28278 + Interview Questions in Maths in Class 12

1.	Let f(x)=[2^(-x^(2))[2x^(2)]],x epsilon R ( [ ] denotes the greatest integer function). Let x_(1)=0,x_(2)=log_(2)3 and x_(3)=sqrt(2). Suppose 0ltx_(4)lt1. Delta=\|(f(x_(1)),f(x_(2)),f(x_(3))),(f(x_(4)),f(x_(4)),f(x_(2))),(f(x_(2)),f(x_(3)),f(x_(1)))\| then Delta is equal to
Answer» `-1` `0` `1` `2log_(2)^(3)` Answer :B

Discussion

2.	If int (1)/(3 sin x + 4 cos x ) " dx = a log"\|(b +2 tan""(x)/(2))/(c - tan""(x)/(2)) \| + Kthen (a, b , c) =
Answer» `((1)/(5), - 1, -4)` `((1)/(5), 1, -4)` `( 5, 1, -(1)/(4) )` `((1)/(5), 1,2 )` ANSWER :D

Discussion

3.	If n(A)=10,n(B)=6 and n( C )=5 for three disjoint sets A, B, C then n(A uu B uu C) equals
Answer» 21 11 1 9 Answer :A

Discussion

4.	Find int(sinx)/(sin(x-a))dx
Answer» ANSWER :`COS a(x+a)-SIN a log\|sin(x+a)\|+C`

Discussion

5.	Match the following. {:("I." 1+(1)/(3) + (1.3)/(3.6) + (1.3.5)/(3.6.9) +…....=, "a)" sqrt2),("II." 1+ (1)/(4) + (1.3)/(4.8) + (1.3. 5) /(4.8.12)=, "b)" 2 sqrt2),( "III." 1+(2)/(6) + (2.5)/(6.12) + (2.5.8)/(6.12.18)+…...=, "c)" sqrt3),( "IV." 1+(3)/(4) + (3.5)/(4.8) + (3.5.7)/(4.8.12)+........=, "d)" root(3)(4)):}
Answer» a, b, C, d d, c, b, a a, c, d, b c, a, d, c Answer :D

Discussion

6.	Let f(x) be a differentiable function satisfying f(x)+f(x+(1)/(2))=f(x),AA x in R and g (x) =int_(0)^(x)f (t) dt . If g(1)=1, then the value ofsum_(n=2)^(infty)((8)/(sum_(k=1)^(n)(g(x+k^(2))-g(x+k)))) is
Answer» ANSWER :`=6`

Discussion

7.	Integrate the following functions : int(2^(x))/(sqrt(1-4^(x)))dx
Answer» Answer :`log_(2)^(E)SIN^(-1)(2x)+C`

Discussion

8.	The modulus of (sqrt(3)+i)/((1+i)(1+sqrt(3)i)) is
Answer» 1 `1//2` `SQRT(2)` `1//sqrt(2)` ANSWER :D

Discussion

9.	If the points (x,y) are equidistant from the points (a+b,b-a) and (a-b,a+b),prove that bx = ay.
Answer» Solution : GIVEN that `bar(AP) = bar(BP)` `therefore SQRT((x-a-b)^2 + (y-b+a)^2)` , = `sqrt((x-a+b)^2 + (y-b+a)^2)` or, `x^2 + a^2 + b^2 -2ax + 2ab - ABX + y^2 +b^2 + a^2 -2by-2ab-2ay` = `x^2 + a^2 + b^2 -2ax-2ab-2by` or, 4bx = 4ay or, bx = ay .

Discussion

10.	The sides of a square are x=4, x=7, y=1, y=4. Then theequation of the circumcircle of the square is
Answer» `X^(2)+y^(2)-11x-5y+32=0` `x^(2)+y^(2)-11x-5y+7=0` `x^(2)+y^(2)-6x-5y+7=0` `x^(2)+y^(2)-5x-2y+15=0` ANSWER :A

Discussion

11.	Iff (x) =x ( x-1) (x-2) , 0 le x le 4and the poind xi satisfies mean values theorem for f (x), then
Answer» `lt xi lt 1` `xi gt 3` `lt xi lt 1/2` `1 lt xi lt 3` ANSWER :B

Discussion

12.	Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4r)/(3).
Answer» ANSWER :`= R(1+(1)/(3))=(4R)/(3)`

Discussion

13.	A set A has 3 elements and another set B has 6 elements. Then
Answer» `3 LE N(A uu B)le 6` `3le n(A uu B)le 9` `6le n(A uu B)le9` `0LE n(A uu B)le 9` Answer :C

