28278 + Interview Questions in Maths in Class 12

1.	A random variable X has the probability distribution: For the events E = { X is a prime number } and F = { X lt 4}, the probability P(E cup F)is ………..
Answer» 0.35 0.77 0.87 `0.50` ANSWER :B

Discussion

2.	If y= (tan^(-1) x)^(2) show that (x^(2) + 1)^(2) y_(2) + 2x (x^(2)+ 1)y_(1) = 2
Answer» ANSWER :2

Discussion

3.	Find an approximate value of the following correctedto 4 decimal places. root(3)(1002)-root(3)(998)
Answer» ANSWER :`0.0133`

Discussion

4.	At random the letters of the word "ARTICLE" are arranged in all possible ways then the probability that the arrangement begins with a vowel is
Answer» `(1)/(7)` `(2)/(7)` `(3)/(7)` `(5)/(7)` Answer :C

Discussion

5.	int tan^(4) x dx=
Answer» ANSWER :`(1)/(4)tan^(-1)X-(1)/(2)tan^(2)x+log\|secx\|+c`

Discussion

6.	Evaluate {:(" Lt"),(xrarroo):}(x^(2)-sinx)/(x^(2)-2)
Answer» ANSWER :1

Discussion

7.	Find 'x' and 'y' if 2[(X,5),(3,y)]=[(4,10),(6,6)].
Answer» ANSWER :`x=2,y=3`

Discussion

8.	Find the values of a,b ,c and d, if 3[{:(a,b),(c,d):}]=[{:(a,6),(-1,2d):}]+[{:(4,a+b),(c+d,3):}]
Answer» ANSWER :`=3`.

Discussion

9.	At any point (x,y) of a curve, the slope of the tangent is twice the slope of the line 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

10.	A circle S of radius 2 units lies in the first quadrant and touches both the coordinate axes. The equation of the circle with centre at (6, 5) and touching the circle S externally is
Answer» `X^(2) + y^(2) - 12X - 10Y + 12 = 0` `x^(2) + y^(2) - 12x - 10y - 12 = 0` `x^(2) + y^(2) - 12x - 10y + 25 = 0` `x^(2) + y^(2) - 12x - 10y + 52 = 0` ANSWER :D

Discussion

11.	How many times 5 comes between 1 to 1000 ?
Answer» 402 301 300 229 Solution :`7_(C_1) XX 1 xx 9 xx 9 + (7_(C_2) xx 1 xx 9) xx 2 +(7_(C_(3)) xx 1)3 = 300`.

Discussion

12.	P=n(n^(2)-1)(n^(2)-4)(n^(2)-9)…(n^(2)-100) is always divisible by, (n in I)
Answer» `2!3!4!5!6!` `(5!)^(4)` `(10!)^(2)` `10!11!` SOLUTION :`(a,b,C,d)` We know that product of `r` consecutive integer is divisible by `r!` We have `P=(N-10)(n-9)(n-8)…(n+10)` is PRODUT of `21` consecutive integers Which is divisible by `21!` `[(n-10)(n-9)(n-8)...n][(n+1)(n+2)(n+3)...(n+10)]` Which is divisible by `11! 10!` `[(n-10)...(n-6)]xx[(n-5)...(n-1)]xx[n(n+1)...(n+4)]xx[(n+5)...(n+9)]xx(n+10)` which is divisible by `(5!)^(4)`. Also it can be shown that `P` is divisible by `2!3!4!5!6!`

Discussion

13.	Let ABCD be a parallelogram whose diagonals intersect at point P. Suppose S is any point in space. If SA+SB+SC+SD=lambdaSP" then "lambda=_______
Answer» ANSWER :4

Discussion

14.	int(e^(tan^-1(x)))/(1+x^(2))(1+x+x^(2))dx=...+c
Answer» ANSWER :`:. I=(E^(TAN^(-1)X))x+c`

Discussion

15.	int e^(x). " cos"^(2) " x dx"
Answer» Answer :`(1)/(2) e^(x) +(1)/(10)e^(x) (2 SIN 2x +COS 2x)+c`

