28278 + Interview Questions in Maths in Class 12

1.	Which of thhe following is equivalent to
Answer» `12x^2-10x-7` `3x^2+5x-28` `3x^2-3x-28` `3x^2-28` ANSWER :B

Discussion

2.	Differentiate the following w.r.t. x: cos (log x+ e^(x)), x gt 0
Answer» Answer :`-sin (log X + e^(x)) [(1)/(x) + e^(x)]`

Discussion

3.	Show that each of the relation R in set A = { x in Z : 0 le x le 12}, given by (i) R = {(a,b) : \|a-b\| is a multiple of 4} (ii) R = {(a,b) : a=b} is an equivalence relation. Find the set of all elements related to 1 in each case.
Answer» ANSWER :(i) ` {1,5,9}, (II) {1}`

Discussion

4.	Fill in the gaps with correct answer . If theta lies in the third quadrant and tan theta = 2 then the value of sin theta is _____
Answer» SOLUTION :`(-2)/(SQRT5)`

Discussion

5.	(1)/(3)+(1)/(2.3^(2))+(1)/(3.3^(3))+(1)/(4.3^(4))+….oo=
Answer» `log_(e )2-log_(e )3` `log_(e )3-log_(e )2` `log_(e )6` `log_(e )3-log_(e )4` Answer :B

Discussion

6.	In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin :(a) 2x + 3y + 4z - 12 = 0(b) 3y + 4z - 6 = 0 (c) x + y + z = 1 (d) 5y + 8 = 0
Answer» Answer :(a) `=((24)/(29),(36)/(29),(48)/(29))` (b)`=(0,(18)/(25),(24)/(25))` (C)`=(1/3,1/3,1/3)` (d) `=(0,-8/5,0)`

Discussion

7.	Statement-1:int_(0)^(1)(cos x)/(1+x^(2))dxgt(pi)/(4)cos1 Statement-2: If f(x) and g(x) are continuous on [a,b], then int_(a)^(b) f(x) g(x)dx=f(c )int_(a)^(b)g(x) for some c in (a,b).
Answer» Statement-1 is TRUE, Statement-2 is True,Statement-2 is a correct EXPLANATION for Statement-1. Statement-1 is True, Statement-2 is not a correct explanation for Statement-1. Statement-1 is True, Statement-2 is False. Statement-1 is False, Statement-2 is True. Solution :Statement-2, being the statement of generalized mean value theorem, is true. Using statement-2, these exists `c in(0,1)` such that `underset(0)overset(1)int (COSX)/(1+x^(2))dx=cos c underset(0)overset(1)int (1)/(1+x^(2))dx=(PI)/(4)cos c` Clearly, `cos c gt cos 1` for all `c in (0,1)` `rArr (pi)/(4)cos c gt (pi)/(4)cops 1` `rArr underset(0)overset(1)int(cos x)/(1+x^(2))dx gt (pi)/(4)cos 1` So, statement-1 is true. Also, statement-2 is a correct explanation for statement-1.

Discussion

8.	If int(dx)/((x-sqrt(x^(2)-1))^(2))=Ax^(3)+Bx^(2)+Cx+D(x^(2)-1)^(3//2)+E, then
Answer» `A=(2)/(3), B=0, C=-1` `A=(1)/(3), B=0, D=(2)/(3)` `A=D=(2)/(3), B=0, C=-2` NONE of these ANSWER :A

Discussion

9.	If alpha, beta , gamma are the roots of x^(3) + qx + q = 0 then the equation whose roots beta gamma + (1)/(alpha), gamma alpha + (1)/(beta) , alpha beta + (1)/(gamma ) is
Answer» `x^(3) - q^(2) - x^(2) - 2qr^(2) x - r^(4) = 0 ` `rx^(3) + q(1 - r) x^(2) + (1 - r)^(3) = 0` `x^(3) - 2Q x^(2) + q^(2) x + r^(2) = 0 ` `r^(2) x^(3) + 3r^(2) x^(2) + (3r^(2) + q^(3)) x + 2q^(3) + r^(2)= 0` Answer :2

Discussion

10.	Calculate the work performed in launching a rocket of weight P from the ground vertically upwards to a height h.
Answer» ANSWER :`(PRH)/(R + H)`

Discussion

11.	Integrate the following function : int(xdx)/(x^(4)+x^(2)+1)
Answer» ANSWER :`(1)/(SQRT3)TAN^(-1)((2x^(2)+1)/(sqrt3))+c`