Discussion

14.	A five digited number is written at random. Find the probability that the number written is such that when the digits are put in reverse order, the new number is also a five digited number equal to the original number.
Answer» ANSWER :0.01

Discussion

15.	If the pair of straight lines given by A x^(2) + 2 H xy + By^(2) = 0 (H^(2) gt AB) forms an equilateral triangle with line ax + by + c = 0 then (A + 3 B) ( 3 A + B) is equal to
Answer» `H^(2)` `- H^(2)` `2 H^(2)` `4 H^(2)` ANSWER :D

Discussion

16.	Let f(x) ={{:(min{x,x^(2)},x le 0),(max {2x","x^(2)-1},xlt0):}thenwhichof the followingis not true ?
Answer» F(X)is continuousat x=0 f(x)is notdifferentiable at x=1 f(x)is notdifferentiableat EXACTLY THREE points noneof these Answer :D

Discussion

17.	(i) Obtain the probability that the birth days of seven people will fall on seven different days of the week, assuming equal probabilities for the seven days. (ii) What is the probability that the birth days of twelve people will fall in twelve different months (assume equal probabilites of the twelve months)
Answer» ANSWER :`(i) (7!)/(7^(7))` `(II) (12!)/(12^(2))`

Discussion

18.	A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force vecF=(30N)hati-(40N)hatj to the cart as it undergoes a displacement vecs=(9.0m)hati-(3.0m)hatj. How much work does the forces you apply do on the grocery cart ?
Answer» `150 J` `390 J` `-150 J` `270 J` SOLUTION :Work= `vecF.vecS=(30xx9)+(40xx3)=390J"""]"`

Discussion

19.	Find the values of the following integrals int(1)/(1+sinx)dx
Answer» ANSWER :`tanx-secx+c`

Discussion

20.	A natural number x is chosen at random from the first 100 natural numbers. Find the probability that ((x-20)(x-40))/((x-30)) lt 0
Answer» ANSWER :`(7)/(25)`

Discussion

21.	Sides AB and AC in an equilateraltriangle ABC with side length 3 is extended to form two rays from point A as shown in the figure. Point P is chosen outside the triangle ABC and between the two rays such that angleABP+angleBCP=180^(@). If the maximum length of CP is M, then M^(2)//2 is equal to :
Answer» ANSWER :6

Discussion

22.	The points of contact of the tangents drawn from the point (4, 6) to the parabola y^(2) = 8x
Answer» (2, 4), (18, 12) (2, 4), (8, 8) (8,8) (18,12) (0,0) `(1,2sqrt(2))` ANSWER :B

Discussion

23.	If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n), then prove that a_(1)+a_(3)+a_(5)+….+a_(2n-1)=(3^(n)-1)/(2)
Answer» `(3^n +1)/(2)` `(3^(n)-1)/(2)` `(3^(n+1))/(2)` `(2^(n-1))/(2)` ANSWER :B

Discussion

24.	Discuss the continuity of the following functions: f(x)=sinx.cosx
Answer» Solution :SIN x and COS x are CONTINUOUS functions SINCE product of continuous functions is continuous, F is continuous

Discussion

25.	Match the column I (the curve 2y^2 = x + 1) with column II (the slope of normals)
Answer» `(A)-2,(B)-4,(C )-3,(D )-1` `(A)-2,(B)-5,(C )-3,(D )-1` `(A)-2,(B)-3,(C )-5,(D )-1` `(A)-2,(B)-5,(C )-1,(D )-3` Answer :B

Discussion

26.	The radius of the circle which touches x^(2) +y^(2) -6x + 6y +17=0
Answer» ` SQRT 2-1 ` `4sqrt2 -1` ` 3sqrt2 -1` `3sqrt2 +1` ANSWER :C

Discussion

27.	One of the partitions of the set {1,2,5,x,y,sqrt(2),sqrt(3)} is
Answer» `{{1,2,X},(x,5,y},{sqrt(2),sqrt(3)}}` `{{1,2,sqrt(2)},{x,y,sqrt(2)},{5,sqrt(2),sqrt(3)}}` `{{1,2},{5,x},{sqrt(2),sqrt(3)}}` `{{1,2,5},{x,y},{sqrt(2),sqrt(3)}}` ANSWER :D

Discussion

28.	Evaluate the following determinants. [[2,-3],[1,-4]]
Answer» SOLUTION :`[[2,-3],[1,-4]]`=-8+3=-5

Discussion

29.	Find the equation of the circle with centre C and radius r where C = ( cos alpha , sin alpha ) , r= 1
Answer» ANSWER :` x^(2) + y ^(2) -2X COS alpha - 2y SIN alpha =0) `