Discussion

16.	The radius of circle having centre at (2,1) and whose on of the chord is diameter of the circle x^(2)+y^(2)-2x-6y+6=0 is
Answer» 1 2 3 4 Answer :C

Discussion

17.	An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?
Answer» ANSWER :`(1)/(52)`

Discussion

18.	If f(x)=cos^(2) x+cos^(2) 2x+cos^2 3x, then the number of vlaues of x in [0,2pi] for which f(x)=1 is
Answer» 4 6 8 10 Answer :D

Discussion

19.	l=inttan^(-1)""((1)/(x^(2)-x+1))dx is equal to
Answer» `xtan^(-1)((1)/(X^(2)-x+1))+log_(e)""(x)/((2-x)sqrt(1+x^(2))sqrt(2x-x^(2)))+c` `xcot^(-1)(x^(2)-x+1)+log_(e)""(x)/((2-x)sqrt(1+x^(2))sqrt(2x-x^(2)))+c` `TAN^(-1)((1)/(x^(2)-x+1))+c` `xtan^(-1)""(1)/(x^(2)-x+1)-tan^(-1)(1-x)+(1)/(2)log""(x^(2)-2x+2)/(x^(2)+1)+c` ANSWER :D

Discussion

20.	Evaluate the following integrals (iii) int_(1)^(2)(log x)/(x^(2))dx
Answer» ANSWER :`(1)/(2)(1- LOG 2)`

Discussion

21.	If (K_n)/( L_n)= 1024 where K_(n) = int_(0)^(1) x^(n) (2-x)^(n) dx, L_(n) = int_(0)^(1) x^(n) (1-x)^(n) dx, then n is equal to
Answer» ANSWER :`2.50`

Discussion

22.	find the percentage of error in calculation of the surface area of a sherical ballon of diameter 14.02 m. if the true diameter is 14m.
Answer»

Discussion

23.	Solve the inequalities : (a) \|x\|-2\| le 1, (b) \|\|2-3x\|-1\|gt 2, (c) (x-2) sqrt(x^(2)+1) gt x^(2)+2
Answer» Answer :`(a) -3 lt xlt -1 or 1 lt X lt 3; (b) x lt -1/3 or x gt 5/3 (c) x-2 gt 0 x(4X^(2)-x+4) lt 0`

Discussion

24.	Cnsider the equation\|2x\|x-4\|=x+4 If P= greast composite number less than 34 satisfying the given equation then p^(2007) has the digit on its units place as
Answer» 8 1 7 0 Answer :C

Discussion

25.	Let f : R toR and g: R toR be the functions defined by f(x) = (x)/(1+ x^2), x in R , g(x) = (x^2) /(1+ x^2) , x in R Then, the correct statement (s) among the following is/are : (a) both f.g are one-one (b) both f.g are onto (c) both f.g are not one-one as well as not onto (d)fand g are onto but not one-one
Answer» A A,B D C Answer :D

Discussion

26.	If a vector a expressed as the sum of two vectors vec(alpha) and vec(beta) along and perpendicular to a given vector b, then vec(beta) =
Answer» `((a XX B)xxb)/(\|b\|^(2))` `(b xx(a xx b))/(\|b\|^(2))` `(b xx (a xx b))/(\|b\|)` ((a.b)/(\|b\|^(2)))b` ANSWER :B

Discussion

27.	Minimum vlaue of \|x-p\| + \|x-15\| +\|x-p-15\|. If p le x le 15 and 0 lt p lt 15 :
Answer» 30 15 10 0 Answer :B

Discussion

28.	Evaluate int_(0)^(100pi) sqrt((1-cos 2 x)/(2))dx
Answer» 100 200 50 400 Answer :B

Discussion

29.	Which function has a double root ?
Answer» `y=X^2 + 4x-4` `y=x^2 + x+ 1` `y=x^2 -4` `y=x^2 + 6x + 9` Answer :D

Discussion

30.	Normal at (3, 4) to the rectangular hyperbola x y - y - 2 x - 2 = 0 meets the curve again at the points
Answer» 1,2 2,3 `-1,0` NONE of these ANSWER :C

