28278 + Interview Questions in Maths in Class 12

1.	A pole stands vertically in the center of a square. When 45° is the elevation of the sun, the tip of its shadow just reaches the side of the square and is at a distance of 30 meters and 40 meters from the ends of that side. The height of the pole is
Answer» 50 METERS 25 meters `25sqrt2` meters `50sqrt2` meters Answer :C

Discussion

2.	the principal value of sin^(-1)(-sqrt3/2) is
Answer» `-2π/3` `-π/3` `4π/3` `5π/3` ANSWER :B

Discussion

3.	On C, the set of complex numbers, define a relation R as follows: z_(1),z_(2) in C, z_(1) Rz_(2) if z_(1)barz_(2) ge 0 then
Answer» R is REFLEXIVE, symmetric but not transitive R is reflexive only R is symmetric only R is an EQUIVALENCE RELATION Answer :A

Discussion

4.	int sqrt(x^2-8x+7) is equal to
Answer» `1/2(x-4)SQRT(x^2-8x+7)+9log \|(x-4)+sqrt(x^2-8x+7)\|+C` `1/2(x-4)sqrt(x^2-8x+7)+9log \|(x+4)+sqrt(x^2-8x+7)\|+c` `1/2(x-4)sqrt(x^2-8x+7)-3sqrt2log \|(x-4)+sqrt(x^2-8x+7)\|+c` `1/2(x-4)sqrt(x^2-8x+7)-9/2log \|(x-4)+sqrt(x^2-8x+7)\|+c` ANSWER :D

Discussion

5.	If y= x^(x) + x^(a) + a^(x) then find (dy)/(dx)
Answer» ANSWER :`(1+ LOG X) x^(x) + AX^(a-1) + a^(x).log a`

Discussion

6.	Verify Property 2 forDelta ={:[( 2,-3,5),(6,0,4),( 1,5,-7)]:}
Answer» ANSWER :`DELTA =0`

Discussion

7.	Two integers x and y are chosen (with replacement) out of the set {0,1,2,…10}. Find the probability that \|x-y\|le 5.
Answer» ANSWER :`(91)/(121)`.

Discussion

8.	P = 1 - (3)/(1!) + 9/(2!) - (27)/(3!) + ....... Q = 1+ (4)/(1!) +(16)/(2!) +(64)/(3!) + ........R=log_(e)^3+((log_e^3)^2)/(2!)+((log_e^3)^3)/(3!)+.....The ascending order of P,Q,R
Answer» <P>Q,P,R P,R,Q P,Q,R R,P,Q Answer :B

Discussion

9.	Theperiodof thefunctionf(theta ) = 4 + 4 sin ^3theta-3 sin thetais
Answer» `(2 PI)/(3)` `(pi)/(3)` `(pi)/(2)` `pi` ANSWER :A

Discussion

10.	For what value ofK, Kf is increasing if f is increasing ?
Answer» SOLUTION :F is INCREASING `rArrfgt0` LET G=Kf g=gf g is increasing for `Kfgt0rArrKgt0rArrKin(0.oo)`

Discussion

11.	(i) Express (x+sqrt(x^(2) + y^(2)) - y^(2)) dx+ xydy = 0 in the form (dy)/(dx) = F((y)/(x)) (ii) Express the differental equation xydx + x^(2)dy - ysqrt(x^(2) + y^(2))dy = 0 in the form (dx)/(dy) = F((x)/(y))
Answer» ANSWER :(i) `F((y)/(X))` , (II) `F((x)/(y))`

Discussion

12.	If a=hati+hatj+hatk, b=2hati+lambda hati+lambdahatj+hatk, c=hati-hatj+4hatk and a.(bxxc)=10 then lambda is equal to
Answer» 6 7 9 10 Solution :Given, `a=hati,hatj+hatk, b=2hati+lambdahatj+hatk and c=hati-hatj+4hatk` Also, given `a.(bxxc)=10` `RIGHTARROW [{:(,1,1,1),(,2,lambda,1),(,1,-1,4):}]=10` `Rightarrow 1(4lambda+1-1(8-1)+1(-2-lambda)=10` `Rightarrow 4lambda+1-7-2-lambda=10` `Rightarrow 3lambda=18` `Rightarrow lambda=6`

Discussion

13.	If x, y, z are all different and not equal to zero and \|{:(1+x,,1,,1),(1,,1+y,,1),(1,,1,,1+z):}\| = 0 then the value of x^(-1) + y^(-1) + z^(-1) is equal to
Answer» a.xyz b.`X^(-1)y^(-1)Z^(-1)` C.`-x-y-z` d.`-1` ANSWER :D

