28278 + Interview Questions in Maths in Class 12

1.	Match the following :
Answer» <P> Answer :`(A) RARR (p), (B) rarr (s), (C ) rarr (q), (D)rarr (R)`

Discussion

2.	If x ^(2) +bx+b is a factor of x ^(3) +2x ^(2)+2x + c (c ne 0), then b+c is :
Answer» 2 `-1` 0 `-2` ANSWER :a

Discussion

3.	If x+(1//x)=2cos(pi//10), then x^5+(1//x^5)=
Answer» 10 2 0 32 Answer :C

Discussion

4.	Two persons A, B have to speak at a function with 10 other persons. If the persons speak at random order, the probability that A speaks immediately before B is
Answer» `(1)/(2)` `(1)/(3)` `(3)/(8)` `(5)/(6)` ANSWER :A

Discussion

5.	From where did the Dewan get 100th tiger?
Answer» At his home Kaziranga PARK People's Park in Madras Both B and C Answer :C

Discussion

6.	A rod 25 ft. Long always has its ends A and B on the X-andY-axes respectively .If A is at 15 ft.from the origin and is moving at the rate of 0.2 ft. //sec, then the area of the triangle formed by the rod with axes is changing at the rate of
Answer» `3 ft.//sec`. `0.875 ft.//sec`. `2ft.//sec`. `-2 ft.//sec`. ANSWER :B

Discussion

7.	sin^(-1)(1-x)-2sin^(-1)x= pi/2,then find x
Answer» 0,1/2 1,1/2 0 44198 Answer :C

Discussion

8.	One cautions sign flashes evergy 4 second, and another caution sign flashes every 10 seconds. Ar a certain instant, the 2 signs flash at the same time. How many seconds elapse until the 2 sign next flash at the same time?
Answer» 6 7 14 20 Answer :D

Discussion

9.	If sum_(r=0)^(n){("^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))}^(3)=(25)/(24), then n is equal to
Answer» `3` `4` `5` `6` Solution :`(C )` LET `t_(r )=('^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))=(1)/(('^(n)C_(r ))/('^(n)C_(r-1))+1)=(1)/((n-r+1)/(r )+1)` `:.t_(r )=(r )/(n+1)` Now, `S=sum_(r=0)^(n){t_(r )}^(3)` `impliesS=sum_(r=0)^(n)(r^(3))/((n+1)^(3))=(1)/((n+1)^(3))sum_(r=0)^(n)r^(3)` `impliesS=(1)/((n+1)^(3)){(n(n+1))/(2)}^(2)impliesS=(n^(2))/(4(n+1))` Now, `S=(25)/(24)` (given) `:.n=5`

Discussion

10.	If int(x+1)/((x^(2)+x+1)sqrt(x^(2)+x+1))dx=(lambda)/(3)(x-1)/(sqrt(x^(2)+x+1))+C then lambda is equal to
Answer» ANSWER :`0.66`

Discussion

11.	Differentiate the functions (log x)^(cos x)
Answer» Answer :`(dy)/(dx)= (LOG X)^(COS x)`

Discussion

12.	2log x-log(x+1)-log(x-1)=
Answer» `X^(2)+(x^(4))/(2)+(x^(6))/(3)+…oo` `(1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+…oo` `-[(1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+….oo]` `(1)/(x^(2))+(1)/(x^(4))+(1)/(x^(6))+…oo` ANSWER :B

Discussion

13.	intxSecx tanx dx=
Answer» xSecx + log `\| TAN ((PI)/(2) + (x)/(2) ) \| + C ` xSecx - log `\| tan ((pi)/(2) + (x)/(2) ) \| + c ` xSecx - log `\| tan ((pi)/(4) + (x)/(2) ) \| + c ` xSecx + log `\| tan "" (x)/(2) \| + c ` ANSWER :C

Discussion

14.	Write the component statement "24 is multiple of 4 and 6 "compound statements and check whether the compound statement is true or false.
Answer» Solution :The component STATEMENT are p:24 is a multiple of 4 Q: 24 is a multiple of 6 The TRUTH value of the statement is .true.

