28278 + Interview Questions in Maths in Class 12

1.	The statement p rarr( q rarr p )is equivalent to
Answer» `p rarr (Q HARR p) ` `p rarr ( p rarr q) ` `p rarr ( p VEE q ) ` `p rarr ( p ^^ q ) ` ANSWER :C

Discussion

2.	If A is matrix of order mxxnand B is a matrix such that AB' and B'A are both defined , then order of matrix B is
Answer» `mxxm` `nxxn` `nxxm` `mxxn` Solution :Let `A=[a_(ij)]_(mxxn)` and `B=[b_(ij)]_(PXXQ)` Now, AB' is defined, so n=q and BA is ALSO defined , so p=m `therefore` Order of `B'=[b_(ij)]_(nxxm)` and order of `B=[b_(ij)]_(mxxn)`

Discussion

3.	int_(-pi/2)^(pi/2)sinxdx = 0
Answer» ANSWER :F

Discussion

4.	Find the slope of the tangent to the curve y=(x-1)/(x-2), x ne 2 at x = 10.
Answer» ANSWER :`-(1)/(64)`

Discussion

5.	The vectors lambda bar(i)+bar(j)+2bar(k),bar(i)+lambda bar(j)-bar(k) and 2bar(i)-bar(j)+lambda bar(k) are coplanar, if …………
Answer» `lambda=-2` `lambda=0` `lambda=1` `lambda=-1` ANSWER :A

Discussion

6.	If Delta=\|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}\| and A_(ij) Cofators of a_(ij) then value of Delta is given by ……..
Answer» `a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)` `a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31)` `a_(21)A_(11)+a_(22)A_(12)+a_(23)A_(31)` `A_(11)A_(11)+a_(21)A_(21)+a_(31)A_(31)` Answer :D

Discussion

7.	2 tan A+ tan B =0
Answer» 2 TAN A - tan B=0 tan A -2 tan B =0 tan A+2 tan B=0 tan A+2tanB=0 Answer :d

Discussion

8.	If x is small and the expansion of (a)/((1-x)^(2)) +(b)/((2+3x)^(2))is 1+x+…oo find(a, b) and coefficient of term containing x^(n).
Answer» SOLUTION :N/A

Discussion

9.	Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2). f'(0) is equal to
Answer» 0 1 F(0) `-f(0)` ANSWER :a

Discussion

10.	1/2+1/4 +1/(8(2)!)+1/(16(3)!)+1/(32(4)!)+ .....oo =
Answer» E `SQRTE` `sqrte/2` `1/e` ANSWER :C

Discussion

11.	If a line through P(-2,3) meets the circle x^(2)+y^(2)-4x+2y+k=0 at A and B such that PA.PB=31 then the radius of the circles is
Answer» 1 2 3 4 Answer :A

Discussion

12.	Using elementary transformations, find the inverseof the matrices [(1,3,-2),(-3,0,-5),(2,5,0)]
Answer» Answer :`[(1,(-2)/(5),(-3)/(5)),((-2)/(5),(4)/(25),(11)/(25)),((-3)/(5),(1)/(25),(9)/(25))]`

Discussion

13.	Find the direct commontangents of the circles x^(2) + y^(2) +22x -4y -100 =0 and x^(2) + y^(2) -22x + 4y +100 =0
Answer» Answer :` 3X+ 4Y -50 =0, 7X -24Y -250 =0`

Discussion

14.	Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f(x) = (x-1)^(1) +3, x in[-3 ,1)
Answer» ANSWER :19, 3

Discussion

15.	If A(3,2,-4),B(4,3,-4),C(3,3,3) and D(4, 2,-3) are given then find the projection of vec(AD) on vec(AB)xx vec(AC).
Answer» ANSWER :`((56)/(99),(-56)/(99),(8)/(99))`

Discussion

16.	Is function f(x) ={{:( ((e^(-x)+x^(2)-a)/(-x))^(-1//x), -1 le x lt0),( ( e^(1//x)+e^(2//x) + e^(3\|x\|))/(ae^(2//x) +be ^(3\|x\|)), 0 lt xlt 1):} continuousat x=0 then
Answer» a=1 `B=e^(-3///2)` `f(0)= e^(3//2)` `f(0) =e^(-1//2)` ANSWER :A::B::C

