28278 + Interview Questions in Maths in Class 12

1.	For the differential equation xy(dy)/(dx)=(x+2)(y+2), find the solution curve passing through the point (1, -1).
Answer» ANSWER :`X+2logabs(x)-2`

Discussion

2.	Differentiate (x+1/x)^(x) w.r.t.x
Answer» ANSWER :`(dy)/(dx) = y[(x^(2)-1)/(x^(2)+1) + log(x+1/x)]`

Discussion

3.	If a sin + b cos (C+x)+b+c =4aThen cot(B)/(2)cot(C )/(2) is equal to
Answer» INFINITE 0 1 none OFTHESE ANSWER :B

Discussion

4.	If a hyperbola passing through the origin has 3x-4y -1=0 and 4x -3y -6=0as its asymptotes , then the equation of its transverse and conjugate axes are
Answer» `x-y-5=0and x+y+1=0 ` ` x-y =0 and x+y +5=0` ` x+y -5=0 and x-y -1=0 ` `x+y-1 =0 and x-y -5=0 ` ANSWER :C

Discussion

5.	{:(1. IF f (x) = x^(x) then f '(e) =A , 2. If f (x) = Sin ^(-1) x then f' (1//2) =B),(3. If f (x) = Tan^(-1) x then f '(0) =C , 4. If f (x) = e ^(x) then f'(e) =D):} The ascending order of A,B,C,D is
Answer» C,B,D,A B,C,D,A A,B,C,D D,C,B,A Answer :A

Discussion

6.	Discuss the continuity of the function defined by f(x) = {(x+2",","if " x lt 0),(-x+2",","if " x gt 0):}
Answer» Answer :Function F is DEFINED for all REAL NUMBER other than ZERO. Hence it is continious

Discussion

7.	If two events are independent, then ………
Answer» They must be MUTUALLY exclusive Sum of their PROBABILITY is 1 (A) and (B) both are correct None of above is correct Answer :D

Discussion

8.	If the angle between two equal circles with centres (3, 10) (-5, 4) is 120^@ then the radius of the circles is
Answer» 10 5 2 1 Answer :A

Discussion

9.	What is the the maximum possibe value of k for which 2013 can be written as sum of k consecutive positive integers ?
Answer» ANSWER :61

Discussion

10.	The order of the differential equation of all parabols whose axis of symmetry is along x-axis, is
Answer» 2 3 1 None of these Answer :A

Discussion

11.	Newton's law of cooling states that the rate of change of the temperature T of an object isproportional to the difference between T and the (constant) temperature tau of the surrounding medium, we can write it as (dT)/(dt) = -k(T - tau) k gt 0 constant An cup of coffee is served at 185^(@)F in a room where the temperature is 65^(@)F. 2 minutes later the temperature of the coffee has dropped to 155^(@)F. log_(e)3 = 1.09872, log_(e).(3)/(4) = 0.2877 Temperature of coffee at time t is given by
Answer» `65+120 e^(-kt)` `75 + 110 e^(-kt)` `65 + 140 e^(-2kt)` `75 + 10 e^(-kt)` Answer :A

Discussion

12.	Newton's law of cooling states that the rate of change of the temperature T of an object isproportional to the difference between T and the (constant) temperature tau of the surrounding medium, we can write it as (dT)/(dt) = -k(T - tau) k gt 0 constant An cup of coffee is served at 185^(@)F in a room where the temperature is 65^(@)F. 2 minutes later the temperature of the coffee has dropped to 155^(@)F. log_(e)3 = 1.09872, log_(e).(3)/(4) = 0.2877 Time required for coffee to have 105^(@)F temperature is
Answer» 6 MINUTE 6.43 minute 7.23 minute 7.63 minute ANSWER :D

Discussion

13.	A: int (2cos x +3sin x)/(4cos x+5 sin x)dx= (-2)/(41)log\|4cos x+5Sinx\|+(23)/(41)x+c R: int (a cos x+b sin x)/(c cos x+d sin x)dx= (ac+bd)/(c^(2)+d^(2))x+(ad-bc)/(c^(2)+d^(2))log\|c cos x+d sin x \|+k
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 correct explanation of A A is true R is FALSE A is false but R is true. Answer :1

