28278 + Interview Questions in Maths in Class 12

1.	Find the middle terms are in the expansion of(2x+3y)^7
Answer» ANSWER :`T_4 = ""^7C_3.2^4.3^4x^4y^3, T_5 = ""^7C_4.2^3.3^4x^3y^4`

Discussion

2.	If (x) is differentiable in [a,b] such that f(a)=2,f(b)=6, then there exists at least one c,a ltcleb, such that (b^(3)-a^(3))f'(c)=
Answer» `C^(2)` `2c^(2)` `-3C^(2)` `12c^(2)` ANSWER :D

Discussion

3.	Consider circles C_(1) and C_(2) touching both the axes and passing through (4, 4), then the x - intercept of the common chord of the circles is
Answer» ANSWER :8

Discussion

4.	If the variance of 1,2,3,4,5 , …., 10 is (99)/(12), then the standard deviation of 3,6,9,12,…..,30 is
Answer» `(297)/(4)` `(3)/(2)sqrt(33)` `(3)/(2)sqrt(99)` `sqrt((99)/(12))` ANSWER :44

Discussion

5.	Find the area of the region bounded by y=1-\|x\| and the x-axis
Answer» ANSWER :`(1)/(2)`

Discussion

6.	L_(1), L_(2),L_(3) are three lines where L_(1) = 2x + y =2, L _(2) = x -2y=-1and L _(3) is any line passing through the point of intersection of L_(1) and L _(2) A line L passing through P(0,1) intersects L _(1), L _(2) and L _(3) at A, B and C respectively. If intercept of L between L _(1) and L _(2) subtends right angle at origin and ((1)/(PA))^(2) + ((1)/(PB)) ^(2) + ((1)/(PC))^(2) =5, then find L _(3) and L.
Answer» Answer :EQUATION of `L_(3) is x + 3Y =3`

Discussion

7.	Evalute the following integrals int (1)/(x (2 + 3" log x"))dx
Answer» ANSWER :1/3(LOG(2+3logx)+ C

Discussion

8.	Let n_(1)and n_(2) be the number of red and black balls, respectively, in box I. Let n_(3) and n_(4) be the numbers of red and black balls, respectively, in the box II. One of the two boxes, box I and II, was selected at random and a ball was drawn randomly our of this box. The ball was found to be red. If the probability that this red with the possible values of n_(1),n_(2),n_(3)and n_(4) is (are)
Answer» `n_(1)=3,n_(2)=3,n_(3)=5, n_(4)=15` `n_(1)=3,n_(2)=6,n_(3)=10, n_(4)=50` `n_(1)=8,n_(2)=6,n_(3)=5, n_(4)=20` `n_(1)=6,n_(2)=12,n_(3)=5, n_(4)=20` Solution :`RED ton_(1)` ` "Box" IltBlack ton_(2)` `Red to n_(3)` `"Box II"lt"Black" to n_(4)` `P(R)=1/2.(n_(1))/(n_(1)+n_(2))+1/2.(n_(3))/(n_(3)+n_(4))` `P (II//R) =(1/2(n_(3))/(n_(3)+n_(4)))/(1/2(n_(1))/(n_(1)+n_(2))+1/2.(n_(3))/(n_(3)+n_(4)))` `((n_(3))/(n_(3)+n_(4)))/((n_(1))/(n_(1)+n_(2))+(n_(3))/(n_(3)+n_(4)))` by OPTION `n_(1)=3,n_(2)=3,n_(3)=5,n_(4)=15` `P(II//R)=(5/20)/(3/6+5/20)=(1/4)/(1/2+1/4)=1/4xx(4)/(2+1)=1/3` ALSO, when `n_(1)=3, n_(2),=6,n_(3)=10, n_(4)=50,P(II//R)=1//3`

Discussion

9.	Differentiate the functions with respect to x in sec(tan (sqrtx))
Answer» ANSWER :`SEC (TAN SQRTX).tan (tan sqrtx).sec^(2) (sqrtx)2 sqrtx`

Discussion

10.	The value of hati.(hatj xxhatk) + hatj.(hati xx hatk) + hatk.( hati xx hatj) is
Answer» 0 `-1` 1 3 Solution :N/A

Discussion

11.	Two numbers are selected at random from 1,2,3,……100 and multiplied. Find the probability that the product thus obtained is divisible by 3.
Answer» ANSWER :0.55 NEARLY