Discussion

17.	If x=sectheta-costhetaandy=sec^(n)theta-cos^(n)theta, then (x^(2)+4 )((dy)/(dx))^(2) is equal to
Answer» `N^(2)(y^(2)-4)` `n^(2)(4-y^(2))` `n^(2)(y^(2)+4)` None of these Answer :C

Discussion

18.	If A=[(cos alpha, -sin alpha),(sin alpha, cos alpha)], and A+A'=I, then the value of alpha is
Answer» `(PI)/(6)` `(pi)/(3)` `pi` `(3pi)/(2)` Answer :B

Discussion

19.	But for all arbitrary constants,intsqrt((1+sintheta-sin^(2)theta-sin^(3)theta)/(2sintheta-1))d theta is equal to
Answer» `(1)/(2)sqrt(sin THETA-cos2 theta)+(3)/(4sqrt(2))log_(e)\|(4sintheta+1)+2sqrt(2)sqrt(sintheta-cos2theta)\|` `(1)/(2)sqrt(sintheta+cos2theta)+(3)/(4sqrt(2))log_(e)\|(4SIN theta -1)+2sqrt(2)sqrt(sintheta+cos2 theta)\|` `(1)/(2sqrt(2))sqrt(sintheta-cos2 theta)+(3)/(4)log_(e)\|(4 sin theta+1)-sqrt(sin theta - COS 2 theta)\|` `(1)/(2)sqrt(sin theta+cos2theta)+(3)/(4sqrt(2))log_(e)\|4sintheta+1-sqrt(sintheta-cos2 theta)\|` ANSWER :a

Discussion

20.	An urn A contains 8 black balls and 5 white balls. A second urn B contains 6 black and 7 white balls. The probability that a blind folded person in one draw shall obtain a white ball
Answer» `5//13` `7//13` `6//13` `5//26` ANSWER :C

Discussion

21.	underset (xrarr0)lim (cos x) ^(x)
Answer» Answer :`underset (xrarr0)LIM (-SIN x)/(COS x) =0`

Discussion

22.	Show that int_(0)^(a)x(a-x)^(n)dx=(a^(n+2))/((n+1)(n+2)). Hence find int_(0)^(2) x sqrt(2- x )dx
Answer» ANSWER :`(16sqrt(2))/(15)`

Discussion

23.	If f'(x)=(x-a)^(2n)(x-b)^(2m+1), where m, n in N, then :
Answer» x = B is a POINT of inflexion x = b is a point of MINIMA x = b is a point of maxima None of these. ANSWER :B

Discussion

24.	If \|x\|lt1, the coefficient of x^(3) in the expansion of log(1+x+x^(2)) in ascending power of x, is
Answer» `(2)/(3)` `(4)/(3)` `(-2)/(3)` `(-4)/(3)` ANSWER :C

Discussion

25.	Intergrate the following: intcos2xcos(x/2)dx
Answer» SOLUTION :`intcos2xcos(x/2)dx` = `1/2 int2cos2x.cos(x/2)dx` `1/2 INT{cos((5X)/2)+cos((3x)/2)}dx` = 1/2 . 2/5sin((5x)/2)+1/2 . 2/3sin((3x)/2)+C =1/5sin((5x)/2)+1/3sin((3x)/2)+C

Discussion

26.	Show that (2^(2) C_(0) )/(12)+(2^(3)C_(1))/(23)+(2^(4) C_(2))/(34)+…+(2^(n+2)*C_(n))/((n+1)(n+2)) = (3^(n+2) - 2n-5)/((n+1)(n+2)) Hence deduce that(C_(0))/(1.2) -(C_(1))/(2.3) +(C_(2))/(3.4) -…=(1)/(n+2)
Answer» `(3^(n+2)-2n-5)/((n+1)(n+2))` `(3^(n+2)+2n+5)/((n+1)(n+2))` `(3^(n+5) -5N +3)/((n+1)^2)` none Answer :A

Discussion

27.	Three dice are thrown. The probability of getting a total of atleast 5 is
Answer» `(1)/(54)` `(53)/(54)` `(5)/(216)` `(211)/(216)` ANSWER :B

Discussion

28.	intsinx/(1+sinx)dx
Answer» SOLUTION :`I=intsinx/(1+sinx)DX` =`INT(1-1/(1+sinx))dx` =`int[1-((1-sinx))/cos^2x]dx` =`int(1-sec^2x+secxtanx)dx` = x-tanx+secx+c