Discussion

15.	Number of zero's at the ends ofprod _(n=5)^(30)(n)^(n+1)is :
Answer» 111 147 137 None ANSWER :C

Discussion

16.	Let A = R -{3} " and " B =R -{1}. " Then " f : A to B : f (x) = ((x-2))/((x-3)) is
Answer» ONE-one and into one -one and onto many-one and into many -one and onto Answer :B

Discussion

17.	The value of (P-Q) is equal to
Answer» 1 -1 `2^(50)` `2^(100)` ANSWER :A

Discussion

18.	The stationary point of f(x) = x^((3)/(5)) (4 -x) occurs at x=
Answer» a) `(3)/(2)` B) `(2)/(3)` C) 0 d) 4 Answer :A

Discussion

19.	underset(x to a)"Lt" (sqrt(a+2x)-sqrt(3x))/(sqrt(1+x^(2))-sqrt(1+x))=
Answer» `2/sqrt3` `1/sqrt3` `(-2)/(3SQRT3)` `(2)/(3sqrt3)` ANSWER :D

Discussion

20.	Evaluate the definite integrals int_(0)^(3)e^xdx
Answer»

Discussion

21.	Ifeither vector A,B,C of a triangle ABC are (1,2,3),(-1,0,0),(0,1,2), respectively , then find angleABC.[angleABC is the angle between the vectors vec(BA)andvec(BC)].
Answer» ANSWER :`COS^(-1)((10)/(SQRT(102)))`

Discussion

22.	If f(x)=(sin^(2)x-1)^(n) (2+cos^(2)x), then x = pi/2 is a point of
Answer» LOCAL MAXIMUM, if N is odd local MINIMUM, if n is odd local maximum, if n is even local minimum, if n is even Answer :A::D

Discussion

23.	int tan^(-1)(sqrt(x))dx=....
Answer» `(x+1)TAN^(-1)SQRT(x)-sqrt(x)+C` `XTAN^(-1)sqrt(x)- sqrt(x)+C` `sqrt(x)-xtan^(-1)sqrt(x)+C` `sqrt(x)-(x+1)tan^(-1)sqrt(x)+C` Answer :A

Discussion

24.	If f(x) is a real valued and differentaible function on R and f(x+y)=(f(x)+f(y))/(1-f(x)f(y)), then show that f'(x)=f'(0)[1+t^(2)(x)].
Answer» ANSWER :`F'(0)[1+t^(2)(X)].`

Discussion

25.	Evaluate the following integrals. int(1)/(4sin^(2)x+9cos^(2)x)dx
Answer» ANSWER :`(1)/(6)tan^(-1)((3)/(2)TANX)+C`

Discussion

26.	Number of different paths of shortest distance from A and B to in the grid which do not pass through M, is
Answer» `.^(11)C_(5)-.^(6)C_(3)` `262` `442` `.^(11)C_(5)-[.^(6)C_(3)xx.^(5)C_(2)]` SOLUTION :Total path.[number of paths passing through `M`] `= .^(11)C_(5)-[.^(6)C_(3)xx.^(5)C_(2)] = 462 - 20 xx 10 = 262`

Discussion

27.	If y=cos^(-1)((1-x^(2))/(1+x^(2))), then Statement I (dy)/(dx)=(2)/(1+x^(2)) for x"inR Statement II cos^(-1)((1-x^(2))/(1+x^(2)))={(2tan^(-1)x,,xle0,),(-2tan^(-1)x,,xlt0,):}
Answer» Both STATEMENT I and Statement II are CORRECT and Statement II is the correct EXPLANATION of Statement I Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I Statement I is correct but Statement II is incorrect Statement II is correct but Statement I is incorrect. Answer :D

Discussion

28.	A particle is fired straight up from the ground to each a height of x feet in t seconds, where x (t) =128t-16t^(2). (1) Compute the maximum height of the particle reached. (2) What is the velocity when the particle hits the ground ?
Answer» ANSWER : 256 TI, `-128` ft/s

Discussion

29.	If two vertices of a triangle are i-j and j+k , then the third vertex can be
Answer» i+k i-2j-k and -2i-j i-k all the above ANSWER :D