Discussion

12.	Integration by partial fraction : int(dx)/(x^(2)+4x+13)=...
Answer» `LOG(X^(2)+4x+13x)+C` `(1)/(3)tan^(-1)((x+3)/(3))+c` `log(2x+4)+c` `(2x+4)/((x^(2)+4x+13)^(2))+c` ANSWER :B

Discussion

13.	Write the value of inte^(x)e^(e^x)e^(e^(e^x))dx.
Answer» Solution :`inte^(X)E^(x^e)e^(e^(e^x))dx=int` DT, (where `t=e^(e^(e^x)))=t+C=e^(e^(e^x))+c`

Discussion

14.	f(x)= {(2x",","if" x lt 0),(0",","if" 0 le x le 1),(4x",","if" x gt 1):}
Answer» ANSWER :x=1

Discussion

15.	If P_1, P_2, P_3 ,………, P_n are n points on the line y = x all lying in the first quadrant, such that (OP_n) = n (OP_(n-1) )(O is origin ) , OP_1 =and P_n = (2520 sqrt2 , 2520 sqrt2) , then n =
Answer» 5 6 7 8 Answer :C

Discussion

16.	If the system of linear equations : x+4y-3z=2 2x+7y+4z=alpha -x-5y+5z= beta has infinitely many solutoins than the ordered pair (alpha, beta) cannot take value :
Answer» (4,-2) (2,-4) (3,-3) (-3,3) ANSWER :D

Discussion

17.	Consider the following: (1) If cot theta =x, thenx+ 1+x = sec theta cosec theta (2) If x+1/x = sin theta,thenx^(2) + (1)/(x^(2))=sin ^(2) theta -2 (3) If x= p sec theta and y=q tan theta,thenx ^(2) q^(2) -y^(2) p^(2) =p^(2) q^(2) (4) The maximum valur of (cos theta - sqrt3 sin theta) is 3 which of these are correct ?
Answer» `(1), (2) and (3)` `(1),(2)` `(2),(3)` `(3),(4)` ANSWER :A

Discussion

18.	The point P(3,2) undergoes the following transformations successively (i) Reflection abouth the line y=x (ii) Translation to a distance of 3 units in the positive direction of X-axis (iii) Rotation through an angle (pi)/(4) about the origin in the counter-clockwise direction Then , the final position of that point is
Answer» A(2,4) B`(sqrt2,4sqrt2,)` C`((1)/(sqrt2) , sqrt2)` D`(sqrt2, 2 sqrt2)` ANSWER :B

Discussion

19.	Two points A (a, 0) and B (0, b) are given, O is the origin and M is a point on the line joining AB such that angle OMA is a right angle. If \|OM\|=8, then AM. BM is equal to
Answer» ANSWER :64

Discussion

20.	If x,y,z in R, then the value of determinant \|((5^(x)+5^(-x))^(2) , (5^(x)-5^(-x))^(2),1),((6^(x)+6^(-x))^(2),(6^(x)-6^(-x))^(2), 1),((7^(x)+7^(-x))^(2),(7^(x)-7^(-x))^(2),1)\| is
Answer» 10 12 1 0 Answer :D

Discussion

21.	If y= (cos x)^((cos x)^((cos x)……oo)), then show that (dy)/(dx)= (y^(2) tan x)/(y.log cos x-1)
Answer» Answer :`(y^(2) TAN X)/(ylog COS x-1)`

Discussion

22.	Let RberelationfromN intoN definedby R ={(a,b) : a,b inN ,a=b^2 }arethe followingtrue?Justifyyour answerin eachcase . (a,b) and(b,c) in Rfor alla,b,c, inNimplies(a,c)inR
Answer» ANSWER :FALSE

Discussion

23.	If (1-10icos theta)/(1-10sqrt(3)isintheta) is purely real, then one of the valus of theta is
Answer» `(PI)/(6)` `(pi)/(4)` `(pi)/(3)` `(pi)/(2)` Answer :A

Discussion

24.	Area of the region bounded by y=[x], the X-axis and the ordinates x = 1, x = 2 is
Answer» 2 1 `(1)/(2)` 3 Answer :B

Discussion

25.	If y=f(x)andx=g(y) are inverse functions of each other, then
Answer» `g''(y)=(1)/(F''(X))` `g''(y)=(f''(x))/((f''(x))^(3))` `g''(y)=(f'(x))/((f'(x))^(3))` None of these Answer :B