Discussion

12.	If the equation of the circle which cuts orthogonally the circlex^(2) +y^(2) - 4x + 2y - 7 = 0 and having centre at (2,3) isx^(2) + y^(2) = 2ax + 2by + c = 0then the assending order of a, b, cis
Answer» a,B,C b,c,a b,a,c a,c,b Answer :A::C

Discussion

13.	x= t^(2) + 3t- 8,y= 2t^(2) -2t- 4. If at point (2, -1), lamda = (dy)/(dx) then the value of lamda= ……..
Answer» 2 `(6)/(7)` `-6` 7 Answer :B

Discussion

14.	f: R rarr R , f(x) = (x-1) (x-2)(x-3)then f is ........
Answer» ONE - one but not ONTO. Onto but not one - one One - one and onto. NEITHER one one nor onto. SOLUTION :N/A

Discussion

15.	Compute the""^7C_3+""^6C_4+""6C_3
Answer» Solution :`""^7C_3+""^6C_4+""^6C_3=""^7C_3+""^6C_4+""^6C_(4-1)` ` =""^7C_3+""^(6+1)C_4 = ""^7C_3+""^7C_4` `( :'""^nC_r+""^nC_(r-1)=""^(n+1)C_r)` ` = ""^7C_4+""^7C_(4-1)=""^(7+1)C_4` `= ""^8C_4=(8!)/(4!(8-4)!)=(8765)/(4321)=70`

Discussion

16.	When 2^(1505) is divided by 9, the remainder is
Answer» 8 7 5 6 Answer :C

Discussion

17.	Match the functions of List-I with their nature in List-II and choose the correct option {:(,"List I",,"List II"),((A),f : R rarr R" defined by",(I),"Injection but"),(,f(x)=cos (112x-37),,"not surjection"),((B),f : A rarr B" defined by "f(x)=x\|x\|,(II),"Surjection but"),(,"when "A=[-2, 2] and B=[-4, 4],,"not injection"),((C),f : R rarr R" defined by",(III),"Bijection"),(,f(x)=(x-2)(x-3)(x-5),,),((D),f : N rarr N" defined by "f(n)=n+1,(IV),"Neither"),(,,,"Injection nor"),(,,,"surjection"),(,,(V),"Composite"),(,,,"function"):} Then, the correct match is
Answer» `{:("A","B","C","D"),(I,II,III,IV):}` `{:("A","B","C","D"),(IV,I,II,III):}` `{:("A","B","C","D"),(IV,III,II,V):}` `{:("A","B","C","D"),(IV,III,II,I):}` Answer :D

Discussion

18.	If f(x+2)=2x^2 -3x+5, then find f(2)
Answer»

Discussion

19.	Using elementary transformations, find the inverseof the matrices [(2,3),(5,7)]
Answer» ANSWER :`[(-7,3),(5,-2)]`

Discussion

20.	Let f(X) = {{:([x]",",-2 le x lt 0),(\|x\|",",0 le x le 2):} (where [.] denotes the greatest integer function) g(x) = sec x, x in R - (2n + 1)pi//2. Match the following statements in Column I with their values in Column II in the interval (-(3pi)/(2),(3pi)/(2)). {:(,"Column I",,"Column II"),((A),"Lemit of fog exist at",(p),-1),((B),"Limit of gof doesn't exist at",(q),pi),((C),"Points of discontinuity of fog is/are",(r),(5pi)/(6)),((C),"Points of differentiability of fog is/are",(s),-pi):}
Answer» <P> ANSWER :`(A) rarr (p, q, s), (B) rarr (p), (C) rarr (q, s), (D) rarr (p,r)`

Discussion

21.	If two cards are drawn from pack of 52 cards at random. Find the probability of getting both club cards.
Answer» ANSWER :`(1)/(17)`

Discussion

22.	A window is in the form of a rectangle, together with a semi-circle on its top side as diameter. If the perimeter of the window is 80 inches, determine the dimensions of the rectangle, so that a maximum amount of light may be admitted.
Answer» ANSWER :`((160)/(PI + 4)) ` inches , `((80)/(pi + 4))` inches

Discussion

23.	int_(0)^(pi//2) (x sec^(2). x/2 + 2 tan. x/2)dx=
Answer» `2 PI` `pi` `pi/2` `pi/4` ANSWER :B

Discussion

24.	int (sin " x")/(cos 3x.cos 2x) dx =
Answer» `(1)/(3) " LOG cos 3X" + (1)/(2) "log cos " 2X + c ` `(1)/(3) " log \| sec 3 X\|" (1)/(2) ` log \| sec 2x \| + c `(1)/(3) ` log \| tan 3x \| - `(1)/(2)` log \| tan 2x \| + c none Answer :B