Discussion

14.	If sin 2 x=n sin 2y then (Tan (x+y))/(Tan(x-y))=
Answer» `(n-1)/(n+1)` `(1-n)/(1+n)` `(1+n)/(1-n)` `(n+1)/(n-1)` ANSWER :D

Discussion

15.	f(x)= sin^(2)x + sin^(2) (x + (pi)/(3)) + cos x cos (x + (pi)/(3))and g(5 / 4)' =1 then (gof)(x) = ………
Answer» 1 `COS^(2)X` 0 sin 2x Answer :C

Discussion

16.	Find the equation of a curve passing through the origin, given that the slope of the tangent of the curve at any point (x,y) is equal to tha sum of the coordinates of the point.
Answer» ANSWER :`X + y + 1= E^(x)`

Discussion

17.	Which of the following ionisation energy order is/are correct.
Answer» `Be^(+)gtB^(2+)` `C^(3+)gtB^(2+)` `N^(4+)ltO^(5+)` `F^(6+)ltO^(3+)` Solution :`I.P.alphaZ_(EFF)ALPHA` oxidation state]

Discussion

18.	Determine the value of k for which the system of equation. kx+3y+3z=03x+ky+3z=03x+3y+kz=0 has a non trivial solutions. (k in z).
Answer» ANSWER :`RARR K = 3` or `-6`

Discussion

19.	Using {0,2,3} at randomm six digited numbers are formed. The probability that the number so formed is even number is
Answer» `(1)/(3)` `(2)/(3)` `(1)/(2)` `(1)/(5)` Answer :B

Discussion

20.	Verify Mean Value Theorem, if f(x)= x^(3)-5x^(2)-3x in the interval [a, b], where a=1 and b=3. Find all c in (1,3) for which f'(c )= 0
Answer» ANSWER :`C= (7)/(3) (1, 3)`

Discussion

21.	The matrix [(0,-5,8),(5,0,12),(-8,-12,0)] is aa) diagonal matrixb) symmetric matrixc) skewsymmetric matrixd) scalarmatrix
Answer» DIAGONAL MATRIX symmetric matrix skew-symmetric matrix SCALAR matrix ANSWER :C

Discussion

22.	Find the slope of the tangent to the curve y=x^(3)-x at x = 2.
Answer» ANSWER :11

Discussion

23.	findthe areaof theregionin thefirst quadrantenclosedbythe X -axis, theliney=xand thecirclex^2+y^2 =32
Answer» `16 PI` `4 pi` `32 pi` ` 24 pi` ANSWER :B

Discussion

24.	""^(m)C_(r+1)+ sum_(k=m)^(n)""^(k)C_(r) is equal to :
Answer» `""^(N)C_(r+1)` `""^(n +1)C_(r +1)` `""^(n)C_(r-1)` `""^(n)C_(r-1)` ANSWER :B

Discussion

25.	A and B throw a die alternatively till one of them gets a '6' and wins the game. Find their respective probabilities of winning, if A starts first.
Answer» ANSWER :`(5)/(11)`

Discussion

26.	Compute A^(-1), if A=[{:(,3,-2,3),(,2,1,-1),(,4,-3,2):}]. Hence sove thje matri equations, [{:(,3,0,3),(,2,1,0),(,4,0,2):}]={:[(,x),(,y),(,z):}]={:[(,8),(,1),(,4):}]+{:[(,2y),(,z),(,3y):}]
Answer» ANSWER :`x=1,y=2,z=3,A^(-1)=(1)/(17)[{:(,1,5,-1),(,8,6,-9),(,10,-1,-7):}]`

Discussion

27.	Minimise and Maximise z=5x+10y subject to constraints : x+2y le 120, x+y ge60, x-2y ge 0, x gt 0 and y ge 0 by graphical method.
Answer» ANSWER :LPP has MULTIPLE SOLUTIONS

Discussion

28.	Evaluation of definite integrals by subsitiution and properties of its : int_(-5)^(5)[3x^(2)-x^(10)sinx+x^(5)sqrt(1+x^(2))]dx=.........
Answer» 486 250 `-100` 0 Answer :B

Discussion

29.	Find the matrix X such that ,[{:(2,-1),(1,0),(-3,4):}]X=[{:(-1,-8,-10),(1,-2,-5),(9,22,15):}].
Answer» ANSWER :`[{:(-1,2,5),(-1,12,20):}]`

Discussion

30.	If f(x) and g(x) are differentiable and increasing functions then which of the following functions alwasys increases?
Answer» Solution :GIVEN that f(x) and g(x) are increasing FUNCTIONS `therefore f(x) ge 0`and`g(x) ge 0` (i) iff(x)+g(x)=`f(x)+g(x)ge0` `therefore`f(x) + g(x) increases. (ii) f(x)g(x)=f(x)g(x)+f(x)g(x)the sign of which depends upon the sign of f(x) and g(x) also. So, f(x)g(x) MAY be increasing or decreasing. (iii) f(x)-g(x)=f(x)-g(x), may be positive or NEGATIVE so , f(x)-g(x) may be incresing or decreasing. (iv) `f(x)/g(x)=(f(x)g(x)-f(x)g(x))/g(x)^(2)`, may be positive or negative. So .`f(x)/g(x)`may be increasing or decreasing .