Discussion

30.	If f(1)=1 and f'(1)=2 then lim_(xto1)((f(x))^(2)-1)/(x^(2)-1) is
Answer» 2 1 `SQRT2` 0 Answer :A

Discussion

31.	Area of the regionbounded by the curve y = "cos" x between x = 0 and x = pi is
Answer» ANSWER :a

Discussion

32.	Two dice are tossed once. If number 4 comes on first dice then find probability of an event that sum of numbers obtain on two dice is 8 or more.
Answer» ANSWER :`(1)/(2)`

Discussion

33.	What work has to be performed to move a body of mass m from the Earth.s surface to infinitely ?
Answer» ANSWER :MGR

Discussion

34.	5^n -1 is divisible by 4.
Answer» <P> Solution :LET `P_n = 5^n -1` When n = 1, ` 5^1 - 1 = 4` is divisible by 4. `THEREFORE P_1` is TRUE. Let `P_k` be true i.e, `5^k -1` = 4m, m in Z Now `5^(k+1)-1 = 5^k . 5 - 5 + 4 = 5(5^k -1) + 4` `5 xx 4m + 4 = 4(5m + 1)` which is divisible by 4. `therefore P_(k+1)` is true. `therefore P_n` is true for all values of `n in N`

Discussion

35.	Prove that if for an exponential function y=a^x (a gt 0, a ne 1) the values of the argument x=x_n (n=1,2,.....) form an arithmetic progression,then the corresponding values of the function y_n=a^(x) (n=1,2,3..) form a geometric progression.
Answer» ANSWER :From `x_(N+1)=x_(n)+d` it FOLLOWS that `y+(n+1)=a^(x_(n+1))=a^(XN+d)=a^(xn) a^(d)`

Discussion

36.	Bag A contains 4 white and 3 black balls. Bag B contains 3 white and 2 black balls. One ball is transferred from bag A to bag B. Now one ball is drawn from bag B. Find the probability that it is white.
Answer» ANSWER :`(25)/(42)`

Discussion

37.	Here, z takes values in the complex plane and Im(z) and Re(z) denote respectively, the imaginary part and the real part of z.
Answer» ANSWER :A::B::C::D

Discussion

38.	Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below have inverses. Find f^(-1) if it existf={(1,2),(2,3),(3,4),(4,1)}
Answer» Solution :F is bijective. HENCE `f^(-1)` exists.`f^(-1)={(2,1),(3,2),(4,3),(1,4)}`

Discussion

39.	If a,b,c,d are conseentive binomial coefficients of (1+x)^n then (a+b)/(a), (b+c)/(b), (c+d)/(c ) are is
Answer» A.P. G.P H.P A.G.P Answer :C

Discussion

40.	If 0lt alphaltpi, then the quadratic question cos(alpha-1)x^(2)+x cosalpha+sinalpha=0, has
Answer» both ROOTS imaginary only ONE ROOT imaginary only one root irrational none of these Answer :D

Discussion

41.	Let a,b and s be the sides of a scalane triangle. IF lamda is a real number such that the roots of the equation x^2+2(a+b+c)x+3 lamda (ab+bc+ca)=0 are real, then the interval in which lamda lies is
Answer» `(INFTY,4/3)` `(5/3,infty)` `(1/3,5/3)` `(4/3,infty)` ANSWER :A

Discussion

42.	If sin x + sin y = (sqrt(3) + 1)/(2) and cos x + cos y = (sqrt(3) - 1)/(2), then tan^(2)((x-y)/(2)) + tan^(2)((x+y)/(2)) =
Answer» `8 + 4sqrt(3)` `6 + 4sqrt(3)` `3 + SQRT(3)` `12 + 6sqrt(3)` ANSWER :A

Discussion

43.	Let f(x)=x+{x}^(2) where {x} is fractional part of x. The area between the curves y=f(x). y=f^(-1)(x), x=0 and x=3/2 is
Answer» `1/2` `1` `3/2` `2` SOLUTION :Required area is `3/2` TIMES the area of LOOP `3/2xx2 int_(0)^(1)[(x+x^(2))-x]dx` `1`

Discussion

44.	Find term which is independent of x in (x^(2)-(1)/(x^(6)))^(16)
Answer» ANSWER :`T_(5)` is INDEPENDENT of X

Discussion

45.	How many sets of 2 and 3 (different) numbers can be formed by using numbers betweeen 0 and 180 (both including) so that 60 is their average?
Answer» ANSWER :4530

Discussion

46.	From a variable point P(t^(2),2t)(1letle3) on the parabola y^(2)=4x, perpendicular PM is drawn to the tangent at the vertex of the parabola. Now from the mid point Q of PM perpendicular QL is drawn to the focal chord of the parabola through P. If maximum length of QLltk, where kinN then find the value of k.
Answer» ANSWER :3

