(2))^14
Answer» ANSWER :`""^14C_6 . (4^5)/(x^12)`

Discussion

35.	If on an average 1 ship in every 10 sinks, find the chance that out of 5 ships atleast 4 will arrive safely.
Answer» Answer :`(7)/(5)((9)/(10))^(4)`

Discussion

36.	Ifalpha , beta , gammaare therootsof2x^3 -2x -1=0thesum( alpha beta)^2 =
Answer» `-1` 1 2 3 Answer :B

Discussion

37.	Using integiation find the area of region bounded by the triangle whose vertices are (-1,0), (1,3) and (3, 2).
Answer» ANSWER :4

Discussion

38.	If X and Y are two sets such that X uu Y has 20 objects, X has 10 objects and Y has 15 objects;how many objects does X nn Yhave ?
Answer» SOLUTION :GIVEN `\|X uu Y \|20` `\|X\|=10 \|Y\|=15` We KNOW that `\|X uu Y\| =\|X\|+\|Y\|-\|X nn Y\|` `implies20 =10+15-\|X nn Y\|` `implies\|XnnY\|=25-20=5` `:.`X nn Y Has 5 elements.

Discussion

39.	The population of a village increases continuously at therate proportional to thenumber of its inhabitants present at any time.If the population of the village was 20,000 in 1999 and 25000 in the year 2004, what will be the population of thevillage in 2009?
Answer» ANSWER :31250

Discussion

40.	If x^2+y^2=25, then log_5[Max(3x+4y)] is
Answer» 2 3 4 5 Answer :A

Discussion

41.	If the roots of the equation x^3 + bx^2 + cx - 1=0 form an increasing G.P, then
Answer» ONE of the ROOTS is 2 one of the roots is 1 one of the roots is -1 one of the roots is -2 Answer :B

Discussion

42.	Find area of the triangle with vertices at the point given in each of the following (1,0),(6,0),(4,3)
Answer» ANSWER :`(15)/2` SQ. UNIT

Discussion

43.	Differentiate(x-1)^2
Answer» SOLUTION :`y=(x-1)^2` Then `dy/dx=2(x-1)`

Discussion

44.	There are eight rooms on the first floor of a hotel, with four rooms on each side of the corridor, symmetrically situated (that is each room is exactly opposite to one other room). Four guests have to be accommodated in four of the eight rooms (that is, one in each) such that no two guests are in adjacent rooms or in opposite rooms. in how many ways can the guests be accommodated?
Answer» ANSWER :48

Discussion

45.	Equation of the parabola whose vertex is (3, -2) and parall to x-axis and latusrectum 4 is
Answer» `(y+2)^(2) = pm 4(X- 1) ` `(y+2)^(2) = pm 16(x- 1) ` `(y+1)^(2) = pm 4(x- 2) ` `(y+1)^(2) = pm 16(x- 2) ` Answer :C

Discussion

46.	Five coins whose face are marked 3, 4 are thrown. The chance of obtaining a total of 18 is
Answer» `(1)/(32)` `(1)/(16)` `(3)/(16)` `(5)/(16)` ANSWER :D

Discussion

47.	Reactify the mistakes if any. All unit vectors are equal.
Answer» SOLUTION :EQUAL MAGNITUDE

Discussion

48.	For a person of age 50 years the probability of his living upto 70 years is (5)/(12). For a person of age 60 years the probability of his living upto 70 years (2)/(7). The probability that atleast one of them to live upto 70 years is
Answer» `(35)/(84)` `(45)/(84)` `(49)/(84)` `(54)/(84)` ANSWER :C

Discussion

49.	Given, z=cos.(2pi)/(2n+1)+i sin.(2pi)/(2n+1),'n' a positive integer , find the equation whose roots are, alpha=z+z^3+……..+z^(2n-1) & beta=z^2+z^4+……..+z^(2n) .
Answer» ANSWER :`z^2=k,y+(sin^2ntheta)/(sin^2theta) ," where " THETA=(2PI)/(2n+1)`

Discussion

50.	No. of term in (1 + 5sqrt2x)^9 + (1 - 5sqrt2x)^9 if x > 0 is
Answer» 3 5 4 6 Answer :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the points where the following function are not differentiable.|x^2-4|

Find the area of the region enclosed by the curves y= 6x -x^(2) and y= 3x

If x=a (cos t+ t sin t) and y= a (sin t - t cos t), find (d^(2)y)/(dx^(2)).

A is one of 6 horses entered for a race and is to be ridden by one of two jockeys P and Q. It is 2 to 1 that P rides A, in which case all the horses are likely to win. If Q rides A, his chace is tribled . The odds favour of his winning are

In thre throws of a dice, the events A and B are defined as follows: A: 4 appears on 3rd throw B: 3 appears on 1st throw and 5 appears on 2nd throw. Find the probability of the occurrence of event A if it is known that event B is already occur.

