28278 + Interview Questions in Maths in Class 12

1.	A box contains 5 pairs of shoes. If 4 shoes are selected, then the number of ways in which exactly one pair of shoes obtained is
Answer» 120 140 160 180 Answer :A

Discussion

2.	Let S_(1), S_(2), ...... S_(101) be consecutive terms of A.P. If 1/(S_(1)S_(2)) + 1/(S_(2)S_(3)) + ...... + 1/(S_(100)S_(101)) = 1/6 and S_(1) + S_(101) = 50, then \|S_(1) - S_(101)\| is equal to
Answer» 10 20 30 40 Answer :A

Discussion

3.	Using the property of determinants andd without expanding in following exercises 1 to 7 prove that \|{:(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y):}\|=2\|{:(a,p,x),(b,q,y),(c,r,z):}\|
Answer» <P> ANSWER :`2\|{:(a,p,X),(b,q,y),(C,r,z):}\|`

Discussion

4.	Find the value of k, if(i) (3x-4)/((x-3)(x+k))=(1)/(x-3)+(2)/(x+k)
Answer» ANSWER :2

Discussion

5.	3.011 xx 10^(22) atoms of an element weight 1.15 g. The atomic mass of the element is :-
Answer» 10 amu 2.3 amu 35.5 amu 23 amu Answer :A

Discussion

6.	Assertion (A) : (Costheta+iSintheta)^(10)+(Costheta-iSintheta)^(10)=2cos10thetaReason (R) : (1+costheta+isintheta)^n+(1+costheta-isintheta)^n=2^(n+1)cos^n(theta/2)cos((ntheta)/(2))
Answer» A) Both A and R are TRUE R is CORRECT explanation to A B) Both A and R are true but R is not correct explanation to A C) A is true R is FALSE D) A is false R is true Answer :B

Discussion

7.	cos ((dy)/(dx)) = a (a ne R), y = 2 when x = 0
Answer» ANSWER :`COS((y - 2)/(X)) = a`

Discussion

8.	If the vectors 2i -- 3j + 4k, I + 2j - k, xi - j + 2k are coplanar then x = 8/5
Answer»

Discussion

9.	Discuss the continuity of the cosine, cosecant, secant and cotangent functions: f(x)= cot x = (1)/(tan x), x in R- {n pi, n in I}
Answer» ANSWER :F(X) = COT x

Discussion

10.	If y= x+(1)/(x), x ne 0, then the equation (x^(2)-3x+1)(x^(2)-5x+1)=6x reduces to
Answer» `y^(2)-8y+7=0` `y^(2)+8y+7=0` `y^(2)-8y-9=0` `y^(2)-8y+9=0` ANSWER :D

Discussion

11.	When a card is drawn from a pack, then the probability of getting a number card is
Answer» `(1)/(13)` `(1)/(4)` `(9)/(13)` `(1)/(2)` ANSWER :C

Discussion

12.	If p and q are true and r is false, then
Answer» <P>`(pvvr)^^Q` is false `(qvvr)^^p` is false `(p^^q)vvr` is true `(~pvvq)^^(~r)` is false Answer :C

Discussion

13.	Considering four sub-intervals, the value of int_(0)^(1)(1)/(1+x)dx by Trapezoidal rule,is
Answer» `0.6870` `0.6677` `0.6977` `0.5970` SOLUTION :`` Tapezoidal rule givee `int _(0)^(1)(1)/(1+x) dx=(h)/(2)[ y_(0)+2(y_(1)+y_(2)+y_(3))+y_(4)]` `=(1-0)/(2xx4)[1+2(0.8+0.67+0.571)+0.5]` `=0.6977`

Discussion

14.	3 ripe apples are mixed with 7 fresh apples and then 3 apples are selected at random. If random variable X denotes numbers of ripe apple. Find mean of such probability distribution.
Answer» ANSWER :0.9

Discussion

15.	Consider the parabola y^(2) = 4ax (i) Write the equation of the rectum and obtain the x co-ordinates of the point of intersection of latus rectum and the parabola. (ii) Find the area of the parabola bounded by the latus rectum.
Answer» ANSWER :`8/3 a^2`

Discussion

16.	If A = [(1,2),(0,1)], then A^(n) is :
Answer» `[(1,2^(N)),(0,1)] ` `[(1,n^(2)),(0,1)] ` `[( 1,2n),(0,1)] ` `[(1,n^(2)),(1,1)] ` ANSWER :C

Discussion

17.	Find the probability of getting atleast one club card when two cards are drawn from pack of 52 cards.
Answer» ANSWER :`(15)/(34)`

Discussion

18.	An operation on Z^() (the set of all non-negative integers) is defined as ab = a-b, AA a, b epsilon Z^(+). Is binary operation on Z^(+)?
Answer» ANSWER :HENCE `**` is not a BINARY OPERATION.

