28278 + Interview Questions in Maths in Class 12

1.	Solve the following Linear Programming Problems graphically : Maximise Z = 3x + 2y subject to x+2y le 10, 3x+y le 15, x, y ge 0
Answer» Answer :The MAXIMUM value of Z = 3x + 2Y is 18 at the POINT P(4, 3)

Discussion

2.	Differentiate the functions with respect to x in cos (sin x)
Answer» ANSWER :`-COS X.SIN (sin x)`

Discussion

3.	Evaluate int sec^(4) x dx
Answer» ANSWER :`(SEC^(2)xtanx)/(3)+(2)/(3)tanx+c`

Discussion

4.	Evaluate the following integrals inttan^(-1)((3x-x^(3))/(1-3x^(2)))dx
Answer» Answer :`3[xtan^(-1)X-(1)/(2)log(1+x^(2))]+C`

Discussion

5.	Statement-I : Area bounded by y =e^(x),y=0 and x=0 is 1 square units Statement -II: Area bounded by y=log _e x ,x=0 and y=0is 1 square units
Answer» STATEMENT -I is TRUE statement -II is a correct EXPLANATION for statement-I Statement -I is true ,Statement-II is not Trueexplanation for Statement-I Statement -I is True Statement-II is FALSE Statement -I is False,Statement -II is True Answer :A

Discussion

6.	Let f:R rarrR be definedasf(x) = 3x Choose the correct answer
Answer» F is one-one onto f is MANY one f is one-one but not onto f is NEITHER one-one nor onto Answer :A

Discussion

7.	Let triangle ABC be an isosceles triangle with AB=AC. Suppose that the angle bisector of its angle B meets the side AC at a point D and that BC=BD+AD. Find angle A (in degrees).
Answer» Solution :`BC=BD+AD` `a=p+q` or `(a)/(p)=1+(q)/(p)` USING SINE law in `DELTAABD` `(sin3x)/(sin2x)=1+(SINX)/(sin4x)implies(sin3x.sin4x-sinx.sin2x)/(sin2x.sin4x)=1` `2sin3x.sin4x-2sinx.sin2x=2sin2x.sin4x` `(cosx-cos7x)-(cosx-cos3x)=cos2x-cos6x` `cos3x-cos7x=cos2x-cos6x` `2sin5x.sin2x=2sin4x.sin2x` as `sin5x=sin4x` `5x+4x=180^(@)""implies""x=20^(@),"""HENCE "angleA=180^(@)-80^(@)=100^(@)`

Discussion

8.	If A and B are symmetric matrices of same order, then AB - BA is a
Answer» SKEW SYMMETRIC MATRIX Symmetric matrix Zero matrix IDENTITY matrix ANSWER :A

Discussion

9.	Find a positive value of m for which the coefficient of x^(2) in the expansion (1 + x)^(m) is 6.
Answer» ANSWER :` m = 4`, SINCE `m` cannot be NEGATIVE

Discussion

10.	Find the distance of the point (-6,0,0) from the plane 2x-3y+6z = 2.
Answer» ANSWER :`= \| (- 12-0+0-2)/( sqrt(49) ) \| = \| ( -14)/( 7) \|=2`

Discussion

11.	Assertion (A): The polar of centre of circle w.r.t same circle does not exist. Reason (R), Distance between parallel tangents of circle is diameter of circle. The correct answer is
Answer» Both A and R are true and R is the correct EXPLANATION of A Both A and R are true and R is not the correct explanation of A A is true but R is false A is false but R is true Answer :B

Discussion

12.	What is the value of {:(""sum""(i+j),-sum""(i+j)),(1leiltle10,1 le i lt 10),("i + j = odd","i+j=even"):} ?
Answer» ANSWER :55

Discussion

13.	Number of permutations of 10 different objects taken all at a time in which particular 4 never comes together is
Answer» `10!xx4!` 10!-4! `(7!6!)/(4!)` 10! -7! 4! ANSWER :D