Discussion

29.	Integrate the functions (cosx)/(sqrt(1+sinx))
Answer» ANSWER :`2sqrt(1+sinx)+C`

Discussion

30.	For what values of a the function e^(ax)is increasing ?
Answer» SOLUTION :`E^(AX)` is INCREASING for `AE^(ax)gt0rArragt0`

Discussion

31.	Evaluate the following integrals int(dx)/(cosx+sinx)
Answer» Answer :`(1)/(sqrt(2))LOG\|(sqrt(2)+tan""(x)/(2)-1)/(sqrt(2)-tan(x)/(2)+1)\|+C`

Discussion

32.	Let f (x) be a function which satisfy the equation f (xy) = f(x) + f(y) for all x gt 0, y gt 0 such that f '(1) =2. Let A be the area of the region bounded by the curves y =f (x), y = \|x ^(3) -6x ^(2)+11 x-6\| and x=0, then find value of(28)/(17)A.
Answer» ANSWER :7

Discussion

33.	A (-2,0) and B(2, 0) are two fixed points and P is a point such that PA-PB=2. Let S be the circle x^(2)+y^(2)=r^(2). Then match the following lists:
Answer» <P> Solution : The locus of point P satisfying `PA-PB=2` is a BRANCH of the HYPERBOLA `x^(2)-y^(2)//3=1`. For r = 2, the circle and the branch of the hyperbola INTERSECT at two points. For r = 1, there is one point of intersection. If m is the SLOPE of the common tangent, then `m^(2)-3=r^(2)(1+m^(2))` `"or"x^(2)=(r^(2)+3)/(1-r^(2))` Hence, there are no common tangents for r gt 1 and two common tangents for r lt 1.

Discussion

34.	ifx in((pi)/(2),pi) ,then( sec x-1)/( sec x+1) isequal to
Answer» `(cosecx+ cotx)^2 ` `(sinx- COS x)^2` `(COSEC x - cot x)^2` `( sec xtanx)^2` ANSWER :C

Discussion

35.	Solve the following system of linear equations 2/x+3/y+(10)/z=4 4/x-6/y+5/z=1 6/x+9/y-(20)/z=2
Answer» ANSWER :`thereforex=2,y=3,z=5`

Discussion

36.	If a, b, c are positive integers and ro is imaginary cube root of unity andf(x) = x^(6a) + x^(6b + 1) + x^(6c + 2) then f(omega) equals
Answer» 0 1 `-1` NONE of these Answer :A

Discussion

37.	Total number of species which have co-ordinate bond N_(2)O_(5),XeF_(6),NH_(4),BF_(4),CO,C_(2)H_(4)
Answer» ANSWER :`4.00`

Discussion

38.	Two cards are drawn in succession from a deck of 52 cards. What is the probability that both cards are of denomination greater than 2 and less than 9?
Answer» Solution :Two cards are drawn in succession from a deck of 52 cards. There are 6 denomination which are GREATER than 2 and LESS than 9. So there are 24 cards whose denominations are greater than 2 and less than 9. `therefore` Their probability= `24/52xx23/51`.

Discussion

39.	underset(0)overset(pi//4)int log ((sin x+cos x)/(cos x))dx
Answer» a. LOG 2 B. `(pi)/(8)log 2` c. `(pi)/(2)log 2` d.`(pi)/(4) log 2` ANSWER :B

Discussion

40.	int f(x) dx=
Answer» `(1)/(6) tan^(-1) ((x^(2)-3X)/(3x))-(1)/(4sqrt(3))LOG \|(x^(2)-sqrt(3)x+3)/(x^(2)+sqrt(3)x+3)\|+c` `(1)/(6) tan^(-1) ((x^(2)-3x)/(3x))+(1)/(4sqrt(3))log \|(x^(2)-sqrt(3)x+3)/(x^(2)+sqrt(3)x+3)\|+c` `(1)/(6) tan^(-1) ((x^(2)+3x)/(3x))+(1)/(4sqrt(3))log \|(x^(2)-sqrt(3)x+3)/(x^(2)+sqrt(3)x-3)\|+c` `(1)/(6) tan^(-1) ((x^(2)+3x)/(3x))+(1)/(4sqrt(3))log \|(x^(2)-sqrt(3)x-3)/(x^(2)+sqrt(3)x-3)\|+c` Answer :A