Discussion

26.	Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel) . Previous years results report that 30% of all students who reside in hostel attain A grade and 20% of day scholrs attain A grade in their annual examination . Atthe end of the year, one student is chosen at random from the college and he has an Agrade, what is the probability that the student is a hostler ?
Answer» ANSWER :`(9)/(13)`

Discussion

27.	How many ways can the letters of the word 'BANANA' be arranged so that no two A's come together
Answer» ANSWER :2

Discussion

28.	Consider all the 7-digit numbers containing each of the digits 1,2,3,4,5,6,7 exactly once, and not divisible by 5. Arrange them in decreasing order. What is the 2015-th number (from the beginning) in this list?
Answer» ANSWER :`4712536`

Discussion

29.	Match the following i. The equation whose roots are multiplied by 3 of""(a)x^(3) - 8x^(2) + 19x - 15 = 0 those of x^(3) + 2x^(2) - 4x + 1 =0 is ii.The equation whose roots are exceedby 1 than""(b) x^(3) + 5x^(2) + 10x + 10 = 0 those of x^(3) - 5x^(2) + 6x - 3 = 0 is iii. The equation whose roots are diminish by 1 than "" (c )4x^(4) - 2x^(3) + 6x^(2) - 3x - 1 =0 those of x^(3) + 2x^(2) + 3x + 4 =0 is iv. The equation whose roots are the reciprocals of the ""(d)x^(3) + 6x^(2) - 36x + 27 = 0 roots of x^(4) + 3x^(3) - 6x^(2) + 2x - 4 = 0 is
Answer» C, d, a, B d, c, b, a, c, a , b, d c, b, a, d ANSWER :2

Discussion

30.	Solve the following differential equations. (x^(2)y-2xy^(2))dx=(x^(3)-3x^(2)y)dy
Answer» ANSWER :`k.x^(2)`

Discussion

31.	Thetermindependent ofxintheexpansions of(sqrtx -(2 ) /(sqrt x )) ^(18)is
Answer» `- ""^(18)C_9 2 ^(9) ` `""^(18) C _ 9 2 ^(12)` `""^(18) C_6 2 ^(6)` `""^(18) C_6 2 ^(8)` Solution : ` (sqrt x-(2 ) /(sqrt x ) ) ^( 18)` LET` T_( r + 1 )=""^(18) c _ r (sqrt x) ^( 18 - r )(( - 2 ) /(sqrt x )) ^r ` `rArrx ^(9 -( r ) /(2) - (r )/(2)) =x ^(0)` `9 - r =0 ` `thereforer=9 ` `thereforeT_(r+ 1 )=""^(18) c _9 (- 2 ) ^(9)` `=""^(-18)c _ 9 2 ^(9) `

Discussion

32.	The vertices of a triangle have integer co- ordinates then the triangle cannot be
Answer» ISOSCELES or equilateral right angles equilateral right ANGLED isosceles Answer :C

Discussion

33.	If a tangent to the ellipse meets major and minor axis at M and N respectively and C is the centre of the ellipse thejn (a^(2))/(CM)^(2)+(b^(2))/(CN)^(2)=
Answer» 1 2 3 4 Answer :A

Discussion

34.	The remainder left out when 8^(2n) - 6(2)^( 2n+1) is divided by 9 is
Answer» 2 7 8 0 Answer :A

Discussion

35.	If A gt 0, c,d,u.v are non-zero constants and the graph of f(x)=abs(Ax+c)+d " and " g(x)=-abs(Ax+u)+v intersect exactly at two points (1,4) and (3,1), then the value of (u+c)/(A) equals
Answer» 4 -4 2 -2 Answer :B

Discussion

36.	If a(x)=b(x)+c(x), where b(x)=3x^2-8x+113 and c(x)=-3x^2 + 18x+7 and x is an integer , than a(x) is always divisible by which of the following ?
Answer» 6 7 10 12 Answer :C

Discussion

37.	A consignment of 15 record players contains 4 defective. The record players are selected at random one by one and examined. The ones examined are not placed back. What is the probability that the 9^(th) one examined is the last defective.
Answer» ANSWER :`(.^(11)C_(5) XX .^(4) C_(3))/(.^(15) C_(8)) xx (1)/(7)`

Discussion

38.	Pigments present in cones of retina are connected with :
Answer» NIGHT blindness Accommodation of eye Colour discrimination Image formation Answer :A