Discussion

14.	Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L _(1) , L _(2)) : L _(1) is parallel to L _(2)}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x +4.
Answer» Answer :The SET of all LINES `y =2X +c, c in R`

Discussion

15.	The probability distribution of a random variable X is given below : The value of k is ……….
Answer» `(1)/(10)` `(2)/(10)` `(3)/(10)` `(7)/(10)` ANSWER :A

Discussion

16.	Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector 3hati+5hatj-6hatk.
Answer» ANSWER :`=7`

Discussion

17.	int_(0)^(pi//2) (dx)/( 2 cos x+ 3) is equal to
Answer» `(2)/( sqrt5) TAN^(-1) (1)/( sqrt5)` `(1)/( sqrt5) tan^(-1) (1)/(sqrt5)` `1` `(2)/( SQRT3) tan^(-1) (1)/( sqrt5)` Answer :A

Discussion

18.	I: In a Delta ABC, if 4s(s-a)(s-b)(s-c)=a^2b^2 then it is right angled triangle II: In a Delta ABC, sin A+ sin B+sin C is maximum then triangle is equilateral
Answer» only I is true only II is true both I, II are true neither I nor II is true Answer :C

Discussion

19.	If the position vectors of points P, Q, R and overline(P), overline(q), overline(r)" are " overline(r)=(2overline(p)+overline(q))/(3), then
Answer» R DIVIDES QP in INTERNALLY in the RATIO 2:2 R divides QP in externally in the ratio 2:2 R divides QP in internally in the ratio 3:2 R divides QP in externally in the ratio 3:2 Answer :B

Discussion

20.	y = Ae^(x) + Be^(2x) + Ce^(2x) satisfies the differental equation
Answer» `y'''- 6Y'' + 11Y'- 6y = 0` `y'''+ 6y'' + 11y'+ 6y = 0` `y'''+ 6y'' - 11y'+ 6y = 0` `y'''- 6y'' - 11y'+ 6y = 0` ANSWER :A

Discussion

21.	If a,b,c,d,e, f are A. M's between 2 and 12 , then find a + b + c +d + e +f.
Answer» ANSWER :`=(6(2 +12))/(2) = 42`

Discussion

22.	Four distinctpoints (a, 0), (0, b), (c , 0) and (0, d) are lie on a plane in such a way that ac = bd, they will
Answer» Form a TRAPEZIUM Form a TRIANGLE Lie on a circle Form a quadrilateral, whose areas is ZERO ANSWER :C

Discussion

23.	At any point (x,y) of a curve, the slope of the tangent is twice the slope of theline segment joining the point of contact to the point(-4, -3).Find the equation of the curve given that it passes through (-2, 1).
Answer» ANSWER :`(X + 4)^(2) = y + 3`

Discussion

24.	Integrate the functions e^(3logx)(x^(4)+1)^(-1)
Answer» ANSWER :`1/4log(X^(4)+1)+C`

Discussion

25.	If x gt 0, then the expression (x ^(100))/( 1 + x + x ^(2) +x ^(3) + ......+ x ^(200)) is always less than or equal to
Answer» ANSWER :`(1)/(201)`

Discussion

26.	Statement -1 \|x^(2)-4\|+\|sinx\|=\|x^(2)+sinx-4\| if x in [2,pi] because Statement -2 \|x\|+\|y\|=\|x+y\| if xy le 0
Answer» `sqrt(ALPHA^(2)-a^(2))/(b^(2))` `sqrt(alpha^(2)-a^(2))/(4b^(2))` `sqrt(alpha^(2)-a^(2))/(16b^(2))` NONE of these ANSWER :c

Discussion

27.	Let F be the set of all onto functions from A = {a_(1), a_(2), …., a_(6)} to B = {b_(1), b_(2), b_(3), b_(4), b_(5)}. If a function is selected at random from F then find the probability that the selected function f is such that f^(-1) (b_(1)) is not a singleton.
Answer» ANSWER :`(1)/(5)`