Discussion

41.	Is the function [x] differentiable at x=2.5?
Answer» SOLUTION :[X] is DIFFERENTIABLE at x=2.5.

Discussion

42.	If 3x^(2) - 11 xy + 10y^(2) - 7x + 13y + k = 0 denotes a pair of straight lines , then the point of intersection of the lines is
Answer» `(1,3)` `(3, 1)` `(-3, 1)` `(1 , - 3)` ANSWER :B

Discussion

43.	An equilateral triangle is inscribed in the parabola y^(2)=8x, with one of its vertices is the vertex of the parabola, Then, the length of the side of that triangle is
Answer» `24sqrt3` `16sqrt3` `8sqrt3` `4sqrt3` ANSWER :B

Discussion

44.	Consider the following data 4,7,8,9,10,12,13,17. (i) Find the mean (ii) Find the mean deviation about the mean.
Answer» ANSWER :`=3`

Discussion

45.	One value of (1+i)^(1//2) is 2^(1//4)e^(ipi//8).The other value is
Answer» `2^(1//4)E^(i(pi//8))` `2^(1//4)R^(i(5pi//8))` `2^(1//4)e^(-i(5pi//8))` `2^(1//4).e^(i(9pi//8)` ANSWER :D

Discussion

46.	"If p then q" (where p and q are statements) says
Answer» If p TS true, then q must be true If p is false, then q must be false Not HAPPENING of p has no effect of happeningof q Both (1) & (3) Answer :D

Discussion

47.	The principal amplitude of (sin 40° + icos 40°)^(5) is
Answer» `70^(@)` `-100^(@)` `110^(@)` `-70^(@)` ANSWER :B

Discussion

48.	A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day ?
Answer» Answer :A manufacturer should produced 3 PACKAGES of NUTS and 3 packages of BOLTS to maximise his PROFIT.

Discussion

49.	(a xx b) . (a xx c) =
Answer» (a.C) (b.c) - (a.b) (b.c) (a.b) (b.c) - (a.b) (a.b) (a.a) (b.c) - (a.b). (a.c) (a.a) (b.b) - (a.b) (a.c) ANSWER :C

Discussion

50.	A page is opened at random from a book containing 600 pages. What is the probability that the number on the page is a perfect square.
Answer» ANSWER :`(7)/(100)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The statement p rarr( q rarr p )is equivalent to

If A is matrix of order mxxnand B is a matrix such that AB' and B'A are both defined , then order of matrix B is

int_(-pi/2)^(pi/2)sinxdx = 0

Find the slope of the tangent to the curve y=(x-1)/(x-2), x ne 2 at x = 10.

The vectors lambda bar(i)+bar(j)+2bar(k),bar(i)+lambda bar(j)-bar(k) and 2bar(i)-bar(j)+lambda bar(k) are coplanar, if …………

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and A_(ij) Cofators of a_(ij) then value of Delta is given by ……..

2 tan A+ tan B =0

If x is small and the expansion of (a)/((1-x)^(2)) +(b)/((2+3x)^(2))is 1+x+…oo find(a, b) and coefficient of term containing x^(n).

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2). f'(0) is equal to

1/2+1/4 +1/(8(2)!)+1/(16(3)!)+1/(32(4)!)+ .....oo =

If a line through P(-2,3) meets the circle x^(2)+y^(2)-4x+2y+k=0 at A and B such that PA.PB=31 then the radius of the circles is

Using elementary transformations, find the inverseof the matrices [(1,3,-2),(-3,0,-5),(2,5,0)]

Find the direct commontangents of the circles x^(2) + y^(2) +22x -4y -100 =0 and x^(2) + y^(2) -22x + 4y +100 =0

Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f(x) = (x-1)^(1) +3, x in[-3 ,1)

If A(3,2,-4),B(4,3,-4),C(3,3,3) and D(4, 2,-3) are given then find the projection of vec(AD) on vec(AB)xx vec(AC).

