28278 + Interview Questions in Maths in Class 12

1.	Evaluate. I = int _(0) ^(1) 2 sin (pt) sin (qt) dt. If : p & q are different roots of the equation, tan x = x.
Answer» ANSWER :g (x) is cont. in `-2,2);g (x)` is diff. `at x =1 ` & not diff. at `x =0.` Not that `; g (x) = [{:(-(x+2), "for", -2 le x le 0),( -2 + x - (x ^(2))/(2) , "for" , 0 lt x lt 1), ((x ^(2))/(2)x-1, "for" , 1 le x le 2):}`

Discussion

2.	Evaluate the following integrals. int(sinxcosx)/(cso^(2)x+3cosx+2)dx
Answer» ANSWER :`LOG\|(cosx+1)/((cosx+2)^(2))\|+C`

Discussion

3.	If A = (1,-2, -1), B = (4, 0, -3) C = (1,2, - 1) and D = (2, -4, -5) then the distance between AB and CD is
Answer» `2//3` `4//2` `3//2` `5//3` ANSWER :B

Discussion

4.	Examine the continuity of the function f(x)= 2x + 3 " at " x=1
Answer» ANSWER :x=1

Discussion

5.	If alpha,beta,gamma are roots of x^(3)-5x^(2)+3=0 then value of \|(alphabeta+4+2alpha-2beta)(gamma-2)\|is
Answer» ANSWER :`9.00`

Discussion

6.	If 3(y-5)=33, then y+4 ?
Answer» 6 `12 2/3` 16 20 Answer :D

Discussion

7.	ABCD is a square and one of its sides AB is also a chord of the circle as shown in the figure. What is the area of the square?
Answer» 3 9 12 18 Answer :D

Discussion

8.	Find the area bounded by y=e^x,y=0,x=4,x=2
Answer» SOLUTION :AREA = `int_2^4e^xdx=[e^x]_2^4=e^4-e^2`

Discussion

9.	The radical centre of the circles x^2+y^2=9, x^2+y^2-2x-2y-5=0 , x^2+y^2+4x+6y-19=0 is
Answer» (0,0) (1,1) (2,2) (3,3) ANSWER :B

Discussion

10.	If(x -4 ) /(x ^ 2- 5x- 2 k )=(2)/(x - 2 )- (1)/(x+ k ) , then k isequalto
Answer» `- 3 ` ` -2 ` `2 ` `3` Solution : ` (x-4 ) /(x ^ 2 - 5x- 2 K)=(2 ) /(x - 2 )- (1)/(x +k ) ` ` RARR(x -4 )/( x ^ 2- 5x - 2k )=(2 (x +k )-(x- 2 ))/((x - 2 )(x + k) ) ` `rArr(x - 2)(x +k)=x ^ 2- 5x- 2 k` `thereforex- 2`isfactorof` x ^ 2-5 x -2k` `therefore(2) ^ 2 -5 (2)- 2k=0 ` ` 4 - 10- 2k= 0 ` `2k=-6 ` ` k=- 3 `

Discussion

11.	Write cot^(-1)(1/(sqrt(x^(2)-1))),xgt1 in the simplest form.
Answer» ANSWER :`SEC^(-1)X`

Discussion

12.	The scores on the SAT math test havea normal distribution with an overall mean of about 500 and standard deviation of 100 for all test takers . Jamal earned a score of 600 for his SAT maths test. Approximatelywhat percentage of test takers earned a higher score ?
Answer» 2.5 5 16 32 Answer :C

Discussion

13.	Let f : R rarr R, such that f'(0) = 1 and f(x + 2y) = f(x) + f(2y) + e^(x + 2y)(x + 2y) - x.e^(x) - 2y.e^(2y) + 4xy, AA x, y in R. Find f(x).
Answer» ANSWER :`F(X) = x^(2) + x.e^(x)`