Discussion

30.	The table above shows the composition of a coed high school tennis team with a total of 40 members. A player who will be selected at random from the team will be selected at random from the ream will be given two free tickets will be given to either a female junior player or a male senior player?
Answer» `(1)/(8)` `(1)/(4)` `(2)/(5)` `(1)/(2)` Answer :C

Discussion

31.	int (x^(4) + x^(2) + 1)/(x^(2) - x +1)dx =
Answer» `(X^(5))/(5) + (x^(3))/(3)` + x + c `(x^(3))/(3) - (x^(2))/(2)` + x + c `(x^(3))/(3) - (x^(2))/(2)`+ c `(x^(3))/(3) + (x^(2))/(2)` + x + c ANSWER :D

Discussion

32.	int (x^(4))/(x^(2)+1)dx
Answer» ANSWER :`(X^(3))/(3)-x+tan^(-1)x+c`

Discussion

33.	For \|x\| lt 1/5, thecoefficient of x^(3) in the expansion of (1)/((1-5x)(1-4x)) is
Answer» 369 370 371 372 Answer :A

Discussion

34.	If Q_1 = Rs. 34.49 andQ_3 = Rs. 49.46 then find Q.D
Answer» ANSWER :RS. 7.48

Discussion

35.	Simplify x^(n-1)x^(2n)(x^(2-n))^(2)
Answer» SOLUTION :This is EQUAL to `X^(n-1)x^(2N)x^(4-2n)=x^(n-1+2n+4-2n)=x^(n+3)`.

Discussion

36.	Initially, the men and women in a room were in the ratio of 5:7. Six women leave the room. If there are 35 men in the room, how many women are left in the room?
Answer» ANSWER :43

Discussion

37.	int(e^x+e^(-x))/(e^x-e^(-x))dx
Answer» SOLUTION :`INT(e^x+e^(-x))/(e^x-e^(-x))DX` [put `(e^x+e^(-x)=t` then `(e^x+e^(-x)dx=dt)` `int(dt/t)=Inabst+C` =`(Inabs(e^x-e^(-x))+C`

Discussion

38.	Evaluation of definite integrals by subsitiution and properties of its : The value of alpha for which 4alphaint_(-1)^(2)e^(-alpha\|x\|)dx=5, is :
Answer» `log_(E)2` `log_(e)sqrt2` `log_(e)((4)/(3))` `log_(e)((3)/(2))` Answer :A

Discussion

39.	Find the mean of the Binomial distribution B(4, (1)/(3))
Answer» ANSWER :`(4)/(3)`

Discussion

40.	If tan beta =cos theta tan alpha then "cot"^(2)(theta)/2=
Answer» `(SIN (alpha+beta))/(sin (alpha-beta))` `(sin(alpha-beta))/(sin (alpha+beta))` `(COS (alpha+beta))/(cos (alpha-beta))` `(cos(alpha-beta))/(cos (alpha+beta))` ANSWER :A

Discussion

41.	If vec(u)=hati xx(vec(a)xx hati)+hatj xx(vec(a)xx hatj)+hatk xx(vec(a)xx hatk) then vec(u) = ………..
Answer» 0 `hati+hatj+hatk` `2vec(a)` `VEC(a)` ANSWER :C

Discussion

42.	If e^((sin^2x+sin^4x+sin^6x+..." upto" oo)In 2) satisfies the equation y^2-5y+4=0," then "(sin x)/(cos x-sin x) is equal to
Answer» `-(2+SQRT 2)` `-(sqrt 2+1)` `sqrt 2-1` `2+sqrt 2` ANSWER :A

Discussion

43.	A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant= kgt 0) . Find the time after which the cone is empty.
Answer» ANSWER :`t= H /K`

Discussion

44.	If (x^(4))/((x-1)(x-2)(x-3))= A.x+B. (1)/((x-1))+C (1)/((x-2))+D. (1)/((x-3))+E, then A+B+C+D+E=
Answer» -12 6 18 32 Answer :D