Is function f(x) ={{:( ((e^(-x)+x^(2)-a)/(-x))^(-1//x), -1 le x lt0),( ( e^(1//x)+e^(2//x) + e^(3|x|))/(ae^(2//x) +be ^(3|x|)), 0 lt xlt 1):} continuousat x=0 then

If x=sectheta-costhetaandy=sec^(n)theta-cos^(n)theta, then (x^(2)+4 )((dy)/(dx))^(2) is equal to

If A=[(cos alpha, -sin alpha),(sin alpha, cos alpha)], and A+A'=I, then the value of alpha is

But for all arbitrary constants,intsqrt((1+sintheta-sin^(2)theta-sin^(3)theta)/(2sintheta-1))d theta is equal to

An urn A contains 8 black balls and 5 white balls. A second urn B contains 6 black and 7 white balls. The probability that a blind folded person in one draw shall obtain a white ball

underset (xrarr0)lim (cos x) ^(x)

Show that int_(0)^(a)x(a-x)^(n)dx=(a^(n+2))/((n+1)(n+2)). Hence find int_(0)^(2) x sqrt(2- x )dx

If f'(x)=(x-a)^(2n)(x-b)^(2m+1), where m, n in N, then :

If |x|lt1, the coefficient of x^(3) in the expansion of log(1+x+x^(2)) in ascending power of x, is

Intergrate the following: intcos2xcos(x/2)dx

Show that (2^(2) *C_(0) )/(1*2)+(2^(3)*C_(1))/(2*3)+(2^(4) *C_(2))/(3*4)+…+(2^(n+2)*C_(n))/((n+1)(n+2)) = (3^(n+2) - 2n-5)/((n+1)(n+2)) Hence deduce that(C_(0))/(1.2) -(C_(1))/(2.3) +(C_(2))/(3.4) -…=(1)/(n+2)

Three dice are thrown. The probability of getting a total of atleast 5 is

intsinx/(1+sinx)dx

Integrate the functions (cosx)/(sqrt(1+sinx))

For what values of a the function e^(ax)is increasing ?

Evaluate the following integrals int(dx)/(cosx+sinx)

Let f (x) be a function which satisfy the equation f (xy) = f(x) + f(y) for all x gt 0, y gt 0 such that f '(1) =2. Let A be the area of the region bounded by the curves y =f (x), y = |x ^(3) -6x ^(2)+11 x-6| and x=0, then find value of(28)/(17)A.

A (-2,0) and B(2, 0) are two fixed points and P is a point such that PA-PB=2. Let S be the circle x^(2)+y^(2)=r^(2). Then match the following lists:

ifx in((pi)/(2),pi) ,then( sec x-1)/( sec x+1) isequal to

Solve the following system of linear equations 2/x+3/y+(10)/z=4 4/x-6/y+5/z=1 6/x+9/y-(20)/z=2

If a, b, c are positive integers and ro is imaginary cube root of unity andf(x) = x^(6a) + x^(6b + 1) + x^(6c + 2) then f(omega) equals

Total number of species which have co-ordinate bond N_(2)O_(5),XeF_(6),NH_(4),BF_(4),CO,C_(2)H_(4)

Two cards are drawn in succession from a deck of 52 cards. What is the probability that both cards are of denomination greater than 2 and less than 9?

underset(0)overset(pi//4)int log ((sin x+cos x)/(cos x))dx

int f(x) dx=

Is the function [x] differentiable at x=2.5?

If 3x^(2) - 11 xy + 10y^(2) - 7x + 13y + k = 0 denotes a pair of straight lines , then the point of intersection of the lines is

An equilateral triangle is inscribed in the parabola y^(2)=8x, with one of its vertices is the vertex of the parabola, Then, the length of the side of that triangle is

Consider the following data 4,7,8,9,10,12,13,17. (i) Find the mean (ii) Find the mean deviation about the mean.

One value of (1+i)^(1//2) is 2^(1//4)e^(ipi//8).The other value is

"If p then q" (where p and q are statements) says

The principal amplitude of (sin 40° + icos 40°)^(5) is

(a xx b) . (a xx c) =

A page is opened at random from a book containing 600 pages. What is the probability that the number on the page is a perfect square.

Show that (2^(2) C_(0) )/(12)+(2^(3)C_(1))/(23)+(2^(4) C_(2))/(34)+…+(2^(n+2)*C_(n))/((n+1)(n+2)) = (3^(n+2) - 2n-5)/((n+1)(n+2)) Hence deduce that(C_(0))/(1.2) -(C_(1))/(2.3) +(C_(2))/(3.4) -…=(1)/(n+2)