Discussion

31.	Find a unit perpendicular to each of the vector vec(a)+vec(b) and vec(a)-vec(b), where vec(a)=3hati+2hatj+2hatk and vec(b)=hati+2hatj-2hatk.
Answer» ANSWER :`+-(2)/(3)HATI+-(2)/(3)hatj+-(1)/(3)hatk`

Discussion

32.	The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm. per second. How fast is the area decreasing when the two equal sides are equal to the base ?
Answer» Answer :`sqrt(3)B cm^(2)//SEC`.

Discussion

33.	Evaluate the following lim_(xto3) (x^2 -9)/(x-3)
Answer» SOLUTION :`lim_(xto3) (x^2 -9)/(x-3)` `lim_(xto3)((x-3)(x+3))/(x-3)` `lim_(xto3)(x+3)=3+3=6`

Discussion

34.	A speaks truth in 75% of the cases and B in 80% of the cases. Then the probability that their statements about an incident do not match , is
Answer» `(7)/(20)` `(3)/(20)` `(2)/(7)` `(5)/(7)` Answer :A

Discussion

35.	int_2^5[x]dx
Answer» SOLUTION :`int_2^5[X]DX` `int_2^3[x]dx+int_3^4[x]dx+int_4^5[x]dx` int_2^3 2dx+int_3^4 3 dx+int_4^5 4dx` 2+3+4=9

Discussion

36.	If L is a line through (-1,3) and (4,2), for what value of k is (3,k) on L?
Answer» -2 0 2.2 2.5 Solution :The SLOPE of the LINE is `(2-3)/(4-(-1))=-(1)/(5)`. Therefore, `(K-2)/(3-4)=-(1)/(5)`. Cross-multiplying yields 5k-10=1, so k`=(11)/(5)=2.2`. [2]

Discussion

37.	For a complex number z, if z^(2)+barz-z=4i and z does not lie in the first quadrant, then ("where "i^(2)=1)
Answer» `\|Z\|=sqrt2` `\|z\|=2sqrt2` `ARG(z)=(-pi)/(4)` `arg(z)=(3pi)/(4)` ANSWER :A

Discussion

38.	EFGH is a rhombus such that the angle EFG is 60^(@). The magnitude of vectorsbar(FH)and {m bar(EG)} are equal where m is a scalar. What is the value of m?
Answer» 3 1.5 `sqrt(2)` `sqrt(3)` Solution : RHOMBUS EFGH, `angle EFG=60^(@)` `angleEFG=30^(@)=angleHFG` From parallelogram of FORCES `vec(FE)+vec(FG)=vec(FG)` Given `\|vec(FE)\|+\|vec(FG)\|=a`(say) `:.vec(FH)=2. (sqrt(3))/(2)vec(a)=sqrt(3)vec(a)` `vec(EG)=vec(EF)+vec(EH)` `=a sin 30^(@)+a sin30^(@)=a. (1)/(2) + a. (1)/(2)=a` Thus, `(vec(FH))/(vec(EG))=(sqrt(3)a)/(a)=sqrt(3)` So, `vec(FH)=sqrt(3) vec(EG)` `rArr m=sqrt(3)`

Discussion

39.	Find the area of the region bounded by the ellipse (x^2)/(4)+(y^2)/(9)=1.
Answer» ANSWER :`6PI`

Discussion

40.	Show thet x^(2) + y^(2) - 6x - 9y + 13 = 0 , x^(2) + y^(2) - 2x - 16 y =0 touch each other. Find the point of contact and the equation of common tangent at their point of contact.
Answer» ANSWER :`4x-7y - 13 = 0`

Discussion

41.	Find the values of each of the expression following : tan^(-1)("tan"(3pi)/4)
Answer» ANSWER :`(-PI)/4`

Discussion

42.	For each of the following functions find the points of discontinuity and determine their character : (a) y=(1)/u^(2)+u-2," where u"=1/(x-1).
Answer» ANSWER :(B) 1 (C) -1