Discussion

19.	The reciprocal of the mean of the reciprocals of n observations is
Answer» A.M. G.M. H.M. Median Answer :C

Discussion

20.	If int sqrt(x+sqrt(x^(2)+2))dx equals k(x+sqrt(x^(2)+2))^(p//2)-(2)/((x+sqrt(x^(2)+2))^((q)/(2)))+c, then value of k, p, q are respectively are
Answer» `(4)/(3), (3)/(2),1` `(1)/(3), 3, 1` `-2, (1)/(3), 1` None of these Answer :B

Discussion

21.	If plane 6x-3y+2z-18 meets co-ordinate axes at points A,B,C, then centroid of triangleABC is
Answer» (1,2,3) (-1,2,3) (1,-2,3) (1,2,1) ANSWER :C

Discussion

22.	Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX- plane.
Answer» <P> ANSWER :`P((17)/(3),0,(23)/(3))`

Discussion

23.	Differentiate the following w.r.t. x : sqrt((e)^(sqrt(x))),x gt 0.
Answer» Answer :`(e^(SQRT(X)))/(4sqrt(xe^(sqrt(x)))), x GT 0`

Discussion

24.	Given tan A and tan B are the roots of x^(2)-ax+b=0. The value of sin^(2)(A+B) is
Answer» `(a^2)/(a^(2)+(1-B)^2)` `(a^2)/(a^(2)+b^(2))` `(a^2)/((a+b)^2)` `(b^2)/(a^(2)+(1-b)^2)` ANSWER :A

Discussion

25.	When the origin is shifted to the point (2 , 3) the transformed equation of a curve isx^(2) + 3xy - 2y^(2) + 17 x - 7y - 11 = 0. Find the original equation of curve.
Answer» ANSWER :`x^2+3xy-2y^2+4x-y-20=0`.

Discussion

26.	Find the domain and range of the following function :f : R rarr R , f(x) = sqrt(9-x^(2))
Answer» SOLUTION :N/A

Discussion

27.	If A and B are two square matrices of the same order , then AB=Ba.
Answer» ANSWER :FALSE

Discussion

28.	Find the unit vector in the direction of the sum of vectors , veca=2hati+2hatj-5hatkandvecb=2hati+hatj+3hatk.
Answer» Answer :`hatc=(4)/(SQRT(29))hati+(3)/(sqrt(29))HATJ-(2)/(sqrt(29))hatk`

Discussion

29.	Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is
Answer» 880 879 630 629 Answer :B

Discussion

30.	Integrate the following functions. int(dx)/(cosx+sqrt(3)sinx)
Answer» Answer :`(1)/(2)logtan((X)/(2)+(PI)/(12))+c`

Discussion

31.	If PQ and Rs are normal chords of the parabola y^(2) = 8x and the points P,Q,R,S are concyclic, then
Answer» tangents at P and R meet on X-axis tangents at P and R meet on Y-axis PR is parallel to Y-axis PR is parallel to X-axis Solution :Equation of normal chords at `P(2t_(1)^(2),4t_(1))` and `R(2t_(2)^(2),4t_(2))` are `y + t_(1)x -4t_(1) -2t_(1)^(3) =0` and `y + t_(2) x - 4t_(2) - 2t_(2)^(3) =0`. Equation of curve through, P,Q,R,S is `(y + t_(1)x -4t_(1)-2t_(1)^(3)) (y + t_(2)x -4t_(2) -2t_(2)^(3)) + lambda (y^(2) - 8x) =0` P,Q,R,S are CONCYCLIC, `t_(1) + t_(2) =0` and `t_(1)t_(2) =1 + lambda`. Thus, point of intersection of tangents i.e., `(at_(1)t_(2),a (t_(1)+t_(2))` lies on X-axis. Slope of `PR = (2)/(t_(1)+t_(2))` Hence, PR is parallel to Y-axis.