Discussion

14.	Newton's law of cooling states that the rate of change of the temperature T of an object isproportional to the difference between T and the (constant) temperature tau of the surrounding medium, we can write it as (dT)/(dt) = -k(T - tau) k gt 0 constant An cup of coffee is served at 185^(@)F in a room where the temperature is 65^(@)F. 2 minutes later the temperature of the coffee has dropped to 155^(@)F. log_(e)3 = 1.09872, log_(e).(3)/(4) = 0.2877 The temperature of any object at t = 2 is
Answer» `tau e^(-k) + [ T(0)] e^(-2K)` `tau e^(k) + [T(0) - tau] e^(-2k)` `tau+[T(0) - tau] e^(-2k)` `tau + 2[T(0)+tau] e^(-)` Answer :C

Discussion

15.	There are 7 Telugu books and 4 Hindi books. From those in how many ways can 4 Telugu and 1 Hindi book be arranged so that the Hindi book is always at the middle is
Answer» 3040 2870 4220 3360 Answer :D

Discussion

16.	int(3x+1)/((x+2)^(2))dx
Answer» ANSWER :`3log\|x+2\|+(5)/(x+2)+C`

Discussion

17.	If the 21st and 22nd terms in the expansion (1+x)^44 are equal then x =
Answer» 7 8 `7//8` `8//7` ANSWER :C

Discussion

18.	Two adjacent sides of a parallelogram ABCD are given by AB=2hati+10hatj+11hatk and AD=-hati+2hatj+2hatk. The side AD is rotated by an acute angle alpha in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the sides AB, then the cosine of the angle alpha is given by
Answer» `(8)/(9)` `(sqrt(17))/(9)` `(1)/(9)` `(4sqrt(5))/(9)` Solution :Now ,AB `= 2 hati+ 10 hatj +11hatk` `AD=- hati + 2 hatj+ 2hatk` `implies\|AB\|=sqrt(4+100+121)=sqrt(225)=15` ` and \|AD\|=sqrt(1+4+4)=sqrt(9)=3` Now `AB.AD=( 2hati+ 10 hatj+11 hatk ).( -hati +2hatj +2hatk)` ` =-2+20+22=40` `thereforecos THETA=(AB.AD)/(\|AB\|\|AD\|)=(40)/(45)=(8)/(9)` ` :'theta+ alpha=90^(@)implies alpha =90^(@)-theta` `impliescos alpha=sintheta= sqrt(1-(64)/(81))=(sqrt(17))/(9)`

Discussion

19.	Prove that the equation x^(4)+2x^(3)+5+ax^(3)+a=0 has at the most two real roots for all values of a epsilon R-{-5}.
Answer» ANSWER :`a=-5`

Discussion

20.	If f(x)=ax^(2)+b,b!=0,xle1 =bx^(2)+ax+c,xgt1, then f(x) is continuous and differentiable at x=1 if :
Answer» `C=0,a=2b` `a=b,c` ARBITRARY `a=b,c=0` `a=b,c!=0`, ANSWER :A

Discussion

21.	If f(x) and g(x) are continuous functions on the interval [0, 4] satisfying f(x)=f(4-x) and g(x)+g(4-x)=3 and int_(0)^(4) f(x)dx=2then int_(0)^(4) f(x)g(x)dx=
Answer» 0 1 2 3 Answer :D

Discussion

22.	Find the number of ways of forming a committee of 5 members from 6 men and 3 ladies.
Answer» ANSWER :`""^9C_4`

Discussion

23.	int_(-1)^(1) (cos h x)/(1+e^(2x))dx=
Answer» `(E^(2))/(2)` `(e^(2)-1)/(2)` `(e^(2)-1)/(2e)` `1-e^(2)` ANSWER :C

Discussion

24.	An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?
Answer» ANSWER :`900 CM^(3)//s`

Discussion

25.	Translate "29 is a prime number which is a sum of two squares" propositions into symbolic form, stating the prime components
Answer» Solution :Let p : 29 is a prime NUMBER. q : It is a SUM of TWO squares `:.` Answer is `p^^q`

Discussion

26.	If (1, a), (b, 2) are conjugate points with renpcet to the circle x^(2)+y^(2)=25, then 4a+2b=
Answer» (3,1) (3,-1) (1,3) (1,-3) ANSWER :B