Discussion

14.	By using the properties of definite integrals, evaluate the integrals int_(-5)^(5)(x+2)dx
Answer»

Discussion

15.	Let S_(1) and S_(2) denote the circles x^(2)+y^(2)+10x - 24y - 87 =0 and x^(2) +y^(2)-10x -24y +153 = 0 respectively. The value of a for which the liney = ax contains the centre of a circle which touches S_(2) externally and S_(1) internally is
Answer» `+-(3)/(10)` `+-(1)/(5)` `+-(SQRT(13))/(10)` `+-(10)/(13)` Solution :`S_(1): C_(1) (-5,12), r_(1) = 16` `S_(2): C_(2) (5,12), r_(2) =4` `C_(1)C_(2) = r +4` (where C is the centre of circle TOUCHING `C_(2)` externally and `C_(1)` INTERNALLY) `C C_(1) = 16 -r` (Not `r -16, :' S_(2)` is contained by `S_(1))` `rArr C C_(1) + C C_(2) = 20` `:.` Locus of C is the ellipse with foci at `C_(1)` and `C_(2)` and LENGTH of major axis= 20 `:.` Locus of C is `(x^(2))/(100) = ((y-12)^(2))/(75) =1` (i) According to question `y = ax` is tangent to the ellipse from (0,0). Equation of tangent having slope m to (i) is `y - 12 = mx +- sqrt(100 m^(2) + 75)` But this is passing through (0,0) `rArr - 12 =- sqrt(100 m^(2) + 75)` `rArr m^(2) = (69)/(100)` `rArr a = +- (sqrt(13))/(10)`

Discussion

16.	If y_(1),y_(2) are the ordinates of two points P and Q on the parabola and y_(3), is the ordinate of the point of intersection of tangents at P and Q, then
Answer» `y_(1), y_(2),y_(3)` are in A.P `y_(1),y_(3),y_(3)` are in A.P. `y_(1),y_(2),y_(3)` are in G.P `y_(1),y_(3),y_(2)` are in G.P Answer :B

Discussion

17.	Consider the vectorsoversetrarra=2overset^^i-3overset^^j+overset^^k"and"oversetrarrb = overset^^i+overset^^j-2overset^^k. Find the projection of oversetrarra "on"oversetrarrb
Answer» Solution :The projection of `veca "on" VECB "is" (veca.vecb)/(\|vecb\|)` `=(-3)/SQRT6=(-3)/(sqrt2 SQRT3)=-sqrt(3//2)`

Discussion

18.	Three friends whose ages form a G.P. divide a certain sum of money in proportion to their ages. If they do that three years later, when the youngest is half the age of the oldest, then he will receive 105 rupees more that he gets now and the middle friend will get 15 rupees more that he gets now, then find the ages of the friends
Answer» ANSWER :`12,18,27`

Discussion

19.	The order, degree of the differential equation of all circles of radius r, having centre on y-axis passing through the origin is (where r is arbitrary constant)
Answer» 1,1 2,1 3,1 4,2 Answer :A

Discussion

20.	Let f(x)=(x)/(1+x^(2)) and g(x)=(e^(-x))/(1+\|x\|) (where [.] denote greatest integer function), then
Answer» DOM `(f+g)=R~[-2,0)` dom `(f+g)=R~[-1,0)` range `f nn` range `g=[-2,1//2]` range `f nn` range `g=[-(1)/(2),(1)/(2)]~{0}` Answer :A::B::C

Discussion

21.	Find the angle between the circles given by the equations x^(2)+y^(2)+6x-10y-135=0, x^(2)+y^(2)-4x+14y-116=0
Answer» ANSWER :`(-1)/2`

Discussion

22.	Find the vector equation of a plane which is at a distance 11 units from the origin and which is normal to the2 hati-2hatj+k.
Answer» ANSWER :`VECR.(2hati-2hatj+hatk)=33`

Discussion

23.	m tan (theta-30)=n tan (theta+120) then (m+n)/(m-n)=
Answer» `COS 2 THETA` `2 cos 2 theta` `sin 2 theta` `2 sin 2 theta` Answer :B

Discussion

24.	Select the correct answer : cos^-1 (1/2) +2sin^-1(1/2)
Answer» `2π/3` `3π/4` `π/4` `π/3` ANSWER :A

Discussion

25.	int_(0.2)^(3.5)[x]dx is equal to
Answer» 1)4 2)`4.5` 3)`3.5` 4)3 Answer :B

Discussion

26.	If sum_(i=0)^(2015) sum_(i=0)^(2015) C_(j)=k, then the value of (k+2)^(1//2016) is where (""^(n)C_(r) =0 AA n lt r & ""^(0)C_(0) =0}
Answer» SOLUTION :`sum_(J=0)^(2015) sum_(i=0)^(2015) ""^(i)C_(j) = sum_(j=0)^(2015) [""^(0)C_(j) + ""^(1)C_(j) + ""^(2)C_(j) + ""^(3)C_(j) +……..+""^(2015)C_(j)]` `2^(1) + 2^(2) + 2^(3) +……….. + 2^(2015)` `=2(2^(2015)-1) =k` `=2^(2016) -2 =k rArr (k+2)^(1/2016) =2`