Discussion

45.	Integration of a binomialdifferential int(dx)/(x^(3)5sqrt(1+(1)/(x))).
Answer» Answer :`(5)/(4)(1+(1)/(X))^(4//5)-(5)/(9)(1+(1)/(x))^(9//5)+C.`

Discussion

46.	Statement1: If a line L touches the hyperbola x ^(2) - y ^(2)=a ^(2) at A then it can also intersect the hyperbola at some other point (s). Statement 2: Any line can intersect a second degree curve at maximum two points.
Answer» Stateme-1 is TRUE, Statement-2 is True, Statemetn-2 is CORRECT EXPLANATION for Statement-1 Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1 Statement-1 is True, Statement-2 is False Statement-1 is False, Statement-2 is ture Answer :D

Discussion

47.	Two parabolas have the same vertex and equal lenghof latus rectum such that their axes are at right angle. Prove that the common tangents touch each at the end of latus rectum.
Answer» Answer :COMMON tangent to the PARABOLA touches the parabola cut `L'= (-2a,a)`

Discussion

48.	i. How many 4 digit number can be formed using the digits 3, 5, 8, 9 if repetition is not allowed? ii. How many of these numbers end in 3? iii. How many of the above numbers mentioned in (i) ends in 3 or 5?
Answer» <P> Answer :i. `""^(4)P_(4)=4! =24` II. `""^(3)P_(3)xx1=3! =6` III. 12

Discussion

49.	If vec(a) = (1,2,3), vec(b) = (2,-1,1), vec(c ) = (3,2,1) and vec(a) xx (vec(b) xx vec(c )) = alpha vec(a) + beta vec(b) + gamma vec(c ), then
Answer» `alpha =1, beta = 10, gamma=3` `alpha = 0, beta = 10, gamma= -3` `alpha + beta + gamma = 8` `alpha = beta = gamma = 0` Answer :B

Discussion

50.	Let ** be a binary operation on the set Q of rational numbers as follows : a "*" b = (a-b)^(2) Find which of the binary operations are commutative and which are associative.
Answer» SOLUTION :N/A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Match the following :

If x ^(2) +bx+b is a factor of x ^(3) +2x ^(2)+2x + c (c ne 0), then b+c is :

If x+(1//x)=2cos(pi//10), then x^5+(1//x^5)=

Two persons A, B have to speak at a function with 10 other persons. If the persons speak at random order, the probability that A speaks immediately before B is

From where did the Dewan get 100th tiger?

A rod 25 ft. Long always has its ends A and B on the X-andY-axes respectively .If A is at 15 ft.from the origin and is moving at the rate of 0.2 ft. //sec, then the area of the triangle formed by the rod with axes is changing at the rate of

sin^(-1)(1-x)-2sin^(-1)x= pi/2,then find x

One cautions sign flashes evergy 4 second, and another caution sign flashes every 10 seconds. Ar a certain instant, the 2 signs flash at the same time. How many seconds elapse until the 2 sign next flash at the same time?

If sum_(r=0)^(n){("^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))}^(3)=(25)/(24), then n is equal to

If int(x+1)/((x^(2)+x+1)sqrt(x^(2)+x+1))dx=(lambda)/(3)(x-1)/(sqrt(x^(2)+x+1))+C then lambda is equal to

Differentiate the functions (log x)^(cos x)

2log x-log(x+1)-log(x-1)=

intxSecx tanx dx=

Write the component statement "24 is multiple of 4 and 6 "compound statements and check whether the compound statement is true or false.

Number of zero's at the ends ofprod _(n=5)^(30)(n)^(n+1)is :

Let A = R -{3} " and " B =R -{1}. " Then " f : A to B : f (x) = ((x-2))/((x-3)) is

The value of (P-Q) is equal to

The stationary point of f(x) = x^((3)/(5)) (4 -x) occurs at x=

underset(x to a)"Lt" (sqrt(a+2x)-sqrt(3x))/(sqrt(1+x^(2))-sqrt(1+x))=

Evaluate the definite integrals int_(0)^(3)e^xdx

Ifeither vector A,B,C of a triangle ABC are (1,2,3),(-1,0,0),(0,1,2), respectively , then find angleABC.[angleABC is the angle between the vectors vec(BA)andvec(BC)].