Discussion

47.	F(X)= {{:(\|x-2\|+a ,"for "x lt 2),(b-\|x-2\|, "for "x ge 2):}}then
Answer» f is not differentiable at x =2for all REAL VALUES of a , B Rf' (2) = 1 LF'(2) = 1 all are correct. Answer :D

Discussion

48.	The probability distribution of a discrete random variable X is given below : The value of k is .........
Answer» 8 16 32 48 Answer :C

Discussion

49.	A relation R on the set of complex numbers is defined by z_1R z_2 if and only if (z_1-z_2)/(z_1+z_3)is real . Show that R is an equivalence realtion.
Answer» Solution :Here `z_1 Rz_2 hArr(z_1 -z_2)/(z_1+z_2)` REAL (i) Reflexive `z_1Rz_2 hArr (z_1-z_1)/(z_1+z_2)` is real `rArr-(z_2 -z_1)/(z_1+z_2)` is real `rArr z_2 Rz_1` `thereforez_1 Rz_2 rArrz_2Rz_1` THEREFORE it is SYMMETRIC (iii) Transitive `z_Rz_2` `rArr(z_1-z_2)` is real and `z_2Rz_3` `rArr(z_2-z_3)/(z_2+z_3)` is real Here LET`z_1 =x_1+ iy_1 , z_2 = x_2 + iy_2 and z_3 = x_3 + iy_3` `therefore(z_1-z_2)/(z_1+z_2) is real rArr((x_1-x_2)+i(y_1-y_2))/((x_1+x_2)+i(y_i+y_2)` is real `rArr ({(x_1-x_2)+i(y_1-y_2)}.{(x_1+x_2)-i(y_2+y_2)})/((x_1+x_2)^2+(y_1+y_2)^2)` `rArr (y_1-y_2)(x_1+x_2)-(x_1-x_2)(y_1+y_2)=0` `rArr2x_2y_1-2y_2x_1=0` `rArr(x_1)/(y_1)=(x_2)/(y_2) ....(i)` SIMILARLY`z_2Rz_3` `rArrx_2/y_2=x_3/y_3 rArr z_1 R z_3` HenceR is and equivalence realation

Discussion

50.	The modulus of the vector barn is 8. makes an angle 45^@ with X -axis. 60^@ with Y - axis an acute angle with Z -axis. The equation of the plane passing through ( sqrt(2) , - 1,1) and having normal barn is ..............
Answer» `bar(r).(sqrt(2) HAT i + hat J + hat k )= 4` `bar r. (sqrt(2) hat i+ hat j + hat k) = 2` `bar r (hat i + hat j + hat k) = 4` None of these Answer :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let f(x)=[2^(-x^(2))[2x^(2)]],x epsilon R ( [ ] denotes the greatest integer function). Let x_(1)=0,x_(2)=log_(2)3 and x_(3)=sqrt(2). Suppose 0ltx_(4)lt1. Delta=|(f(x_(1)),f(x_(2)),f(x_(3))),(f(x_(4)),f(x_(4)),f(x_(2))),(f(x_(2)),f(x_(3)),f(x_(1)))| then Delta is equal to

If int (1)/(3 sin x + 4 cos x ) " dx = a log"|(b +2 tan""(x)/(2))/(c - tan""(x)/(2)) | + Kthen (a, b , c) =

If n(A)=10,n(B)=6 and n( C )=5 for three disjoint sets A, B, C then n(A uu B uu C) equals

Find int(sinx)/(sin(x-a))dx

Let f(x) be a differentiable function satisfying f(x)+f(x+(1)/(2))=f(x),AA x in R and g (x) =int_(0)^(x)f (t) dt . If g(1)=1, then the value ofsum_(n=2)^(infty)((8)/(sum_(k=1)^(n)(g(x+k^(2))-g(x+k)))) is

Integrate the following functions : int(2^(x))/(sqrt(1-4^(x)))dx

The modulus of (sqrt(3)+i)/((1+i)(1+sqrt(3)i)) is

If the points (x,y) are equidistant from the points (a+b,b-a) and (a-b,a+b),prove that bx = ay.

The sides of a square are x=4, x=7, y=1, y=4. Then theequation of the circumcircle of the square is

Iff (x) =x ( x-1) (x-2) , 0 le x le 4and the poind xi satisfies mean values theorem for f (x), then

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4r)/(3).

A set A has 3 elements and another set B has 6 elements. Then

A five digited number is written at random. Find the probability that the number written is such that when the digits are put in reverse order, the new number is also a five digited number equal to the original number.