Discussion

27.	Integrate the rational functions (3x-1)/((x+2)^(2))
Answer» ANSWER :`3log\|x+2\|+(7)/((x+2))+C`

Discussion

28.	Solve the differential equation : (1 - x^(2)) (dy)/(dx) - xy = x
Answer» ANSWER :`(1 + y) SQRT(1 - X^(2)) = A `

Discussion

29.	Find the coefficient of x^11 in (2x^2 + (3)/(x^3))^13
Answer» ANSWER :`286 XX 2^10 xx 3^3`

Discussion

30.	The mean and standard deviation of a random variable X are 10 and 5 respectively. Match the following.
Answer» `(i) : (Q), (ii) : (R ), (III) : (p), (IV) : (s) ` `(i) : (r ), (ii) : (q), (iii) : (s), (iv) : (p)` `(i) : (r ), (ii) : (q), (iii) : (p), (iv) : (s) ` `(i) : (p), (ii) : (q), (iii) : (r ), (iv) : (s) ` ANSWER :C

Discussion

31.	A fair coin is tossed 99 times. If X is the number of times tail occurs, then P(X=r) is maximum where r is given by
Answer» 49 51 50 None of these Answer :A::C

Discussion

32.	Find square root of 4ab -2(a^2-b^2) sqrt(-1)
Answer» SOLUTION :`4av-2(a^2-b^2)SQRT(-1)` `=(a+b)^2-(a-b)^2-2(a^2-b^2)i` `=(a+b)^2+(a-b)^2i^2-2(a+b)(a-b)i` `=(a+b)-i(a-b)^2` `:. Sqrt(4ab-2(a^2-b^2)sqrt(-1))` `= +-[(a+b)-i(a-b)]`

Discussion

33.	Determaine the approximate value of(correct to 3 places of decimals).
Answer» ANSWER :5.004

Discussion

34.	If the difference of the accentric angles of two points P and Q on the ellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is (pi)/(2) and R is the point of intersection of tangents of P and Q then POQR is necessarily (where O is the origin) a
Answer» rectangle parallelogram cyclic quadrilateral square Answer :B

Discussion

35.	Find a if the vectors vecx=2hati-3hatj+4hatk and vecy=ahati+6hatj-8hatk are collinear?
Answer» 4 `-4` 2 `-2` ANSWER :B

Discussion

36.	Let A, B and C be three non-empty sets. Suppose f : A to Band g : B to C. Then which of the following is not true?
Answer» if G o F is one-to-one, then/is one-to-one if g of is ONTO, then g is onto if g o f is one-to-one and onto, then/is one-to-one and onto if f is one-to-one and g is one-to-one, then g . F is one-to-one Answer :A

Discussion

37.	Matrix[{:(0,5,-7),(-5,0,11),(7,-11,0):}]is a ..... matrix.
Answer» SKEW symmetric Symmetric Diagonal Zero Answer :A

Discussion

38.	The value of c in Lagrange's Mean Value theorem for the function f(x) = x + (1)/(x) ,I n[1,4] is
Answer» `-2` 3 2 `(7)/(2)` ANSWER :C

Discussion

39.	The smallest positive integer value of x satisfyingx/4 le (5x-2)/(3) - (7x-3)/(5) is
Answer» 2 4 3 5 Answer :D

Discussion

40.	If H is the orthocentre of Delta ABC, then AH=
Answer» COS A R cos A 2 R cos A None ANSWER :C

Discussion

41.	Let f':N rarr Rbe a function defined as f'(x) = 4x^(2) + 12x + 15 . Show that f:N rarrS , where, S is the range of f, is invertible. Find the inverse of f.
Answer» SOLUTION :N/A

Discussion

42.	The smallest value of the polynomial x^(3)-18x^(2)+96x in [0, 9] is …………..
Answer» 126 0 135 160 Answer :B

Discussion

43.	The probability that a boy A will get a scholarship is 0.9 and that another boy B will get is 0.8. What is the probability that atleast one of them will get the scholarship?
Answer» ANSWER :`0.98`