If f(x)=(sin^(2)x-1)^(n) (2+cos^(2)x), then x = pi/2 is a point of

int tan^(-1)(sqrt(x))dx=....

If f(x) is a real valued and differentaible function on R and f(x+y)=(f(x)+f(y))/(1-f(x)f(y)), then show that f'(x)=f'(0)[1+t^(2)(x)].

Evaluate the following integrals. int(1)/(4sin^(2)x+9cos^(2)x)dx

Number of different paths of shortest distance from A and B to in the grid which do not pass through M, is

If y=cos^(-1)((1-x^(2))/(1+x^(2))), then Statement I (dy)/(dx)=(2)/(1+x^(2)) for x"inR Statement II cos^(-1)((1-x^(2))/(1+x^(2)))={(2tan^(-1)x,,xle0,),(-2tan^(-1)x,,xlt0,):}

A particle is fired straight up from the ground to each a height of x feet in t seconds, where x (t) =128t-16t^(2). (1) Compute the maximum height of the particle reached. (2) What is the velocity when the particle hits the ground ?

If two vertices of a triangle are i-j and j+k , then the third vertex can be

The table above shows the composition of a coed high school tennis team with a total of 40 members. A player who will be selected at random from the team will be selected at random from the ream will be given two free tickets will be given to either a female junior player or a male senior player?

int (x^(4) + x^(2) + 1)/(x^(2) - x +1)dx =

int (x^(4))/(x^(2)+1)dx

For |x| lt 1/5, thecoefficient of x^(3) in the expansion of (1)/((1-5x)(1-4x)) is

If Q_1 = Rs. 34.49 andQ_3 = Rs. 49.46 then find Q.D

Simplify x^(n-1)*x^(2n)*(x^(2-n))^(2)

Initially, the men and women in a room were in the ratio of 5:7. Six women leave the room. If there are 35 men in the room, how many women are left in the room?

int(e^x+e^(-x))/(e^x-e^(-x))dx

Evaluation of definite integrals by subsitiution and properties of its : The value of alpha for which 4alphaint_(-1)^(2)e^(-alpha|x|)dx=5, is :

Find the mean of the Binomial distribution B(4, (1)/(3))

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

If vec(u)=hati xx(vec(a)xx hati)+hatj xx(vec(a)xx hatj)+hatk xx(vec(a)xx hatk) then vec(u) = ………..

If e^((sin^2x+sin^4x+sin^6x+..." upto" oo)In 2) satisfies the equation y^2-5y+4=0," then "(sin x)/(cos x-sin x) is equal to

A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant= kgt 0) . Find the time after which the cone is empty.

If (x^(4))/((x-1)(x-2)(x-3))= A.x+B. (1)/((x-1))+C (1)/((x-2))+D. (1)/((x-3))+E, then A+B+C+D+E=

Integration of a binomialdifferential int(dx)/(x^(3)5sqrt(1+(1)/(x))).

Statement1: If a line L touches the hyperbola x ^(2) - y ^(2)=a ^(2) at A then it can also intersect the hyperbola at some other point (s). Statement 2: Any line can intersect a second degree curve at maximum two points.

Two parabolas have the same vertex and equal lenghof latus rectum such that their axes are at right angle. Prove that the common tangents touch each at the end of latus rectum.

i. How many 4 digit number can be formed using the digits 3, 5, 8, 9 if repetition is not allowed? ii. How many of these numbers end in 3? iii. How many of the above numbers mentioned in (i) ends in 3 or 5?

If vec(a) = (1,2,3), vec(b) = (2,-1,1), vec(c ) = (3,2,1) and vec(a) xx (vec(b) xx vec(c )) = alpha vec(a) + beta vec(b) + gamma vec(c ), then

Let ** be a binary operation on the set Q of rational numbers as follows : a "*" b = (a-b)^(2) Find which of the binary operations are commutative and which are associative.

Simplify x^(n-1)x^(2n)(x^(2-n))^(2)