Discussion

25.	Find the equation of the circum circle of the triangle formed by the lines x+ y + 1 =0 , 3x + y -5 =0 , 2x + y -5=0
Answer» ANSWER :` X^(2)+ y^(2) -30X -10Y +25=0 `

Discussion

26.	Let f(x)=min{sin^(-1)x,cos^(-1) x, (pi)/6},x in [0,1]. If area bounded by y=f(x) and X-axis, between the lines x=0 and x=1 is (a-X)/(b(sqrt(3)+1)). Then , (a-b) is".......".
Answer» ANSWER :3

Discussion

27.	The rate of change of volume of a cylinder w.r.t. radius whose radius is equal to its height is ……….
Answer» 4 (area of BASE) 3 (area of base) 2 (area of base) (area of base) ANSWER :B

Discussion

28.	Find the number of injections from a set A containing 4 elements into a set B containing 6 elements.
Answer» ANSWER :360

Discussion

29.	Find the maximum and minimum values of x + sin 2x on [0, 2pi].
Answer» ANSWER :Maximum at x = `2pi`, maximum VALUE `= 2pi`; MINIMUM at x = 0, minimum value = 0

Discussion

30.	Evalute the following integrals intcos ecx log (cos ecx - cot x ) dx
Answer» ANSWER :`(1)/(2) * [log(COSEC X - COT x )]^2+ c `

Discussion

31.	Using determinants show that points A (a, b+ c) , B (b,c+ a) and C ( c, a+ b) are collinear.
Answer» ANSWER :`=0`

Discussion

32.	Find the unit vectors perpendicular to the vectors. hati, hatk
Answer» SOLUTION :If hatn is the UNIT VECTOR PERPENDICULAR to the VECTORS `veca` and `vecb` then `hatn` = `+- (vecaxxvecb)/\|vecaxxvecb\|` `hatn` = `(+-(hatixxhatk))/(\|hatixxhatk\|)` = `(+-hatj)/\|-hatj\|` = `+-hatj`

Discussion

33.	int e^(x//2) sin ((pi)/(4)+ (pi)/(2) )dx =
Answer» `sqrt(2) e(X//2) SIN""(x)/(2) +c` `sqrt(2) e(x//2) COS""(x)/(2) +c` `- sqrt(2) e(x//2) sin""(x)/(2) +c` `-sqrt(2) e(x//2) cos""(x)/(2) +c` Answer :A

Discussion

34.	The normal to the curve x^(2) = 4y passing (1,2) is
Answer» X + y = 3 x – y = 3 x + y = 1 x – y = 1 Answer :A

Discussion

35.	A particle is moving along x-axis. Velocity of particle changes as v=sqrtx with x-coordinate .Choose the INCORRECT option.
Answer» ACCELERATION of PARTICLE is VARIABLE Acceleration of particle is constant At x=3 acceleration of particle is 0.5 Speed of particle INCREASES when x is INCREASED.

Discussion

36.	Matching :
Answer» In a `triangleABC" if " cos A+ cos B+ cos C= (5)/(3)` then `(6r)/(R )` (P) 5 If a chord of length unity SUBTENDS an angle `theta` at the CIRCUMFERNCE of a circle whose radius = R then `4 R sin theta` is(Q) 3 In a `triangleABC` if `r= (1)/(3)` and `ALPHA,BETA,gamma` are length of altitudes then the value of `(1)/(alpha)+(1)/(beta)+(1)/(gamma)+2 =?` (R )2 Incircle of radius 4 cm of a `triangleABC` touches side BC at D. If BD= 6 cm, DC= 8 cm an `triangle` is area of triangle, then `sqrt(sqrt(triangle-3))=` (S) 4 Answer :A::B::C::D

Discussion

37.	The total number of injective mapping from a set with m elements to a set with n elements for, m gt n, is
Answer» `(m!)/(N!(m-n)!)` `(m!)/((m-n)!)` `n^(m)` zero Answer :D

Discussion

38.	If ""^(n)C_(4),""^(n)C_(5) and ""^(n)_(C)6 are in A.P., then n is
Answer» 3 7 14 4 Answer :B::C

Discussion

39.	A coin is tossed a given number of times. IF the probability of getting 7 heads is equal to that of 8 heads. Find the probability of getting 2 heads.
Answer» ANSWER :`(105)/(2^(15))`

Discussion

40.	An equilateral triangle is inscribed in the parabola y^(2)=16ax with one of its vertices at the origin. Then, the centroid of that triangle is
Answer» `(8a, 0)` `(16a, 0)` `(32a, 0)` `(48A, 0)` ANSWER :C

Discussion

41.	Differentiate the functions with respect to x in Exerecises 1 to 8. (sin (ax+b))/(cos (cx+d))
Answer» ANSWER :`a COS (ax+b)SEC(cx+d)+c sin (ax+b)tan (cx+d)sec(cx+d)`.