Discussion

44.	If the roots of x^(4) - 8x^(3) + 14x^(2) + 8x - 15 = 0are in A.P then the roots are
Answer» `-1, 1, 3, 5` 1,1, -3, -5 1/2, 1/2, -6 `-2` 1/2 ,3 Answer :1

Discussion

45.	Let A,B and I (identity matrix) be the matrices of order 4 such that A=[a_(I)]_(4xx4)'where a_(lj){{:(0 if i = j),(1 if i ne j):}and A =B -I{:(,"Column-I",,"Column-II"),((A),\|B\|=,,(P)4),((B),\|B^(2)-4B+I\|=,,(Q)0),((C),-4+\|B^(3)+B^(2)-8B\|=,,(R)-1),((D),-1+\|A^(-1)+I\|"is greater than",,(S)-4),(,,,(T)1):}
Answer» SOLUTION :`A=[(0,1,1,1),(1,0,1,1),(1,1,0,1),(1,1,1,0)]""&""B=[(1,1,1,1),(1,1,1,1),(1,1,1,1),(1,1,1,1)]`

Discussion

46.	If A denotes the area bounded by f(x)=\|("sin"x + "cos"x)/(x)\|, X-axis, x=pi and x=3 pi,then
Answer» `1 LT A lt 2` `0 lt A lt 2` `2 lt A lt 2` None of these Answer :B

Discussion

47.	Given that p(x_(1),y_(1)) is interior point of the circle S=x^(2)+y^(2)+2gc+2fy+c=0 I: Polar of P and tangent at P coincide II: Polar of P exists, chord of contact of P does not exist. Which of the following is correct?
Answer» I is TRUE , II is true I is false , II is false I is false, II is true I is true, II is false. Answer :C

Discussion

48.	Find the area bounded by the curve x=y^2 and the straight lines x = 0, y = 1.
Answer» SOLUTION :

Discussion

49.	Integration by partial fraction : int (x)/(x^(4)-1)dx=...
Answer» `(1)/(4)LOG[(X^(2)-1)/(x^(2)+1)]+c` `(1)/(4)log[(x^(2)+1)/(x^(2)-1)]+c` `(1)/(2)log[(x^(2)-1)/(x^(2)+1)]+c` `(1)/(2)log[(x^(2)+1)/(x^(2)-1)]+c` ANSWER :A

Discussion

50.	IF thereare 6periodsin eachworkingdayof a school, thenthe numberof waysthatyou canarrange5subjectstheworkingdayis
Answer» ANSWER :1800

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Evaluate. I = int _(0) ^(1) 2 sin (pt) sin (qt) dt. If : p & q are different roots of the equation, tan x = x.

Evaluate the following integrals. int(sinxcosx)/(cso^(2)x+3cosx+2)dx

If A = (1,-2, -1), B = (4, 0, -3) C = (1,2, - 1) and D = (2, -4, -5) then the distance between AB and CD is

Examine the continuity of the function f(x)= 2x + 3 " at " x=1

If alpha,beta,gamma are roots of x^(3)-5x^(2)+3=0 then value of |(alphabeta+4+2alpha-2beta)(gamma-2)|is

If 3(y-5)=33, then y+4 ?

ABCD is a square and one of its sides AB is also a chord of the circle as shown in the figure. What is the area of the square?

Find the area bounded by y=e^x,y=0,x=4,x=2

The radical centre of the circles x^2+y^2=9, x^2+y^2-2x-2y-5=0 , x^2+y^2+4x+6y-19=0 is

If(x -4 ) /(x ^ 2- 5x- 2 k )=(2)/(x - 2 )- (1)/(x+ k ) , then k isequalto

Write cot^(-1)(1/(sqrt(x^(2)-1))),xgt1 in the simplest form.

The scores on the SAT math test havea normal distribution with an overall mean of about 500 and standard deviation of 100 for all test takers . Jamal earned a score of 600 for his SAT maths test. Approximatelywhat percentage of test takers earned a higher score ?

Let f : R rarr R, such that f'(0) = 1 and f(x + 2y) = f(x) + f(2y) + e^(x + 2y)(x + 2y) - x.e^(x) - 2y.e^(2y) + 4xy, AA x, y in R. Find f(x).