Discussion

31.	The next term of G.P. x, x^(2) + 2 and x^(3) + 10 is -
Answer» `S_(40) = -820` `S_(2N) GT S_(2n + 2)` `S_(51) = 1275` `S_(2n+1) gt S_(2n-1)` ANSWER :A,D

Discussion

32.	A bag contains some white and some black balls, all combinations being equally likely. The total number of balls in the bag is 12. Four balls are drawn at random from the bag at random without replacement.
Answer» <P>`{:(q,s,s,r):}` `{:(r,s,q,p):}` `{:(q,s,r,p):}` `{:(q,p,r,q):}` Solution :Let `E_(i)` denote the event that the bag contains I black and `(12-i)` white balls `(i=0,1,2,…,)` and A denote the event that the four balls drawn are black. Then `P(E_(i))1/13(i=0,1,2...,12)` `P((A)/(E_(i)))=(""^(i)C_(4))/(""^(12)C_(4))"for"ige4` a. `P(A)underset(i=0)overset(12)sumP(E_(i))P((A)/(E_(i)))` `=1/13xx(1)/(""^(12)C_(4))[""^(4)C_(4)+""^(5)C_(4)+...+""^(12)C_(4)]` `=(""^(13)C_(5))/(13xx""^(12)C_(4))=1/5` b. CLEARLY, `P((A)/(E_(10)))=(""^(10)C_(4))/(""^(12)C_(4))=14/33` c. By Bayer's THEOREM, `P((E_(10))/(A))=(P(E_(10))((A)/(E_(10))))/(P(A))` `(1/13xx14/33)/(1/5)=70/429` d. Let B denote the probability of drawing 2 white and 2 black balls. Then `P((B)/(E_(i)))=0if i=0,1or11,12` `P((B)/(E_(i)))=(""^(i)C_(2)xx""^(12-i)C_(2))/(""^(12)C_(4))"for"i =2,3,...,10` `P(B)=underset(i=0)overset(12)sumP(E_(i))P((B)/(E_(i))` `=1/13xx(1)/(""^(12)C_(4))[2{""^(2)C_(2)xx""^(3)C_(2)+...+""^(10)C_(2)xx""^(2)C_(2)]` `=1/13xx(1)/(""^(12)C_(4))[2{""^(2)C_(2)""^(10)C_(2)+""^(3)C_(2)+""^(9)C_(2)+...+""^(5)C_(2)xx""^(7)C_(2)}+""^(6)C_(2)xx""^(6)C_(2)]` `=1/13xx1/495(1287)=1/5`

Discussion

33.	Out of the following which statement is true for x in (0,1) ?
Answer» `E^(X)LT 1+x` `log_(e )(1+x)lt x` `sin x gt x` `log_(e )x gt x-1` ANSWER :B

Discussion

34.	Shortest distance between the linesbar (r ) (2i- j) + lambda (2i+j-3k) and bar ( r ) = (i- j + 2k ) + mu (2i + j - 5k) is
Answer» `3/(SQRT(20))` `1/(sqrt(5))` `2/(sqrt(5))` `3/(sqrt(5))` Answer :B

Discussion

35.	If t_(1),t_(2),t_(3) are the feet of normals drawn from (x_(1),y_(1)) to the parabola y^(2)=4ax then the value of t_(1)t_(2)t_(3) =
Answer» 0 `(y_(1))/(a)` `(2a-x_(1))/(a)` `(x_(1)-2a)/(a)` ANSWER :B

Discussion

36.	If (x-3)^(2)
Answer» 2.67 2 1.5 1.2 Answer :C

Discussion

37.	int_0^picos^2xsinxdx
Answer» SOLUTION :`int_0^picos^2x.sinxdx` [PUT cosx=t, Then sindx=-DT When x=0, t=1, When `x=pi`, t=-1] =`int_1^-1t^2(-dt)=int_-1^1t^2dt=[t^3/3]_-1^1` =1/3+1/3=2/3