Discussion

42.	There are 3 black and 4 white balls in one bag. 4 black and 3 white balls in the second bag. A die is rolled and the first bag is selected if it is 1 or 3 and the second bag for the rest. Find the probability of drawing a black ball from the bag thus selected.
Answer» ANSWER :`(11)/(21)`

Discussion

43.	1,alpha_1,alpha_2,alpha_3…..alpha_(n-1) are the n^(th) roots of unity and n is an even natural number ,then(1+alpha_1)(1+alpha_2)(1+alpha_3)….(1+alpha_(n-1))=
Answer» 1 0 -1 2 Answer :B

Discussion

44.	If the angular bisectors of the coordinates axes cut the parabola y^(2) =4axat the points O, A, B then the area ofDelta OABis (O is the origin)
Answer» `3a^(2) ` ` 16 a^(2) ` ` 64 a^(2) ` ` 8A^(2)` Answer :B

Discussion

45.	If A+B+C=90^(@) then cos^(2)A+cos^(2)B+cos^(2)C=
Answer» `1-COS A cos B cos C` `1+2 cos A cos B cos C` `2(1+cos A cos B cos C)` None Answer :B

Discussion

46.	The vector bar(a)=(x,y,z) makes an obtuse angle with y- axis. bar(b)=(y,-2z,3x) and bar( c )=(2z,3x,-y). The vector bar(a) makes equal angle with bar(b) and bar( c ).bar(a) is perpendicular to bar(d)=(1,-1,2). If \|bar(a)\|=2sqrt(3) then bar(a) = ...........
Answer» (1, 2, 3) (2, -2, -2) (-1, 2, 4) NONE of these Answer :B

Discussion

47.	Choose the correct answer. For all real values of x , the minimum value of (1-x+x^2)/(1+x+x^2) isa)0b)1 c)3d)1/3
Answer» 0 1 3 `1/3` ANSWER :D

Discussion

48.	Evalute the following integrals int (1)/((x + 2) sqrt(x + 1)) " dx on"(- 1, infty)
Answer» ANSWER :`2 tan^(-1) (sqrt(X + 1)) + C `

Discussion

49.	The solution set of the inequation sqrt(x^(2)+6x+5)gt (8-x) is
Answer» `(8,oo)` `((59)/(22),8)` `((59)/(22),oo)` `(-1,oo)` ANSWER :C

Discussion

50.	If a point is selected at random inside the rectangle formed by the four lines x=0, y=0, x=2, y=4. Findthe probability that the point lies inside the parabola y^(2)=x. (This problem is to be discussed after Areas in Integral Calculus is over)
Answer» ANSWER :`(1)/(3sqrt(2))`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Which of thhe following is equivalent to

Differentiate the following w.r.t. x: cos (log x+ e^(x)), x gt 0

Show that each of the relation R in set A = { x in Z : 0 le x le 12}, given by (i) R = {(a,b) : |a-b| is a multiple of 4} (ii) R = {(a,b) : a=b} is an equivalence relation. Find the set of all elements related to 1 in each case.

Fill in the gaps with correct answer . If theta lies in the third quadrant and tan theta = 2 then the value of sin theta is _____

(1)/(3)+(1)/(2.3^(2))+(1)/(3.3^(3))+(1)/(4.3^(4))+….oo=

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin :(a) 2x + 3y + 4z - 12 = 0(b) 3y + 4z - 6 = 0 (c) x + y + z = 1 (d) 5y + 8 = 0

Statement-1:int_(0)^(1)(cos x)/(1+x^(2))dxgt(pi)/(4)cos1 Statement-2: If f(x) and g(x) are continuous on [a,b], then int_(a)^(b) f(x) g(x)dx=f(c )int_(a)^(b)g(x) for some c in (a,b).

If int(dx)/((x-sqrt(x^(2)-1))^(2))=Ax^(3)+Bx^(2)+Cx+D(x^(2)-1)^(3//2)+E, then

If alpha, beta , gamma are the roots of x^(3) + qx + q = 0 then the equation whose roots beta gamma + (1)/(alpha), gamma alpha + (1)/(beta) , alpha beta + (1)/(gamma ) is

Calculate the work performed in launching a rocket of weight P from the ground vertically upwards to a height h.