Discussion

27.	The point in the interval [0, pi] for which the curve y =(1//2)x and y= sin x are farthest apart is
Answer» `PI//2` `pi//4` `pi//6` `pi` ANSWER :D

Discussion

28.	For any vector a, then the value of (axxhati)^(2)+(a xxhatj)^(2)+(axxhatk)^(2) is
Answer» `4a^(2)` `2a^(2)` `a^(2)` `3a^(2)` SOLUTION :Let `a = a_1hati + a_(2) HATJ + a_3hatk` SINCE, `(a xx hati) . (a xx hati) = \|{:(a.a,a.hati),(hati.a,1):}\| = \|a\|^(2) - a_(1)^(2)` Similarly , `(axxhatj)^(2) =\|a\|^(2) - a_2^(2)` and `(a xx hatk)^(2) = \|a\|^(2) -a_(3)^(2)` `:. (a xx hati)+ (a xx hatj)^(2) + (a xx hatk)^(2) = 3\|a\|^(2) - (a_(1)^(2)+ a_(2)^(2) + a_(3)^(2))` `= 3\|a\|^(2) - \|a\|^(2)` `= 2\|a\|^(2) = 2a^(2)`

Discussion

29.	Find P(A//B)," if "P(B)=0.5 and P(A cap B) =0.32
Answer» <P> ANSWER :`P(A\|B)=(16)/(25)`

Discussion

30.	If three vectors 2hat(i)-hat(j)-hat(k), hat(i)+2hat(j)-3hat(k) and 3hat(i)+lambda hat(j)+5hat(k) are coplanar, then the value of lambda is
Answer» `-4` `-2` `-1` `-8` Solution :Let`a=2 hati-hatj-hatk, ` `b=hati+2hatj-3hatkand c=3 hati+lamdahatj+5 hatk` It these vectors are COPLANAR, then [a b c] =0 `implies\|{:(2,-1,-1),(1,2,-3),(3, LAMDA,5):}\|=0` `implies2(10+3 lamda)+(5+9)-(lamda-6)=0` `=20+6 lamda+14-lamda +6=0` `implies5 lamda +40=0 implies lamda=-8`

Discussion

31.	If (1+2x +3x^2)^10 = a_0 +a_1x +a_2x^2 + ……+a_20x^20 then a_2/a_1 =
Answer» 10.5 21 10 5.5 Answer :A

Discussion

32.	If x=3 prod_(r=2)^(n) log_((2n-1))(2n+1) then the value of log_3\|cospix\| is :-
Answer» 0 1 2 3

Discussion

33.	intsqrt((x-1)/(x))dx=
Answer» `SQRT(x^2-x)+log\|x-(1)/(2)+sqrt(x^2-x)\|+C` `sqrt(x^2-x)-log\|x-(1)/(2)+sqrt(x^2-x)\|+c` `sqrt(x^2-x)+(1)/(2)log\|x-(1)/(2)+sqrt(x^2-x)\|+c` `sqrt(x^2-x)-(1)/(2)log\|x-(1)/(2)+sqrt(x^2-x)\|+c` ANSWER :D

Discussion

34.	What is the median of the data given below ? 18,25,19,41,23,29,35,19
Answer» 32 26 25 24 Answer :D

Discussion

35.	writethesimplestformcot^(-1)""((1)/(sqrt(x^2-1))),xgt 1
Answer» ANSWER :`= SEC^(-1) X`

Discussion

36.	Given that p is 'false' and q is 'true' then the statement which is 'false' is
Answer» <P>`~ p to ~ Q` `p to (q ^^ p)` `p to ~q` `q to ~ p` ANSWER :A

Discussion

37.	If graph of the quadratic y = ax ^(2)+bx+c is given below : then:
Answer» `alt 0, b gt 0, C gt 0` `a LT 0, b gt 0, c lt 0` `a lt 0, b lt 0, c gt 0` `a lt 0, b lt 0, c lt 0` Answer :C

Discussion

38.	Find the moment about a line through (0, 0, 0) having the direction 2hat(i)-2hat(j)+hat(k) due to a 20 kg force acting at (-4, 2,5) in the direction of 12 hat(i)-4hat(j)-3hat(k).
Answer» ANSWER :`=-(1520)/(39)` UNITS.