Discussion

43.	If the lines y=-4x+b are tangents to the curve y=1/x, then b =
Answer» `PM4` `PM2` `pm1` `pm8` ANSWER :A

Discussion

44.	int(x^(3)-6x^(2)+11-6)/(sqrt(x^(2)+4x+3))dx.
Answer» Answer :`(1)/(3)(X^(2)-14X + 111)SQRT(x^(2)+4x+3)-66 In\|x+2+sqrt(x^(2)+4x+3)\|+C.`

Discussion

45.	Let barr is a position vector of a variable point in Cartesian OXY plane such that (10hati-8hati-barr)=40 and p_1=max(barr+2hati-3hatj)^2),p_2=min{(barr+2hati-3hatj)^2}. A tangent line is drawn to the curve y=8/x^2 at the point A with abscissa 2. The drawn line cuts x axis at a point B. p_2 is equal to 1. 9 2.2sqrt2-1 3.6sqrt2+3 4. 9-4sqrt2 p_1+p_2 is equal to 1. 2 2. 10 3. 18 4. 5
Answer» ANSWER :D,C

Discussion

46.	If [x] represents greatest integer le x then int_(1)^(3//2) [2x +1]dx=
Answer» `1` `3` `1/2` `3/2` ANSWER :D

Discussion

47.	Find all common tangents of the following pairs of circles. x^(2) + y^(2) + 4x + 2y -4 =0 and x^(2) + y^(2) - 4x - 2y + 4 =0
Answer» ANSWER :`X - 1 = 0, 3X + 4Y - 5 =0`

Discussion

48.	If B=[(3,4),(4,3)] and C=[(3,-4),(-2,3)] and X=BC, find X^(n)
Answer» 0 `I` `2I` NONE of these Answer :B

Discussion

49.	A coin is tossed three times is succession. If E is the event that there are at least two heads and F is the event in which first throw is a head, then P(E \| F)= ………
Answer» `(3)/(4)` `(3)/(8)` `(1)/(2)` `(1)/(8)` ANSWER :A

Discussion

50.	The set of solutions of the equation,(sqrt3-1)sin theta + (sqrt3+1)cos theta =2 is
Answer» `{2npipmpi/4+pi/12 : N in Z}` `{2npipmpi/4-pi/12 : n in Z}` `{NPI+(-1)^n pi/4+pi/12 : n in Z}` `{npi+(-1)^n pi/4-pi/12 : n in Z}` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A pole stands vertically in the center of a square. When 45° is the elevation of the sun, the tip of its shadow just reaches the side of the square and is at a distance of 30 meters and 40 meters from the ends of that side. The height of the pole is

the principal value of sin^(-1)(-sqrt3/2) is

On C, the set of complex numbers, define a relation R as follows: z_(1),z_(2) in C, z_(1) Rz_(2) if z_(1)barz_(2) ge 0 then

int sqrt(x^2-8x+7) is equal to

If y= x^(x) + x^(a) + a^(x) then find (dy)/(dx)

Verify Property 2 forDelta ={:[( 2,-3,5),(6,0,4),( 1,5,-7)]:}

Two integers x and y are chosen (with replacement) out of the set {0,1,2,…10}. Find the probability that |x-y|le 5.

P = 1 - (3)/(1!) + 9/(2!) - (27)/(3!) + ....... Q = 1+ (4)/(1!) +(16)/(2!) +(64)/(3!) + ........R=log_(e)^3+((log_e^3)^2)/(2!)+((log_e^3)^3)/(3!)+.....The ascending order of P,Q,R

Theperiodof thefunctionf(theta ) = 4 + 4 sin ^3theta-3 sin thetais

For what value ofK, Kf is increasing if f is increasing ?

(i) Express (x+sqrt(x^(2) + y^(2)) - y^(2)) dx+ xydy = 0 in the form (dy)/(dx) = F((y)/(x)) (ii) Express the differental equation xydx + x^(2)dy - ysqrt(x^(2) + y^(2))dy = 0 in the form (dx)/(dy) = F((x)/(y))

If a=hati+hatj+hatk, b=2hati+lambda hati+lambdahatj+hatk, c=hati-hatj+4hatk and a.(bxxc)=10 then lambda is equal to

If x, y, z are all different and not equal to zero and |{:(1+x,,1,,1),(1,,1+y,,1),(1,,1,,1+z):}| = 0 then the value of x^(-1) + y^(-1) + z^(-1) is equal to

If sin 2 x=n sin 2y then (Tan (x+y))/(Tan(x-y))=

f(x)= sin^(2)x + sin^(2) (x + (pi)/(3)) + cos x cos (x + (pi)/(3))and g(5 / 4)' =1 then (gof)(x) = ………

Find the equation of a curve passing through the origin, given that the slope of the tangent of the curve at any point (x,y) is equal to tha sum of the coordinates of the point.