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

Let S_(1) and S_(2) denote the circles x^(2)+y^(2)+10x - 24y - 87 =0 and x^(2) +y^(2)-10x -24y +153 = 0 respectively. The value of a for which the liney = ax contains the centre of a circle which touches S_(2) externally and S_(1) internally is

If y_(1),y_(2) are the ordinates of two points P and Q on the parabola and y_(3), is the ordinate of the point of intersection of tangents at P and Q, then

Consider the vectorsoversetrarra=2overset^^i-3overset^^j+overset^^k"and"oversetrarrb = overset^^i+overset^^j-2overset^^k. Find the projection of oversetrarra "on"oversetrarrb

The order, degree of the differential equation of all circles of radius r, having centre on y-axis passing through the origin is (where r is arbitrary constant)

Let f(x)=(x)/(1+x^(2)) and g(x)=(e^(-x))/(1+|x|) (where [.] denote greatest integer function), then

Find the angle between the circles given by the equations x^(2)+y^(2)+6x-10y-135=0, x^(2)+y^(2)-4x+14y-116=0

Find the vector equation of a plane which is at a distance 11 units from the origin and which is normal to the2 hati-2hatj+k.

m tan (theta-30)=n tan (theta+120) then (m+n)/(m-n)=

Select the correct answer : cos^-1 (1/2) +2sin^-1(1/2)

int_(0.2)^(3.5)[x]dx is equal to

If sum_(i=0)^(2015) sum_(i=0)^(2015) C_(j)=k, then the value of (k+2)^(1//2016) is where (""^(n)C_(r) =0 AA n lt r & ""^(0)C_(0) =0}

Integrate the rational functions (3x-1)/((x+2)^(2))

Solve the differential equation : (1 - x^(2)) (dy)/(dx) - xy = x

Find the coefficient of x^11 in (2x^2 + (3)/(x^3))^13

The mean and standard deviation of a random variable X are 10 and 5 respectively. Match the following.

A fair coin is tossed 99 times. If X is the number of times tail occurs, then P(X=r) is maximum where r is given by

Find square root of 4ab -2(a^2-b^2) sqrt(-1)

Determaine the approximate value of(correct to 3 places of decimals).

If the difference of the accentric angles of two points P and Q on the ellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is (pi)/(2) and R is the point of intersection of tangents of P and Q then POQR is necessarily (where O is the origin) a

Find a if the vectors vecx=2hati-3hatj+4hatk and vecy=ahati+6hatj-8hatk are collinear?

Let A, B and C be three non-empty sets. Suppose f : A to Band g : B to C. Then which of the following is not true?

Matrix[{:(0,5,-7),(-5,0,11),(7,-11,0):}]is a ..... matrix.

The value of c in Lagrange's Mean Value theorem for the function f(x) = x + (1)/(x) ,I n[1,4] is

The smallest positive integer value of x satisfyingx/4 le (5x-2)/(3) - (7x-3)/(5) is

If H is the orthocentre of Delta ABC, then AH=

Let f':N rarr Rbe a function defined as f'(x) = 4x^(2) + 12x + 15 . Show that f:N rarrS , where, S is the range of f, is invertible. Find the inverse of f.

The smallest value of the polynomial x^(3)-18x^(2)+96x in [0, 9] is …………..

The probability that a boy A will get a scholarship is 0.9 and that another boy B will get is 0.8. What is the probability that atleast one of them will get the scholarship?

If the roots of x^(4) - 8x^(3) + 14x^(2) + 8x - 15 = 0are in A.P then the roots are

If A denotes the area bounded by f(x)=|("sin"x + "cos"x)/(x)|, X-axis, x=pi and x=3 pi,then

Given that p(x_(1),y_(1)) is interior point of the circle S=x^(2)+y^(2)+2gc+2fy+c=0 I: Polar of P and tangent at P coincide II: Polar of P exists, chord of contact of P does not exist. Which of the following is correct?

Find the area bounded by the curve x=y^2 and the straight lines x = 0, y = 1.

Integration by partial fraction : int (x)/(x^(4)-1)dx=...

IF thereare 6periodsin eachworkingdayof a school, thenthe numberof waysthatyou canarrange5subjectstheworkingdayis