Discussion

28.	While in Rastapopolous’s Island, Tintin notices many corrupt practices being held there, one of them being gambling. He decides to bring an end to it and walks up to The Trick- ler, the self-proclaimed biggest gambler of the island. After an angry conversation with him, they decide if Tintin beats him, he would stop gambling forever. They decide to play a game. The Trickler controls three ‘rat’ pieces, while Tintin controls a single ‘snake’ piece. Initially, all four pieces are placed somewhere on a two-dimen- sional plane. They take turns making moves, with The Trickler going first. Each move, a player is allowed to move one of her pieces a distance of at most one unit along the straight line. Tintin wins if his ‘snake’ piece can catch one of the rabbit pieces.
Answer» YES No Depends on POSITION None of these Solution :Bonus for All …..Want to KNOW the solution ?? Check Juniors paper for correctQuestion and Solution !

Discussion

29.	The smallest value of of the constant m gt 0 for which f(x) = 9mx - 1 + (1)/(x)ge 0 for all x gt 0, is
Answer» `(1)/(9)` `(1)/(16)` `(1)/(36)` `(1)/(81)` ANSWER :c

Discussion

30.	The remainder when 7^(n) - 6n - 50 (n in N) is divided by 36, is
Answer» 22 23 1 21 Answer :B

Discussion

31.	A point moves such that the sum of the square of its distances from two fixed straight lines intersecting at antle 2alpha is a constant. The locus of points is an ellipse os eccentricity
Answer» <P>`(sqrt(cos 2 alpha))/(sin alpha)if alphalt(pi)/(4)` `(sqrt(-cos 2 alpha))/(cos alpha)if alphalt(pi)/(4)` `(sqrt(cos 2 alpha))/(cos alpha)if alphalt(pi)/(4)` `(sqrt(-cos 2 alpha))/(sin alpha)if alphalt(pi)/(4)` Solution :Letus CHOSSE the point of intersection of the givne lines as the origin and their angular bisector as the x-axis. Thenequation of the two lines will bey mx and y=-mx , where = `TAN alpha`, Let P(h,k) be the point whose locus is to be foud. Then accroding toe the GIVEN condition, `PA^(2)+PB^(2)`= Constant `RARR((k-mh)^(2))/(1+m^(2))+((k+mh)^(2))/(1+m^(2))"" ("c is constant")` `rArr 2(k^(2)+m^(2)h^(2))=c(1+m^(2))` Therfore, the locus of pointP is `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` where `a^(2)=(c(1+m^(2)))/(2m^(2)) and b^(2)=(c(1+m^(2)))/(2)` M If `alpha lt pi //4`, then `m lt1, and a^(2)gtb^(2)` `:.`Ecentricity `=sqrt(1-(b^(2))/(a^(2)))=sqrt(1-m^(2))=(sqrt(cos2alpha))/(cos alpha)` If `alpha gt pi//4` then `mgt1 and a^(2)ltb^(2)` `:.` Ecentricity `=sqrt(1-(b^(2))/(a^(2)))=sqrt(1-(1)/(m^(2)))=(sqrt(-cos 2 alpha))/(sin alpha)`

Discussion

32.	Point P represent the complex number z=x + iy and point Q represents the complex numberz+1/z. If P moves on thecircle \|z\| = 2, then the eccentricity of locus of point Q is
Answer» `3//5` `4//5` `3//4` `1//2` Solution :Let `Q-=alpha+ibeta` GIVEN that \|z\|=2, where z=x+iy `:. x^(2)+y^(2)=4` Now, `alpha+ibeta=z+(1)/(z)=(x+iy)+(1)/(x+iy)` `=(x+iy)+((x-iy)/(4))=(5x)/(4)+(3iy)/(4)` `:. alpha=(5x)/(4)and beta=(3y)/(4)` Since `x^(2)+y^(2)=4` `(16alpha^(2))/(25)+(16beta^(2))/(9)=4` ltbr So, LOCUS of point Q is `(x^(2))/(25)+(y^(2))/(9)=(1)/(4)` Eccentricity of theis conic is given by `e^(2)=1-(9)/(25)=(16)/(25)`