Discussion

39.	Five coins are tossed 3200 times using poission distribution, find the probability of getting five heads 2 times.
Answer» ANSWER :`(E^(-100) XX (100)^(2))/(2)`

Discussion

40.	Let f: [0, infty) to R be such that f(16/sqrt(1+sqrt(x))) = x AA x ge 0, Then f(8)=
Answer» ANSWER :9

Discussion

41.	A five digit number is formed by the digits 1,2,3,4, 5 with no digit being repeated. The probability that the number is divisible by 4, is
Answer» `(1)/(5)` `(2)/(5)` `(3)/(5)` `(4)/(5)` Answer :A

Discussion

42.	Write the number of solution of the following system of equation. x+y+z=1 x+y+z=2 2x+3y+z=0
Answer» SOLUTION :No solution

Discussion

43.	A point is randomly chosen inside the circumcircle of an equilateral triangle. Find the probability that it lies inside the inscribed circle of that triangle.
Answer» ANSWER :`(1)/(4)`

Discussion

44.	Find the shortest distance between the following pair of lines :(x-1)/(2) = (y-2)/(3)=(z-3)/(4),(x-2)/(3)=(y-3)/(4)=(z-5)/(5)
Answer» ANSWER :`3/sqrt2`

Discussion

45.	India and Australia play a series of 7 one-day matches. Each team has equal probabilityof winning a match. No match ends in a draw. If the probabilitythat India wins atleast threeconsecutivematches can be expressed as(p)/(q) where p and q are relatively prime positive integers.Find the unit digit of p.
Answer» ANSWER :7

Discussion

46.	If root3(y)root2(x)=root6((x+y)^(5)) , then (dy)/(dx)
Answer» x-y `x/y` `y/x` x+y Answer :C

Discussion

47.	The point on the curve f (x) = sqrt(x ^(2) - 4) defined in [2,4] where the tangentis parallel to the chord joining the end points on the curve is
Answer» `( SQRT(2) , sqrt(6))` `( sqrt(6) , 2)` ` ( sqrt(2), 6)` `( sqrt(6), sqrt(2))` ANSWER :D

Discussion

48.	Identify the quantifier in the following statements and write the negation of the statement.(i)There exists a number which is equal to its square.
Answer» SOLUTION :There EXISTS

Discussion

49.	int (3cos x+2 sin x)/(4 cos x+3 sin x)dx=
Answer» ANSWER :`(18)/(25)X+(1)/(25)log\|4cosx+3sinx\|+k`

Discussion

50.	Ifalpha, beta , gammaare therootsof x^3+ 3x^2 -4x +2=0thenthe equationwhoserootsare (1)/(alpha beta) ,(1)/( beta gamma),(1)/( gamma alpha) is
Answer» `4X^3 -6x^2 +4x +1=0` `4x^3 +6x^2 -4x -1=0` `4x^3 +6x^2 -4x +1=0` `4x^3 -6x^2 -4x -1=0` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

For the differential equation xy(dy)/(dx)=(x+2)(y+2), find the solution curve passing through the point (1, -1).

Differentiate (x+1/x)^(x) w.r.t.x

If a sin + b cos (C+x)+b+c =4aThen cot(B)/(2)cot(C )/(2) is equal to

If a hyperbola passing through the origin has 3x-4y -1=0 and 4x -3y -6=0as its asymptotes , then the equation of its transverse and conjugate axes are

{:(1. IF f (x) = x^(x) then f '(e) =A , 2. If f (x) = Sin ^(-1) x then f' (1//2) =B),(3. If f (x) = Tan^(-1) x then f '(0) =C , 4. If f (x) = e ^(x) then f'(e) =D):} The ascending order of A,B,C,D is

Discuss the continuity of the function defined by f(x) = {(x+2",","if " x lt 0),(-x+2",","if " x gt 0):}

If two events are independent, then ………

If the angle between two equal circles with centres (3, 10) (-5, 4) is 120^@ then the radius of the circles is

What is the the maximum possibe value of k for which 2013 can be written as sum of k consecutive positive integers ?