Discussion

38.	Find the second order derivatives of the functions x.cos x
Answer» ANSWER :`-(X COS x+ 2 SIN x)`

Discussion

39.	If alpha, beta are the roots of the quadratic equation ax^(2)+bx +c=0 and 3b^(2)=16ac, then
Answer» `ALPHA=4beta or BETA = 4 alpha` `alpha=-4beta or beta =- 4alpha` `alpha=3beta or beta =3alpha` `alpha= -3beta or beta = -3alpha` ANSWER :C

Discussion

40.	Find the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3)/(1) and vecr=(-3veci-7hatj+6veck)+t(-3veci+2hatj+4veck)
Answer» SOLUTION :N/A

Discussion

41.	If two of the roots of 2x^(3) - 3x^(2) - 3x + 2 = 0are differ by 3 then the roots are
Answer» `-1,` 1/3, 2 `-3`/2, -4/3, -5/3 `-1`, 1/2, 2 2, 2, -1 Answer :3

Discussion

42.	Using mathematical induction, the numbers a_(n)'s are defined by,a_(0)=1, a_(n+1) = 3n^(2)+n + a_(n), (n ge 0). Then, a_(n) is equal to
Answer» `N^(3)+n^(2)+1` `n^(3)+n^(2)+1` `n^(3)-n^(2)+1` `n^(3)-n^(2)` Answer :B

Discussion

43.	Let A be the set of all 3 xx 3 determinants with entries 0 or 1 only and B be the subset of A consisting of all determinants with value 1. If C is the subset of A consisting of all determinates with value - 1, then
Answer» `N(C)=0` `n(B)= n(C)` `A=B CUP C` `n(B)=2N(A)` ANSWER :B

Discussion

44.	Let S = sum _(r=1)^(30) (""^(30+r)C_(r) (2r-1))/(""^(30)C_(r)(30+r)),K=sum_(r=0)^(30) (""^(30)C_(r))^(2) and G=sum_(r=0)^(60) (-1)^(r)(""^(60)C_(r) )^(2) The value of K + G is
Answer» 2 S - 2 2 S - 1 2 S + 1 2 S + 2 Solution :`because S = sum _(r=1)^(30) (""^(30+r)C_(r) (2r-1))/(""^(30)C_(r)(30+r))=sum_(r=0)^(30) (""^(30+r)C_(r))/(""^(30)C_(r))(1-(30-r+1)/(30+r))` `=sum_(r=0)^(30)[ (""^(30+r)C_(r))/(""^(30)C_(r)) -(""^(30+r)C_(r))/(""^(30)C_(r))CDOT ((30-r+1))/((30+r))]` `=sum_(r=0)^(30)[ (""^(30+r)C_(r))/(""^(30)C_(r)) -""^((30+r)/(r)cdot ^(29+r)C_(r-1))/(""^(30)C_(r))cdot ((30-r+1))/(30+r)]` `=sum_(r=0)^(30)[ (""^(30+r)C_(r))/(""^(30)C_(r)) -( ""^(29+r)C_(r-1))/(""^(30)C_(r-1)) ][because (""^(n)C_(r))/(""^(n)C_(r-1))=(n-r+1)/r]` For n = 30 `((31-r)/rcdot ""^(30)C_(r)=""^(30)C_(r-1))` `=(""^(30+30)C_(30))/ (""^(30)C_(30)) - (""^(29-1)C_(0))/(""^(30)C_(0))= ""^(60)C_(30)-1` `K = sum _(r=1) ^(30) (""^(30)C_(r))^(2) = ""^(60)C_(30) and G = sum_(r=0)^(60) (-1)^(r) (""^(60)C_(r))^(2)` `(""^(60)C_(0))^(2) - (""^(60)C_(1))^(2)+(""^(60)C_(2))^(2)-...+(""^(60)C_(60))=""^(60)C_(30)` [`because n=60` is even ] `K+ G=2 cdot ""^(60)C_(30) = 2 (S+1) = 2 S+2`