Discussion

39.	A restaurant decides on the following production model, where N is the number of ounces of flour the restaurant purchases each month, based on the number of ounces , x , the restaurant uses during the preceding month, N=x^2-600x-160,000 . According to this model , what is the greatest quantity offlour, in number of ounces, that the restaurant can use during a month , without having to purchase any new flour the next month ?
Answer» 800 550 400 350 Answer :A

Discussion

40.	The total area of a page is 150 square inchese. The combined width of the margin at the top and bottom is 3'' and the side is 2''. What must be the dimension of the page in order that the area of the printed matter may be maximum.
Answer» ANSWER :15, 10

Discussion

41.	Find the value of x for which x(hati+hatj+hatk) is a unit vector.
Answer» ANSWER :`+-(1)/(SQRT(3))`

Discussion

42.	Iff: N to Ndefined as f(x)=x^(2)AA x in N,then f is :
Answer» many-one one-one ONTO NONE of these ANSWER :B

Discussion

43.	1 (d)/(dx) (Cos ^(-1) x + Sin ^(-1) x ) = A 2. (d)/(dx) { Tan ^(-1) ((1+ sin x )/( cos x))]=B 2 If f (x) = (x+ sqrt(x ^(2) +1)) then f '(1)=C 4 If f (x) = Cos ^(-1) (4x ^(3) - 3x) then f'(0) =D The ascending order A,B,C,D is
Answer» D,A,C,B A,B,C,D A,D,C,B B,C,A,D Answer :D

Discussion

44.	Out of the following planes , which plane is passing through theline of intersection of the palnes x-y+2z = 3 and 4x-3y-z = 1.
Answer» 11X + 10 y -5z=0 7x+7y+4z = 0 5x+2y-z = 2 None to these Answer :A

Discussion

45.	Let Q be the set of all rational numbers and let be a binary operation on QxxQ defined by (a,b)(c,d)=(ac,b+ad). Determine whether is commutative and associative. Find the identity element for and invertible elements of QxxQ. Or Let f:[0,oo) toR be a function defined by f(x) =9x^(2)+6x-5. Prove that f is not invertible. modify only the condomin of f to make f invertible and then find its inverse.
Answer» Answer :`` is not COMMUTATIVE, ``isassociative, (1,0) is the INDENTITY, inverse of (a,b) is `((1)/(a),(-b)/(a))` Or, `f^(-1)(y)=(SQRT(y+6)-1)/(3)`

Discussion

46.	Differentiate w.r.t.x, the following functions : log_(7)( logx).
Answer» ANSWER :`= (1)/(X LOG 7 log x)`

Discussion

47.	Write a logarithmic functions which is differentiable atevery point in R.
Answer» SOLUTION :`F(X)=log_3(2^x)`is DIFFERENTIABLE for all `x in R`

Discussion

48.	Prove that if the function f(x): (1) is defined and monotonic on the interval [a, b], (2) traverses all intermediate values between fla) and fb). then it is continuous on the interval (a, b).
Answer» ANSWER :`"MIN"(x_(0)-x_(1), x_(2)-x_(0)`

Discussion

49.	A box contains N coins, m of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is 1/2, while it is 2/3 when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. What is the probability that the coin drawn is fair ?
Answer» ANSWER :`(9M)//(8N + m)`

Discussion

50.	Integrate the following functions : e^(sqrtx)
Answer» ANSWER :`2[SQRTX.E^(sqrtx)-e^(sqrtx)]+C`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the middle terms are in the expansion of(2x+3y)^7

If (x) is differentiable in [a,b] such that f(a)=2,f(b)=6, then there exists at least one c,a ltcleb, such that (b^(3)-a^(3))f'(c)=

Consider circles C_(1) and C_(2) touching both the axes and passing through (4, 4), then the x - intercept of the common chord of the circles is

If the variance of 1,2,3,4,5 , …., 10 is (99)/(12), then the standard deviation of 3,6,9,12,…..,30 is

Find the area of the region bounded by y=1-|x| and the x-axis

Evalute the following integrals int (1)/(x (2 + 3" log x"))dx

Differentiate the functions with respect to x in sec(tan (sqrtx))

The value of hati.(hatj xxhatk) + hatj.(hati xx hatk) + hatk.( hati xx hatj) is

Two numbers are selected at random from 1,2,3,……100 and multiplied. Find the probability that the product thus obtained is divisible by 3.

Integration by partial fraction : int(dx)/(x^(2)+4x+13)=...