Discussion

33.	Construct a3xx2 matrix whose elements are given by a_(ij)=e^(ix).sin(jx).
Answer» Answer :`=[{:(E^(X)SINX,e^(x)sin(2X)),(e^(2x)sinx,e^(2x)sin(2x)),(e^(3x)sinx,e^(3x)sin(2x)):}]_(3xx2)`

Discussion

34.	A = {theta \|2cos ^(2)theta + sintheta le 2)} B={theta\|pi/2 le theta le (3pi)/2\|}: Find A cap B.
Answer» SOLUTION :`A cap B= {theta\|theta int [pi/2, pi] CUP [(7pi)/6, (3pi)/2]}`

Discussion

35.	Differentiate.e^(e^x)
Answer» SOLUTION :`y=6^(E^x)` Then `dy/dx=e^(e^x)xxd/dx(e^x)=e^(e^x).e^x=e^((x+e^x))`

Discussion

36.	If tan20^(@)+tan40^(@)+tan80^(@)-tan60^(@)=lambda sin40^(@), then lambda/4 is equal to
Answer» ANSWER :2

Discussion

37.	Let bara,barb,barc be three coplanar unit vectors such that bara+barb+barc=barc. If three vectors barp,barq,barr parallel to bara,barb,barc respectively and having integral but different magnitudes , then among the following options \|barp+barq+barr\| can take a value equal to
Answer» 1 0 `SQRT3` 2 Answer :C::D

Discussion

38.	A telephone company in a town has 500 subscribers on its list and collects fixed charges of Rs. 300/- per subscriber per year. The company proposes to increase the annual subscription and it is beloeved that for every increase of Rs. 1/- one subscriber will discontinue the service. Find what increase will bring maximum profit ?
Answer» ANSWER :X = 100

Discussion

39.	.Differentiate.e^x(tanx-cot x)
Answer» SOLUTION :`y=e^x(tanx-cotx)` dy/DX=(dcdot)/dx(e^x)(tanx-cotx)+e^xd/dx(tanx-catx)` `e^x(tanx-cotx)+e^x(sec^2xcosec^2x)

Discussion

40.	The locus of the point such that the sum of the squares of its distances from the planes x+y+z = 0, x - y = 0 and x + y - 2z = 0 is equal to the double of the square of its distance from the plane x=z is
Answer» `x^2 + XY= 0` `x^2 + 2YZ = 0` `y^2 = zx` `y^2 + 2 zx= 0` Answer :D

Discussion

41.	Equation of a line passing through the point (2, -3, 2) and equally inclined to the line L _(1) and L _(2) may be equal to :
Answer» `(x-2)/(2) = (y-3)/(-1) = (z-3)/(1)` `(x-2)/(-2) y + 3 =z-2` `(x-2)/(-4) = (y+4)/(3) = (z-5)/(2)` `(x+2)/(4) = (y+3)/(3) = (z-2)/(-5)` ANSWER :B

Discussion

42.	Find A=[(0,2y,z),(x,y,-z),(x,-y,z)]satisfies A^(T) = A^(-1)
Answer» `pm1/sqrt2` `pm1/sqrt3` `pm1/sqrt6` NONE of these Answer :C

Discussion

43.	{:("sphere", "centre"),(I. r^(2) - 2r (3i + 4j - 5k) + 1 = 0, a.i + j + k),(II. (r - 3i + 2j - 5k). (r + i + j + 3k) = 0, b. 3i + 4j - 5k),(III. i^(1) + y^(2) + z^(2) - 6x + 2y - 4x - 1 = 0, c. 3i + 2j - 5k),(IV. (r - 3i - 2j + 5k)^(2) = 49, d. 3i - j + 2k):}
Answer» B,a,d,c d,b,c,a c,a,d,b a,d,b,c Answer :A

Discussion

44.	Let P(x) be polynominal of degree atmost 5 which leaves remainders -1 and 1 upon division by (x-1)^(3) " and " (x+1)^(3), respectively. The maximum value of y=p''(x) can be obtained atx is equal to
Answer» `-1/sqrt(3)` 0 `1/sqrt(3)` 1 Answer :C