If sum_(n=3)^(oo) (""^nC_3)/(n!) =a.e^(b) +c then descending orderof a, b, c is

Ifalpha,beta, gammaarerootsof x^3+ ax^2 + bx + ab =0findthe equationwhoseroots arealpha^3, beta^3 , gamma ^3

If (a+b). (a-b) = 8 and |a| = 8 |b|, then the values of |a| and |b| are

If (21.4)^(a) = (0.00214)_(b) = 100, then the value of (1)/(a)-(1)/(b) is

The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is actually 110. Then the true mean and median are

If the Boolean expression (p oplusq)wedge (~p Theta q) is equivalent to p wedge q, where oplus, Theta in {vee, wedge}, then the ordered pair (oplus, Theta) is

A randdom variable X takes the values 1, 2, 3 and 4 such that 2P(X=1)=3P (X=2)=P(X=3)=5P(X=4). If sigma^(2) is the variance and mu is the mean of X. Then, sigma^(2)+mu^(2)=

If ln 2=x and ln 3=y find the value of ln 18 in terms of x and y.

The solution of (1)/(x)(dy)/(dx) + y e^(x) = e^((1-x)^(e^(x))) is

Determine P(E/F) Two coins are tossed once, where i. E: tail appears on one coin, F: one coin shows head ii E: no tail appears, F: no head appears

int_(0)^(a)f(x)dx=lambda and int_(0)^(a)f(2a-x)dx=mu then int_(0)^(2a)f(x) dx is equal to

If x and y are positive integers and xdivy has a remainder of 5, what is the smallest. Possible value of xy?

For a function f:AtoB such that n(A)=a,n(B)=b(a,b in N) then which of the following statements must be CORRECT?

10C_0=

Prove that vecR+([vecR.(vecbetaxx(vecbetaxxvecalpha))]vecalpha)/(|vecalphaxxvecbeta|^(2))+([vecR.(vecalphaxx(vecalphaxxvecbeta))]vecbeta)/(|vecalphaxxvecbeta|^(2))=([vecRvecalphavecbeta](vecalphaxx vecbeta))/(|vecalphaxx vecbeta|^(2))

If the circles x^(2)+y^(2)-4x+6y+8=0, x^(2)+y^(2)-10x-6y+14=0 touch each other, then the point of contact is

If f(x)=|x| then show that f(3) =1

Prove that the function f:R to R defined by f(x) = 4x + 3 is invertible and find the inverse of 'f'.

A plane which passes through the point (3,2,0) and the line (x-3)/(1)=(y-6)/(5)=(z-4)/(4) is

int_(0)^(a)x^(3)(ax-x^(2))^(3//2)dx=

If Delta is the area of the triangle formed by the positive x-axis and the normal and tangent to the circle x^2+y^2=4 (1,root()3), then Delta is equal to

Maximum number of electrons in a subshell can be calculated by following formula ?

Integrate the following functions: sin 3x cos4x

Using calculus prove that Hmle GM le AM forpositiverealnumbers.

Find least non negative integer r such that 6xx18xx27xx(-225) -= r "(mod 8)"

Find the domain and range of those relations in a which are functions. {(a,1),(b,1),(c,1)}

Integrate the following functions xsqrt(1+2x^2)

Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%.

Write down and simplify 7th term in ((4)/(x^3) + (x^2)/(2))^14

If on an average 1 ship in every 10 sinks, find the chance that out of 5 ships atleast 4 will arrive safely.

Ifalpha , beta , gammaare therootsof2x^3 -2x -1=0thesum( alpha beta)^2 =

Using integiation find the area of region bounded by the triangle whose vertices are (-1,0), (1,3) and (3, 2).

If X and Y are two sets such that X uu Y has 20 objects, X has 10 objects and Y has 15 objects;how many objects does X nn Yhave ?

The population of a village increases continuously at therate proportional to thenumber of its inhabitants present at any time.If the population of the village was 20,000 in 1999 and 25000 in the year 2004, what will be the population of thevillage in 2009?

If x^2+y^2=25, then log_5[Max(3x+4y)] is

If the roots of the equation x^3 + bx^2 + cx - 1=0 form an increasing G.P, then

Find area of the triangle with vertices at the point given in each of the following (1,0),(6,0),(4,3)

Differentiate(x-1)^2

Equation of the parabola whose vertex is (3, -2) and parall to x-axis and latusrectum 4 is

Five coins whose face are marked 3, 4 are thrown. The chance of obtaining a total of 18 is

Reactify the mistakes if any. All unit vectors are equal.

For a person of age 50 years the probability of his living upto 70 years is (5)/(12). For a person of age 60 years the probability of his living upto 70 years (2)/(7). The probability that atleast one of them to live upto 70 years is

Given, z=cos.(2pi)/(2n+1)+i sin.(2pi)/(2n+1),'n' a positive integer , find the equation whose roots are, alpha=z+z^3+……..+z^(2n-1) & beta=z^2+z^4+……..+z^(2n) .

No. of term in (1 + 5sqrt2x)^9 + (1 - 5sqrt2x)^9 if x > 0 is