Write the value of inte^(x)e^(e^x)e^(e^(e^x))dx.

f(x)= {(2x",","if" x lt 0),(0",","if" 0 le x le 1),(4x",","if" x gt 1):}

If P_1, P_2, P_3 ,………, P_n are n points on the line y = x all lying in the first quadrant, such that (OP_n) = n (OP_(n-1) )(O is origin ) , OP_1 =and P_n = (2520 sqrt2 , 2520 sqrt2) , then n =

If the system of linear equations : x+4y-3z=2 2x+7y+4z=alpha -x-5y+5z= beta has infinitely many solutoins than the ordered pair (alpha, beta) cannot take value :

Two points A (a, 0) and B (0, b) are given, O is the origin and M is a point on the line joining AB such that angle OMA is a right angle. If |OM|=8, then AM. BM is equal to

If x,y,z in R, then the value of determinant |((5^(x)+5^(-x))^(2) , (5^(x)-5^(-x))^(2),1),((6^(x)+6^(-x))^(2),(6^(x)-6^(-x))^(2), 1),((7^(x)+7^(-x))^(2),(7^(x)-7^(-x))^(2),1)| is

If y= (cos x)^((cos x)^((cos x)……oo)), then show that (dy)/(dx)= (y^(2) tan x)/(y.log cos x-1)

Let RberelationfromN intoN definedby R ={(a,b) : a,b inN ,a=b^2 }arethe followingtrue?Justifyyour answerin eachcase . (a,b) and(b,c) in Rfor alla,b,c, inNimplies(a,c)inR

If (1-10icos theta)/(1-10sqrt(3)isintheta) is purely real, then one of the valus of theta is

Area of the region bounded by y=[x], the X-axis and the ordinates x = 1, x = 2 is

If y=f(x)andx=g(y) are inverse functions of each other, then

How many ways can the letters of the word 'BANANA' be arranged so that no two A's come together

Consider all the 7-digit numbers containing each of the digits 1,2,3,4,5,6,7 exactly once, and not divisible by 5. Arrange them in decreasing order. What is the 2015-th number (from the beginning) in this list?

Solve the following differential equations. (x^(2)y-2xy^(2))dx=(x^(3)-3x^(2)y)dy

Thetermindependent ofxintheexpansions of(sqrtx -(2 ) /(sqrt x )) ^(18)is

The vertices of a triangle have integer co-﻿ ordinates then the triangle cannot be

If a tangent to the ellipse meets major and minor axis at M and N respectively and C is the centre of the ellipse thejn (a^(2))/(CM)^(2)+(b^(2))/(CN)^(2)=

The remainder left out when 8^(2n) - 6(2)^( 2n+1) is divided by 9 is

If A gt 0, c,d,u.v are non-zero constants and the graph of f(x)=abs(Ax+c)+d " and " g(x)=-abs(Ax+u)+v intersect exactly at two points (1,4) and (3,1), then the value of (u+c)/(A) equals

If a(x)=b(x)+c(x), where b(x)=3x^2-8x+113 and c(x)=-3x^2 + 18x+7 and x is an integer , than a(x) is always divisible by which of the following ?

A consignment of 15 record players contains 4 defective. The record players are selected at random one by one and examined. The ones examined are not placed back. What is the probability that the 9^(th) one examined is the last defective.

Pigments present in cones of retina are connected with :

The total area of a page is 150 square inchese. The combined width of the margin at the top and bottom is 3'' and the side is 2''. What must be the dimension of the page in order that the area of the printed matter may be maximum.

Find the value of x for which x(hati+hatj+hatk) is a unit vector.

Iff: N to Ndefined as f(x)=x^(2)AA x in N,then f is :

1 (d)/(dx) (Cos ^(-1) x + Sin ^(-1) x ) = A 2. (d)/(dx) { Tan ^(-1) ((1+ sin x )/( cos x))]=B 2 If f (x) = (x+ sqrt(x ^(2) +1)) then f '(1)=C 4 If f (x) = Cos ^(-1) (4x ^(3) - 3x) then f'(0) =D The ascending order A,B,C,D is

Out of the following planes , which plane is passing through theline of intersection of the palnes x-y+2z = 3 and 4x-3y-z = 1.

Differentiate w.r.t.x, the following functions : log_(7)( logx).

Write a logarithmic functions which is differentiable atevery point in R.

Prove that if the function f(x): (1) is defined and monotonic on the interval [a, b], (2) traverses all intermediate values between fla) and fb). then it is continuous on the interval (a, b).

Integrate the following functions : e^(sqrtx)

The vertices of a triangle have integer co- ordinates then the triangle cannot be