Discussion

45.	Evaluate the following integrals. int(x+1)/(sqrt(x^(2)-x+1))dx
Answer» Answer :`SQRT(x^(2)-x+1)+(3)/(2)sinh^(-1)((2x-1)/(sqrt(3)))+C`

Discussion

46.	Let veca=hati+2hatjandvecb=2hati+hatj. Is \|veca\|=\|vecb\|?Are the vectors vecaandvecbequal?
Answer» Answer :`\|vec(a)\|=\|vec(B)\|` but the two vectors are not equal SINCE their CORRESPONDING components are distinct.

Discussion

47.	If the circle x^2+y^2+2x+3y+1=0 cuts another circle x^2+y^2+4x+3y+2=0 in A and B , then the equation of the circle with AB as a diameter is
Answer» `2x^2+2y^2+2x+6y+1=0` `x^2+y^2+x+3y+3=0` `x^2+y^2+x+6y+1=0` `2x^2+2y^2+x+3y+1=0` ANSWER :A

Discussion

48.	Find the locus of the foot of the perpen- dircular drawn from the origin to any chord of the circle S-= x^(2) + y^(2) + 2gx + 2fy+ c = 0which subtends a right angle at the origin.
Answer» Answer :`2 (x^(2) + y^(2)) + 2GX + 2FY + C = 0`

Discussion

49.	Given then which of the following true
Answer» `m +1 lt n` `m lt n ` `m lt n +1` `m GT n +1` Answer :B::C

Discussion

50.	Evaluate intsec ^(2) x * cosec^(2) x dx
Answer» ANSWER :`TAN X - COT x + C`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve the following Linear Programming Problems graphically : Maximise Z = 3x + 2y subject to x+2y le 10, 3x+y le 15, x, y ge 0

Differentiate the functions with respect to x in cos (sin x)

Evaluate int sec^(4) x dx

Evaluate the following integrals inttan^(-1)((3x-x^(3))/(1-3x^(2)))dx

Statement-I : Area bounded by y =e^(x),y=0 and x=0 is 1 square units Statement -II: Area bounded by y=log _e x ,x=0 and y=0is 1 square units

Let f:R rarrR be definedasf(x) = 3x Choose the correct answer

Let triangle ABC be an isosceles triangle with AB=AC. Suppose that the angle bisector of its angle B meets the side AC at a point D and that BC=BD+AD. Find angle A (in degrees).

If A and B are symmetric matrices of same order, then AB - BA is a

Find a positive value of m for which the coefficient of x^(2) in the expansion (1 + x)^(m) is 6.

Find the distance of the point (-6,0,0) from the plane 2x-3y+6z = 2.

Assertion (A): The polar of centre of circle w.r.t same circle does not exist. Reason (R), Distance between parallel tangents of circle is diameter of circle. The correct answer is

What is the value of {:(""sum""(i+j),-sum""(i+j)),(1leiltle10,1 le i lt 10),("i + j = odd","i+j=even"):} ?

Number of permutations of 10 different objects taken all at a time in which particular 4 never comes together is

Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L _(1) , L _(2)) : L _(1) is parallel to L _(2)}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x +4.

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

Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector 3hati+5hatj-6hatk.

int_(0)^(pi//2) (dx)/( 2 cos x+ 3) is equal to

I: In a Delta ABC, if 4s(s-a)(s-b)(s-c)=a^2b^2 then it is right angled triangle II: In a Delta ABC, sin A+ sin B+sin C is maximum then triangle is equilateral

If the position vectors of points P, Q, R and overline(P), overline(q), overline(r)" are " overline(r)=(2overline(p)+overline(q))/(3), then

y = Ae^(x) + Be^(2x) + Ce^(2x) satisfies the differental equation

If a,b,c,d,e, f are A. M's between 2 and 12 , then find a + b + c +d + e +f.