Discussion

32.	If2(cos(x-y)+cos(y-z)+cos(z-x))=-3, then :
Answer» `COS X cos ycosz=1` `cos x+COSY+cos z=0` `sinx+siny+sinz=1` `cos 3x+cos3y+cos3z=12 cosx cosy cosz` Answer :B::D

Discussion

33.	Let L = lim _(n to oo) (((2.1+n))/(1^(2)+n .1 +n^(2))+((2.2+n))/(2 ^(2)+n.2+n^(2))+((2.3+n))/(3 ^(2) +n.3 +n^(2))+ ...... + ((2.n +n))/(3n^(2))) then value of e ^(L) is:
Answer» 2 3 4 `3/2` ANSWER :B

Discussion

34.	Find the number of ion(s) having radius greater then Li^+. Rb^+, Ba^(2+), Be^(2+),Al^(3+), Mg^(2+), H^(-), F^(-)
Answer» ANSWER :`4.00`

Discussion

35.	int_(0)^(100pi)(\|sin^(3)x\|+\|cos^(3)x\|)dx=
Answer» 400 800 `800/3` NONE of these Answer :C

Discussion

36.	Construct Collection of writing instruments in the form of set and describe it with the help of proposition.
Answer» SOLUTION :A = {pen, pencil,PAPER,ink} ={x :x is a WRITING instrument }

Discussion

37.	With usual notation in Delta ABC , the numerical value of((a+b+c)/(r_(1)+r_(2)+r_(3)))((a)/(r_(1))+(b)/(r_(2))+(c )/(r_(3))) is .
Answer» ANSWER :4

Discussion

38.	Differentiate the functions with respect to x in Exerecises 1 to 8. cos (sqrt(x)).
Answer» ANSWER :`-(sinsqrt(X))/(2sqrt(x))`

Discussion

39.	Product of solutions of the equation 7^(log_7^2x) + X^(log_7^x)=98 is :-
Answer» 1 7 2 `1/7`

Discussion

40.	A fair4sideddiewith facenumbersfrom1 to4is rolledtwice. LetA andB beresults of1^(st ) and2^(nd)respectivelyifr={ "max " (A,B ) = m} andS= { min(A,B)=2} then matchthe probailtityP((R )/(S )) wrtcorrespondingvaluesof m
Answer» ANSWER :A::B::C::D

Discussion

41.	Statement-1 (Assertion) and Statement-2 (Reason) Each of the these examples also has four laternative choices , only one of which is the correct answer. You have to select the correct choice as given below. Number of distincet terms in the sum of expansion(1 + ax)^(10)+ (1-ax)^(10)is 22.
Answer» Statement-1 is TURE ,Statement-2 is treu, Statement-2 is a CORRECT explanation for Statement-1 Statement-1 is ture ,Statement-2 is treu, Statement-2 is nota correct explanation for Statement-1 Statement-1 is TRUE ,Statement-2 is false Statement-1 is true ,Statement-2 is ture Solution :NUMBER of terms in the expansion of `(1 + X)^(n)` in ` n+ 1AA n in N ` `because (1 + ax)^(10) + (1 + ax)^(10) = 2 {1 + ""^(10)C_(2) (ax)^(2)` ` + ""^(10)C_(4) (ax)^(4) + ""^(10)C_(4) (ax)^(4) + ""^(10)C_(6) (ax)^(6) + ""^(10)C_(8) (ax)^(8) + ""^(10)C_(10) (ax)^(10)}` ` therefore ` Number of distinct terms = 6 `rArr ` Statement-1 is false but Statement-2 is obviously true .

Discussion

42.	Let f be a one - to - one function from the set of natural number to itself such that f(mn) = f(m) f (n) for all natural numbers m and n. What is the least possible value f (999) ?
Answer» ANSWER :24

Discussion

43.	Usingintegration, findthe areaof triangularregionformedby the lines x+2y =2 , y-x=1 and2x +y=7
Answer» ANSWER :12 SQ. UNIT