Discussion

45.	The maximum possible number of points of intersection of 8 straightlines and 4 circles is
Answer» 164 76 104 32 Answer :C

Discussion

46.	Sound is transmitted form middle ear to internal ear due to :-
Answer» VIBRATIONS of tympanum Vibrations of STAPES STRIKING of stapes on OVAL window All the above Answer :A

Discussion

47.	Let f(x) = sin x (1+cos x) , x in (0,2pi). Find thenumberof criticalpointsof f(x) . Also identify whichof these critical points are points of Maxima//Minima.
Answer» Answer :THREE `X=(PI)/(3)` ispointof maxima. `x =pi` is nota pointof extrema. `x=(5PI)/(3k)` ispoint ofminima.

Discussion

48.	If y=(tan^(-1)x)^(2) show that (x^(2)+1)^(2)y_(2)+2x(x^(2)+1)y_(1)=2
Answer» 4 0 2 1 Answer :C

Discussion

49.	Consider two lines in the xy-plane , as shown above. If line 1 has equation y=m_1x + b_1, and line 2 has equation y=m_2x + b_2. Which is a true statement ?
Answer» `m_1 LT m_2` `b_1 lt b_2` `b_2 lt 0` `m_2 GT 0` ANSWER :B

Discussion

50.	Let f(x)={{:([x]",",-2lexle-(1)/(2)),(2x^(2)-1",",-(1)/(2)ltxle2):}" and "g(x)=f(\|x\|)+\|f(x)\| [where [x] represents the greatest integer function.] The number of points where g ( x)is non -differentiable is -
Answer» 4 5 2 3 Answer :D

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A random variable X has the probability distribution: For the events E = { X is a prime number } and F = { X lt 4}, the probability P(E cup F)is ………..

If y= (tan^(-1) x)^(2) show that (x^(2) + 1)^(2) y_(2) + 2x (x^(2)+ 1)y_(1) = 2

Find an approximate value of the following correctedto 4 decimal places. root(3)(1002)-root(3)(998)

At random the letters of the word "ARTICLE" are arranged in all possible ways then the probability that the arrangement begins with a vowel is

int tan^(4) x dx=

Evaluate {:(" Lt"),(xrarroo):}(x^(2)-sinx)/(x^(2)-2)

Find 'x' and 'y' if 2[(X,5),(3,y)]=[(4,10),(6,6)].

Find the values of a,b ,c and d, if 3[{:(a,b),(c,d):}]=[{:(a,6),(-1,2d):}]+[{:(4,a+b),(c+d,3):}]

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

A circle S of radius 2 units lies in the first quadrant and touches both the coordinate axes. The equation of the circle with centre at (6, 5) and touching the circle S externally is

How many times 5 comes between 1 to 1000 ?

P=n(n^(2)-1)(n^(2)-4)(n^(2)-9)…(n^(2)-100) is always divisible by, (n in I)

Let ABCD be a parallelogram whose diagonals intersect at point P. Suppose S is any point in space. If SA+SB+SC+SD=lambdaSP" then "lambda=_______

int(e^(tan^-1(x)))/(1+x^(2))(1+x+x^(2))dx=...+c

int e^(x). " cos"^(2) " x dx"

The radius of circle having centre at (2,1) and whose on of the chord is diameter of the circle x^(2)+y^(2)-2x-6y+6=0 is

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000﻿ truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively.﻿ One of the insured persons meets with an accident. What is the probability that﻿ he is a scooter driver?