If the pair of straight lines given by A x^(2) + 2 H xy + By^(2) = 0 (H^(2) gt AB) forms an equilateral triangle with line ax + by + c = 0 then (A + 3 B) ( 3 A + B) is equal to

Let f(x) ={{:(min{x,x^(2)},x le 0),(max {2x","x^(2)-1},xlt0):}thenwhichof the followingis not true ?

A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force vecF=(30N)hati-(40N)hatj to the cart as it undergoes a displacement vecs=(9.0m)hati-(3.0m)hatj. How much work does the forces you apply do on the grocery cart ?

Find the values of the following integrals int(1)/(1+sinx)dx

A natural number x is chosen at random from the first 100 natural numbers. Find the probability that ((x-20)(x-40))/((x-30)) lt 0

Sides AB and AC in an equilateraltriangle ABC with side length 3 is extended to form two rays from point A as shown in the figure. Point P is chosen outside the triangle ABC and between the two rays such that angleABP+angleBCP=180^(@). If the maximum length of CP is M, then M^(2)//2 is equal to :

The points of contact of the tangents drawn from the point (4, 6) to the parabola y^(2) = 8x

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n), then prove that a_(1)+a_(3)+a_(5)+….+a_(2n-1)=(3^(n)-1)/(2)

Discuss the continuity of the following functions: f(x)=sinx.cosx

Match the column I (the curve 2y^2 = x + 1) with column II (the slope of normals)

The radius of the circle which touches x^(2) +y^(2) -6x + 6y +17=0

One of the partitions of the set {1,2,5,x,y,sqrt(2),sqrt(3)} is

Evaluate the following determinants. [[2,-3],[1,-4]]

Find the equation of the circle with centre C and radius r where C = ( cos alpha , sin alpha ) , r= 1

If f(1)=1 and f'(1)=2 then lim_(xto1)((f(x))^(2)-1)/(x^(2)-1) is

Area of the regionbounded by the curve y = "cos" x between x = 0 and x = pi is

Two dice are tossed once. If number 4 comes on first dice then find probability of an event that sum of numbers obtain on two dice is 8 or more.

What work has to be performed to move a body of mass m from the Earth.s surface to infinitely ?

5^n -1 is divisible by 4.

Prove that if for an exponential function y=a^x (a gt 0, a ne 1) the values of the argument x=x_n (n=1,2,.....) form an arithmetic progression,then the corresponding values of the function y_n=a^(x) (n=1,2,3..) form a geometric progression.

Bag A contains 4 white and 3 black balls. Bag B contains 3 white and 2 black balls. One ball is transferred from bag A to bag B. Now one ball is drawn from bag B. Find the probability that it is white.

Here, z takes values in the complex plane and Im(z) and Re(z) denote respectively, the imaginary part and the real part of z.

Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below have inverses. Find f^(-1) if it existf={(1,2),(2,3),(3,4),(4,1)}

If a,b,c,d are conseentive binomial coefficients of (1+x)^n then (a+b)/(a), (b+c)/(b), (c+d)/(c ) are is

If 0lt alphaltpi, then the quadratic question cos(alpha-1)x^(2)+x cosalpha+sinalpha=0, has

Let a,b and s be the sides of a scalane triangle. IF lamda is a real number such that the roots of the equation x^2+2(a+b+c)x+3 lamda (ab+bc+ca)=0 are real, then the interval in which lamda lies is

If sin x + sin y = (sqrt(3) + 1)/(2) and cos x + cos y = (sqrt(3) - 1)/(2), then tan^(2)((x-y)/(2)) + tan^(2)((x+y)/(2)) =

Let f(x)=x+{x}^(2) where {x} is fractional part of x. The area between the curves y=f(x). y=f^(-1)(x), x=0 and x=3/2 is

Find term which is independent of x in (x^(2)-(1)/(x^(6)))^(16)

How many sets of 2 and 3 (different) numbers can be formed by using numbers betweeen 0 and 180 (both including) so that 60 is their average?

F(X)= {{:(|x-2|+a ,"for "x lt 2),(b-|x-2|, "for "x ge 2):}}then

The probability distribution of a discrete random variable X is given below : The value of k is .........

A relation R on the set of complex numbers is defined by z_1R z_2 if and only if (z_1-z_2)/(z_1+z_3)is real . Show that R is an equivalence realtion.

The modulus of the vector barn is 8. makes an angle 45^@ with X -axis. 60^@ with Y - axis an acute angle with Z -axis. The equation of the plane passing through ( sqrt(2) , - 1,1) and having normal barn is ..............