Which of the following ionisation energy order is/are correct.

Determine the value of k for which the system of equation. kx+3y+3z=03x+ky+3z=03x+3y+kz=0 has a non trivial solutions. (k in z).

Using {0,2,3} at randomm six digited numbers are formed. The probability that the number so formed is even number is

Verify Mean Value Theorem, if f(x)= x^(3)-5x^(2)-3x in the interval [a, b], where a=1 and b=3. Find all c in (1,3) for which f'(c )= 0

The matrix [(0,-5,8),(5,0,12),(-8,-12,0)] is aa) diagonal matrixb) symmetric matrixc) skewsymmetric matrixd) scalarmatrix

Find the slope of the tangent to the curve y=x^(3)-x at x = 2.

findthe areaof theregionin thefirst quadrantenclosedbythe X -axis, theliney=xand thecirclex^2+y^2 =32

""^(m)C_(r+1)+ sum_(k=m)^(n)""^(k)C_(r) is equal to :

A and B throw a die alternatively till one of them gets a '6' and wins the﻿ game. Find their respective probabilities of winning, if A starts first.﻿

Compute A^(-1), if A=[{:(,3,-2,3),(,2,1,-1),(,4,-3,2):}]. Hence sove thje matri equations, [{:(,3,0,3),(,2,1,0),(,4,0,2):}]={:[(,x),(,y),(,z):}]={:[(,8),(,1),(,4):}]+{:[(,2y),(,z),(,3y):}]

Minimise and Maximise z=5x+10y subject to constraints : x+2y le 120, x+y ge60, x-2y ge 0, x gt 0 and y ge 0 by graphical method.

Evaluation of definite integrals by subsitiution and properties of its : int_(-5)^(5)[3x^(2)-x^(10)sinx+x^(5)sqrt(1+x^(2))]dx=.........

Find the matrix X such that ,[{:(2,-1),(1,0),(-3,4):}]X=[{:(-1,-8,-10),(1,-2,-5),(9,22,15):}].

If f(x) and g(x) are differentiable and increasing functions then which of the following functions alwasys increases?

Find a unit perpendicular to each of the vector vec(a)+vec(b) and vec(a)-vec(b), where vec(a)=3hati+2hatj+2hatk and vec(b)=hati+2hatj-2hatk.

The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm. per second. How fast is the area decreasing when the two equal sides are equal to the base ?

Evaluate the following lim_(xto3) (x^2 -9)/(x-3)

A speaks truth in 75% of the cases and B in 80% of the cases. Then the probability that their statements about an incident do not match , is

int_2^5[x]dx

If L is a line through (-1,3) and (4,2), for what value of k is (3,k) on L?

For a complex number z, if z^(2)+barz-z=4i and z does not lie in the first quadrant, then ("where "i^(2)=1)

EFGH is a rhombus such that the angle EFG is 60^(@). The magnitude of vectorsbar(FH)and {m bar(EG)} are equal where m is a scalar. What is the value of m?

Find the area of the region bounded by the ellipse (x^2)/(4)+(y^2)/(9)=1.

Show thet x^(2) + y^(2) - 6x - 9y + 13 = 0 , x^(2) + y^(2) - 2x - 16 y =0 touch each other. Find the point of contact and the equation of common tangent at their point of contact.

Find the values of each of the expression following : tan^(-1)("tan"(3pi)/4)

For each of the following functions find the points of discontinuity and determine their character : (a) y=(1)/u^(2)+u-2," where u"=1/(x-1).

If the lines y=-4x+b are tangents to the curve y=1/x, then b =

int(x^(3)-6x^(2)+11-6)/(sqrt(x^(2)+4x+3))dx.

If [x] represents greatest integer le x then int_(1)^(3//2) [2x +1]dx=

Find all common tangents of the following pairs of circles. x^(2) + y^(2) + 4x + 2y -4 =0 and x^(2) + y^(2) - 4x - 2y + 4 =0

If B=[(3,4),(4,3)] and C=[(3,-4),(-2,3)] and X=BC, find X^(n)

A coin is tossed three times is succession. If E is the event that there are at least two heads and F is the event in which first throw is a head, then P(E | F)= ………

The set of solutions of the equation,(sqrt3-1)sin theta + (sqrt3+1)cos theta =2 is

A and B throw a die alternatively till one of them gets a '6' and wins the game. Find their respective probabilities of winning, if A starts first.