Four distinctpoints (a, 0), (0, b), (c , 0) and (0, d) are lie on a plane in such a way that ac = bd, they will

At any point (x,y) of a curve, the slope of the tangent is twice the slope of theline segment joining the point of contact to the point(-4, -3).Find the equation of the curve given that it passes through (-2, 1).

Integrate the functions e^(3logx)(x^(4)+1)^(-1)

If x gt 0, then the expression (x ^(100))/( 1 + x + x ^(2) +x ^(3) + ......+ x ^(200)) is always less than or equal to

Statement -1 |x^(2)-4|+|sinx|=|x^(2)+sinx-4| if x in [2,pi] because Statement -2 |x|+|y|=|x+y| if xy le 0

Let F be the set of all onto functions from A = {a_(1), a_(2), …., a_(6)} to B = {b_(1), b_(2), b_(3), b_(4), b_(5)}. If a function is selected at random from F then find the probability that the selected function f is such that f^(-1) (b_(1)) is not a singleton.

The smallest value of of the constant m gt 0 for which f(x) = 9mx - 1 + (1)/(x)ge 0 for all x gt 0, is

The remainder when 7^(n) - 6n - 50 (n in N) is divided by 36, is

A point moves such that the sum of the square of its distances from two fixed straight lines intersecting at antle 2alpha is a constant. The locus of points is an ellipse os eccentricity

Point P represent the complex number z=x + iy and point Q represents the complex numberz+1/z. If P moves on thecircle |z| = 2, then the eccentricity of locus of point Q is

Construct a3xx2 matrix whose elements are given by a_(ij)=e^(ix).sin(jx).

A = {theta |2cos ^(2)theta + sintheta le 2)} B={theta|pi/2 le theta le (3pi)/2|}: Find A cap B.

Differentiate.e^(e^x)

If tan20^(@)+tan40^(@)+tan80^(@)-tan60^(@)=lambda sin40^(@), then lambda/4 is equal to

Let bara,barb,barc be three coplanar unit vectors such that bara+barb+barc=barc. If three vectors barp,barq,barr parallel to bara,barb,barc respectively and having integral but different magnitudes , then among the following options |barp+barq+barr| can take a value equal to

.Differentiate.e^x(tanx-cot x)

The locus of the point such that the sum of the squares of its distances from the planes x+y+z = 0, x - y = 0 and x + y - 2z = 0 is equal to the double of the square of its distance from the plane x=z is

Equation of a line passing through the point (2, -3, 2) and equally inclined to the line L _(1) and L _(2) may be equal to :

Find A=[(0,2y,z),(x,y,-z),(x,-y,z)]satisfies A^(T) = A^(-1)

{:("sphere", "centre"),(I. r^(2) - 2r (3i + 4j - 5k) + 1 = 0, a.i + j + k),(II. (r - 3i + 2j - 5k). (r + i + j + 3k) = 0, b. 3i + 4j - 5k),(III. i^(1) + y^(2) + z^(2) - 6x + 2y - 4x - 1 = 0, c. 3i + 2j - 5k),(IV. (r - 3i - 2j + 5k)^(2) = 49, d. 3i - j + 2k):}

Let P(x) be polynominal of degree atmost 5 which leaves remainders -1 and 1 upon division by (x-1)^(3) " and " (x+1)^(3), respectively. The maximum value of y=p''(x) can be obtained atx is equal to

Evaluate the following integrals. int(x+1)/(sqrt(x^(2)-x+1))dx

Let veca=hati+2hatjandvecb=2hati+hatj. Is |veca|=|vecb|?Are the vectors vecaandvecbequal?

If the circle x^2+y^2+2x+3y+1=0 cuts another circle x^2+y^2+4x+3y+2=0 in A and B , then the equation of the circle with AB as a diameter is

Find the locus of the foot of the perpen- dircular drawn from the origin to any chord of the circle S-= x^(2) + y^(2) + 2gx + 2fy+ c = 0which subtends a right angle at the origin.

Given then which of the following true

Evaluate intsec ^(2) x * cosec^(2) x dx