If f(x)=cos^(2) x+cos^(2) 2x+cos^2 3x, then the number of vlaues of x in [0,2pi] for which f(x)=1 is

l=inttan^(-1)""((1)/(x^(2)-x+1))dx is equal to

Evaluate the following integrals (iii) int_(1)^(2)(log x)/(x^(2))dx

If (K_n)/( L_n)= 1024 where K_(n) = int_(0)^(1) x^(n) (2-x)^(n) dx, L_(n) = int_(0)^(1) x^(n) (1-x)^(n) dx, then n is equal to

find the percentage of error in calculation of the surface area of a sherical ballon of diameter 14.02 m. if the true diameter is 14m.

Solve the inequalities : (a) |x|-2| le 1, (b) ||2-3x|-1|gt 2, (c) (x-2) sqrt(x^(2)+1) gt x^(2)+2

Cnsider the equation|2x|x-4|=x+4 If P= greast composite number less than 34 satisfying the given equation then p^(2007) has the digit on its units place as

If a vector a expressed as the sum of two vectors vec(alpha) and vec(beta) along and perpendicular to a given vector b, then vec(beta) =

Minimum vlaue of |x-p| + |x-15| +|x-p-15|. If p le x le 15 and 0 lt p lt 15 :

Evaluate int_(0)^(100pi) sqrt((1-cos 2 x)/(2))dx

Which function has a double root ?

Normal at (3, 4) to the rectangular hyperbola x y - y - 2 x - 2 = 0 meets the curve again at the points

The next term of G.P. x, x^(2) + 2 and x^(3) + 10 is -

A bag contains some white and some black balls, all combinations being equally likely. The total number of balls in the bag is 12. Four balls are drawn at random from the bag at random without replacement.

Out of the following which statement is true for x in (0,1) ?

Shortest distance between the linesbar (r ) (2i- j) + lambda (2i+j-3k) and bar ( r ) = (i- j + 2k ) + mu (2i + j - 5k) is

If t_(1),t_(2),t_(3) are the feet of normals drawn from (x_(1),y_(1)) to the parabola y^(2)=4ax then the value of t_(1)t_(2)t_(3) =

If (x-3)^(2)

int_0^picos^2xsinxdx

Find the second order derivatives of the functions x.cos x

If alpha, beta are the roots of the quadratic equation ax^(2)+bx +c=0 and 3b^(2)=16ac, then

Find the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3)/(1) and vecr=(-3veci-7hatj+6veck)+t(-3veci+2hatj+4veck)

If two of the roots of 2x^(3) - 3x^(2) - 3x + 2 = 0are differ by 3 then the roots are

Using mathematical induction, the numbers a_(n)'s are defined by,a_(0)=1, a_(n+1) = 3n^(2)+n + a_(n), (n ge 0). Then, a_(n) is equal to

Let A be the set of all 3 xx 3 determinants with entries 0 or 1 only and B be the subset of A consisting of all determinants with value 1. If C is the subset of A consisting of all determinates with value - 1, then

Let S = sum _(r=1)^(30) (""^(30+r)C_(r) (2r-1))/(""^(30)C_(r)(30+r)),K=sum_(r=0)^(30) (""^(30)C_(r))^(2) and G=sum_(r=0)^(60) (-1)^(r)(""^(60)C_(r) )^(2) The value of K + G is

The maximum possible number of points of intersection of 8 straightlines and 4 circles is

Sound is transmitted form middle ear to internal ear due to :-

Let f(x) = sin x (1+cos x) , x in (0,2pi). Find thenumberof criticalpointsof f(x) . Also identify whichof these critical points are points of Maxima//Minima.

If y=(tan^(-1)x)^(2) show that (x^(2)+1)^(2)y_(2)+2x(x^(2)+1)y_(1)=2

Consider two lines in the xy-plane , as shown above. If line 1 has equation y=m_1x + b_1, and line 2 has equation y=m_2x + b_2. Which is a true statement ?

Let f(x)={{:([x]",",-2lexle-(1)/(2)),(2x^(2)-1",",-(1)/(2)ltxle2):}" and "g(x)=f(|x|)+|f(x)| [where [x] represents the greatest integer function.] The number of points where g ( x)is non -differentiable is -

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?