Discussion

44.	Let f(x) = cos (ln x) , x gt 0. If f(xy) + f(x/y) = kf(x)f(y) AA x, y gt 0 then k = ……………….
Answer» ANSWER :2

Discussion

45.	The longest distance from (-3,2) to the circle
Answer» 8 4 18 6 Answer :D

Discussion

46.	Let vec(a)=a_(1)hat(i)+a_(2)hat(j)+a_(3)hat(k),vec(b)=b_(1)hat(i)+b_(2)hat(j)+b_(3)hat(k)andvec(c)=c_(1)hat(i)+c_(2)hat(j)+c_(3)hat(k) be three non-zero vectors such that vec(c) is a unit vector perpendicular to both vec(a)andvec(b). If the angle between vec(a)andvec(b)" is "(pi)/(6), then {:""\|(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))\|"":}^(2)" is equal to"
Answer» 0 1 `(1)/(4)(a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))` `(3)/(4)(a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))(c_(1)^(2)+c_(2)^(2)+c_(3)^(2))` Answer :C

Discussion

47.	Find the value of lambda so that the vectors veca and vecb are perpendicular to each other. veca = hati+hatj+lambdahatk, vecb = 4hati-3hatk
Answer» SOLUTION :If `veca` and `vecb` are PERPENDICULAR then `veca.vecb = 0` `implies (hati+hatj+lambdahatk).(4hati-3hatk) = 0` `implies = 4+0-3lambda = 0 implies LAMBDA = 4/3`

Discussion

48.	The tangent to the hyperbola xy=c^2 at the point P intersects the x-axis at T and the y-axis at T. The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N. The areas of the triangles PNT and PNT are Delta and Delta respectively, then (1)/(Delta)+(1)/(Delta) is
Answer» EQUAL to 1 depends on t depends on C equal 2 Answer :C

Discussion

49.	underset(n to 0)lim""(1)/(n)(underset(y)overset( c )int e^(sin^(2)t)dt-underset(x+y)overset(x)int sin^(2)t dt) is equal to (c being constant) :
Answer» `E^(SIN^(2)y)` `sin2ye^(sin^(2)y)` 0 None of these. ANSWER :C

Discussion

50.	If 4 boys and 20 girls are arranged along a row at random. Find the probability that atmost 28 girls may be seated together.
Answer» ANSWER :`(10601)/(10626)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A box contains 5 pairs of shoes. If 4 shoes are selected, then the number of ways in which exactly one pair of shoes obtained is

Let S_(1), S_(2), ...... S_(101) be consecutive terms of A.P. If 1/(S_(1)S_(2)) + 1/(S_(2)S_(3)) + ...... + 1/(S_(100)S_(101)) = 1/6 and S_(1) + S_(101) = 50, then |S_(1) - S_(101)| is equal to

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y):}|=2|{:(a,p,x),(b,q,y),(c,r,z):}|

Find the value of k, if(i) (3x-4)/((x-3)(x+k))=(1)/(x-3)+(2)/(x+k)

3.011 xx 10^(22) atoms of an element weight 1.15 g. The atomic mass of the element is :-

Assertion (A) : (Costheta+iSintheta)^(10)+(Costheta-iSintheta)^(10)=2cos10thetaReason (R) : (1+costheta+isintheta)^n+(1+costheta-isintheta)^n=2^(n+1)cos^n(theta/2)cos((ntheta)/(2))

cos ((dy)/(dx)) = a (a ne R), y = 2 when x = 0

If the vectors 2i -- 3j + 4k, I + 2j - k, xi - j + 2k are coplanar then x = 8/5

Discuss the continuity of the cosine, cosecant, secant and cotangent functions: f(x)= cot x = (1)/(tan x), x in R- {n pi, n in I}

If y= x+(1)/(x), x ne 0, then the equation (x^(2)-3x+1)(x^(2)-5x+1)=6x reduces to

When a card is drawn from a pack, then the probability of getting a number card is

If p and q are true and r is false, then

Considering four sub-intervals, the value of int_(0)^(1)(1)/(1+x)dx by Trapezoidal rule,is

3 ripe apples are mixed with 7 fresh apples and then 3 apples are selected at random. If random variable X denotes numbers of ripe apple. Find mean of such probability distribution.

Consider the parabola y^(2) = 4ax (i) Write the equation of the rectum and obtain the x co-ordinates of the point of intersection of latus rectum and the parabola. (ii) Find the area of the parabola bounded by the latus rectum.

If A = [(1,2),(0,1)], then A^(n) is :

Find the probability of getting atleast one club card when two cards are drawn from pack of 52 cards.

An operation ** on Z^(**) (the set of all non-negative integers) is defined as a**b = a-b, AA a, b epsilon Z^(+). Is ** binary operation on Z^(+)?