Integrate the following function : int(xdx)/(x^(4)+x^(2)+1)

If the equation of the circle which cuts orthogonally the circlex^(2) +y^(2) - 4x + 2y - 7 = 0 and having centre at (2,3) isx^(2) + y^(2) = 2ax + 2by + c = 0then the assending order of a, b, cis

x= t^(2) + 3t- 8,y= 2t^(2) -2t- 4. If at point (2, -1), lamda = (dy)/(dx) then the value of lamda= ……..

f: R rarr R , f(x) = (x-1) (x-2)(x-3)then f is ........

Compute the""^7C_3+""^6C_4+""6C_3

When 2^(1505) is divided by 9, the remainder is

If f(x+2)=2x^2 -3x+5, then find f(2)

Using elementary transformations, find the inverseof the matrices [(2,3),(5,7)]

If two cards are drawn from pack of 52 cards at random. Find the probability of getting both club cards.

A window is in the form of a rectangle, together with a semi-circle on its top side as diameter. If the perimeter of the window is 80 inches, determine the dimensions of the rectangle, so that a maximum amount of light may be admitted.

int_(0)^(pi//2) (x sec^(2). x/2 + 2 tan. x/2)dx=

int (sin " x")/(cos 3x.cos 2x) dx =

Find the equation of the circum circle of the triangle formed by the lines x+ y + 1 =0 , 3x + y -5 =0 , 2x + y -5=0

Let f(x)=min{sin^(-1)x,cos^(-1) x, (pi)/6},x in [0,1]. If area bounded by y=f(x) and X-axis, between the lines x=0 and x=1 is (a-X)/(b(sqrt(3)+1)). Then , (a-b) is".......".

The rate of change of volume of a cylinder w.r.t. radius whose radius is equal to its height is ……….

Find the number of injections from a set A containing 4 elements into a set B containing 6 elements.

Find the maximum and minimum values of x + sin 2x on [0, 2pi].

Evalute the following integrals intcos ecx log (cos ecx - cot x ) dx

Using determinants show that points A (a, b+ c) , B (b,c+ a) and C ( c, a+ b) are collinear.

Find the unit vectors perpendicular to the vectors. hati, hatk

int e^(x//2) sin ((pi)/(4)+ (pi)/(2) )dx =

The normal to the curve x^(2) = 4y passing (1,2) is

A particle is moving along x-axis. Velocity of particle changes as v=sqrtx with x-coordinate .Choose the INCORRECT option.

Matching :

The total number of injective mapping from a set with m elements to a set with n elements for, m gt n, is

If ""^(n)C_(4),""^(n)C_(5) and ""^(n)_(C)6 are in A.P., then n is

A coin is tossed a given number of times. IF the probability of getting 7 heads is equal to that of 8 heads. Find the probability of getting 2 heads.

An equilateral triangle is inscribed in the parabola y^(2)=16ax with one of its vertices at the origin. Then, the centroid of that triangle is

Differentiate the functions with respect to x in Exerecises 1 to 8. (sin (ax+b))/(cos (cx+d))

There are 3 black and 4 white balls in one bag. 4 black and 3 white balls in the second bag. A die is rolled and the first bag is selected if it is 1 or 3 and the second bag for the rest. Find the probability of drawing a black ball from the bag thus selected.

1,alpha_1,alpha_2,alpha_3…..alpha_(n-1) are the n^(th) roots of unity and n is an even natural number ,then(1+alpha_1)(1+alpha_2)(1+alpha_3)….(1+alpha_(n-1))=

If the angular bisectors of the coordinates axes cut the parabola y^(2) =4axat the points O, A, B then the area ofDelta OABis (O is the origin)

If A+B+C=90^(@) then cos^(2)A+cos^(2)B+cos^(2)C=

The vector bar(a)=(x,y,z) makes an obtuse angle with y- axis. bar(b)=(y,-2z,3x) and bar( c )=(2z,3x,-y). The vector bar(a) makes equal angle with bar(b) and bar( c ).bar(a) is perpendicular to bar(d)=(1,-1,2). If |bar(a)|=2sqrt(3) then bar(a) = ...........

Choose the correct answer. For all real values of x , the minimum value of (1-x+x^2)/(1+x+x^2) isa)0b)1 c)3d)1/3

Evalute the following integrals int (1)/((x + 2) sqrt(x + 1)) " dx on"(- 1, infty)

The solution set of the inequation sqrt(x^(2)+6x+5)gt (8-x) is

If a point is selected at random inside the rectangle formed by the four lines x=0, y=0, x=2, y=4. Findthe probability that the point lies inside the parabola y^(2)=x. (This problem is to be discussed after Areas in Integral Calculus is over)