The order of the differential equation of all parabols whose axis of symmetry is along x-axis, is

A: int (2cos x +3sin x)/(4cos x+5 sin x)dx= (-2)/(41)log|4cos x+5Sinx|+(23)/(41)x+c R: int (a cos x+b sin x)/(c cos x+d sin x)dx= (ac+bd)/(c^(2)+d^(2))x+(ad-bc)/(c^(2)+d^(2))log|c cos x+d sin x |+k

There are 7 Telugu books and 4 Hindi books. From those in how many ways can 4 Telugu and 1 Hindi book be arranged so that the Hindi book is always at the middle is

int(3x+1)/((x+2)^(2))dx

If the 21st and 22nd terms in the expansion (1+x)^44 are equal then x =

Prove that the equation x^(4)+2x^(3)+5+ax^(3)+a=0 has at the most two real roots for all values of a epsilon R-{-5}.

If f(x)=ax^(2)+b,b!=0,xle1 =bx^(2)+ax+c,xgt1, then f(x) is continuous and differentiable at x=1 if :

If f(x) and g(x) are continuous functions on the interval [0, 4] satisfying f(x)=f(4-x) and g(x)+g(4-x)=3 and int_(0)^(4) f(x)dx=2then int_(0)^(4) f(x)g(x)dx=

Find the number of ways of forming a committee of 5 members from 6 men and 3 ladies.

int_(-1)^(1) (cos h x)/(1+e^(2x))dx=

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

Translate "29 is a prime number which is a sum of two squares" propositions into symbolic form, stating the prime components

If (1, a), (b, 2) are conjugate points with renpcet to the circle x^(2)+y^(2)=25, then 4a+2b=

The point in the interval [0, pi] for which the curve y =(1//2)x and y= sin x are farthest apart is

For any vector a, then the value of (axxhati)^(2)+(a xxhatj)^(2)+(axxhatk)^(2) is

Find P(A//B)," if "P(B)=0.5 and P(A cap B) =0.32

If three vectors 2hat(i)-hat(j)-hat(k), hat(i)+2hat(j)-3hat(k) and 3hat(i)+lambda hat(j)+5hat(k) are coplanar, then the value of lambda is

If (1+2x +3x^2)^10 = a_0 +a_1x +a_2x^2 + ……+a_20x^20 then a_2/a_1 =

If x=3 prod_(r=2)^(n) log_((2n-1))(2n+1) then the value of log_3|cospix| is :-

intsqrt((x-1)/(x))dx=

What is the median of the data given below ? 18,25,19,41,23,29,35,19

writethesimplestformcot^(-1)""((1)/(sqrt(x^2-1))),xgt 1

Given that p is 'false' and q is 'true' then the statement which is 'false' is

If graph of the quadratic y = ax ^(2)+bx+c is given below : then:

Find the moment about a line through (0, 0, 0) having the direction 2hat(i)-2hat(j)+hat(k) due to a 20 kg force acting at (-4, 2,5) in the direction of 12 hat(i)-4hat(j)-3hat(k).

Five coins are tossed 3200 times using poission distribution, find the probability of getting five heads 2 times.

Let f: [0, infty) to R be such that f(16/sqrt(1+sqrt(x))) = x AA x ge 0, Then f(8)=

A five digit number is formed by the digits 1,2,3,4, 5 with no digit being repeated. The probability that the number is divisible by 4, is

Write the number of solution of the following system of equation. x+y+z=1 x+y+z=2 2x+3y+z=0

A point is randomly chosen inside the circumcircle of an equilateral triangle. Find the probability that it lies inside the inscribed circle of that triangle.

Find the shortest distance between the following pair of lines :(x-1)/(2) = (y-2)/(3)=(z-3)/(4),(x-2)/(3)=(y-3)/(4)=(z-5)/(5)

If root3(y)root2(x)=root6((x+y)^(5)) , then (dy)/(dx)

The point on the curve f (x) = sqrt(x ^(2) - 4) defined in [2,4] where the tangentis parallel to the chord joining the end points on the curve is

Identify the quantifier in the following statements and write the negation of the statement.(i)There exists a number which is equal to its square.

int (3cos x+2 sin x)/(4 cos x+3 sin x)dx=

Ifalpha, beta , gammaare therootsof x^3+ 3x^2 -4x +2=0thenthe equationwhoserootsare (1)/(alpha beta) ,(1)/( beta gamma),(1)/( gamma alpha) is