The reciprocal of the mean of the reciprocals of n observations is

If int sqrt(x+sqrt(x^(2)+2))dx equals k(x+sqrt(x^(2)+2))^(p//2)-(2)/((x+sqrt(x^(2)+2))^((q)/(2)))+c, then value of k, p, q are respectively are

If plane 6x-3y+2z-18 meets co-ordinate axes at points A,B,C, then centroid of triangleABC is

Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX- plane.

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

Given tan A and tan B are the roots of x^(2)-ax+b=0. The value of sin^(2)(A+B) is

When the origin is shifted to the point (2 , 3) the transformed equation of a curve isx^(2) + 3xy - 2y^(2) + 17 x - 7y - 11 = 0. Find the original equation of curve.

Find the domain and range of the following function :f : R rarr R , f(x) = sqrt(9-x^(2))

If A and B are two square matrices of the same order , then AB=Ba.

Find the unit vector in the direction of the sum of vectors , veca=2hati+2hatj-5hatkandvecb=2hati+hatj+3hatk.

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

Integrate the following functions. int(dx)/(cosx+sqrt(3)sinx)

If PQ and Rs are normal chords of the parabola y^(2) = 8x and the points P,Q,R,S are concyclic, then

If2(cos(x-y)+cos(y-z)+cos(z-x))=-3, then :

Let L = lim _(n to oo) (((2.1+n))/(1^(2)+n .1 +n^(2))+((2.2+n))/(2 ^(2)+n.2+n^(2))+((2.3+n))/(3 ^(2) +n.3 +n^(2))+ ...... + ((2.n +n))/(3n^(2))) then value of e ^(L) is:

Find the number of ion(s) having radius greater then Li^+. Rb^+, Ba^(2+), Be^(2+),Al^(3+), Mg^(2+), H^(-), F^(-)

int_(0)^(100pi)(|sin^(3)x|+|cos^(3)x|)dx=

Construct Collection of writing instruments in the form of set and describe it with the help of proposition.

With usual notation in Delta ABC , the numerical value of((a+b+c)/(r_(1)+r_(2)+r_(3)))((a)/(r_(1))+(b)/(r_(2))+(c )/(r_(3))) is .

Differentiate the functions with respect to x in Exerecises 1 to 8. cos (sqrt(x)).

Product of solutions of the equation 7^(log_7^2x) + X^(log_7^x)=98 is :-

A fair4sideddiewith facenumbersfrom1 to4is rolledtwice. LetA andB beresults of1^(st ) and2^(nd)respectivelyifr={ "max " (A,B ) = m} andS= { min(A,B)=2} then matchthe probailtityP((R )/(S )) wrtcorrespondingvaluesof m

Statement-1 (Assertion) and Statement-2 (Reason) Each of the these examples also has four laternative choices , only one of which is the correct answer. You have to select the correct choice as given below. Number of distincet terms in the sum of expansion(1 + ax)^(10)+ (1-ax)^(10)is 22.

Let f be a one - to - one function from the set of natural number to itself such that f(mn) = f(m) f (n) for all natural numbers m and n. What is the least possible value f (999) ?

Usingintegration, findthe areaof triangularregionformedby the lines x+2y =2 , y-x=1 and2x +y=7

Let f(x) = cos (ln x) , x gt 0. If f(xy) + f(x/y) = kf(x)f(y) AA x, y gt 0 then k = ……………….

The longest distance from (-3,2) to the circle

Find the value of lambda so that the vectors veca and vecb are perpendicular to each other. veca = hati+hatj+lambdahatk, vecb = 4hati-3hatk

The tangent to the hyperbola xy=c^2 at the point P intersects the x-axis at T and the y-axis at T. The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N. The areas of the triangles PNT and PNT are Delta and Delta respectively, then (1)/(Delta)+(1)/(Delta) is

underset(n to 0)lim""(1)/(n)(underset(y)overset( c )int e^(sin^(2)t)dt-underset(x+y)overset(x)int sin^(2)t dt) is equal to (c being constant) :

If 4 boys and 20 girls are arranged along a row at random. Find the probability that atmost 28 girls may be seated together.

An operation on Z^() (the set of all non-negative integers) is defined as ab = a-b, AA a, b epsilon Z^(+). Is binary operation on Z^(+)?