28278 + Interview Questions in Maths in Class 12

1.	Find underset(-a)overset(a)int(x^(2)+sqrt(a^(2)-x^(2)))dx
Answer» ANSWER :`(2)/(3)a^(3) + (PI)/(2)a^(2)`

Discussion

2.	A binomial distribution has mean 5 and variance 4. Find the number of trials.
Answer» SOLUTION :GIVEN np=5 and npq=4 `rArrq=4/5rArrp=1-q=1-4/5=1/5` THUS n=25

Discussion

3.	If the normal at any point P on the ellipse meets the axes in G and g respectively. Find the ratio PG : Pg.
Answer» ANSWER :`B^(2).a^(2)`

Discussion

4.	If the absolute term (independent of x ) in the expansion of (sqrtx-k//x^2)^10 is 405 then k=
Answer» `PM 3^(1//4)` `pm 4^(1//3)` `pm 2` `pm 3` ANSWER :D

Discussion

5.	Which of the followingstatements are true where phi(x) is a polynomial.
Answer» between any two ROOTS of `phi(x)=0` lies atleast one ROOT of `phi(x) + gammaphi(x)=0` between any two roots of `phi(x)= 0` lies atleast one root of x`phi(x) + gammaphi(x)=0` between any two roots of `phi(x)=0` lies atleast one root of `(x^(2) + 1)phi(x) + phi(x)=0` between any two roots of `phi(x)=0` lies atleast one root of `phi'(x) + xphi(x)=0` Answer :A::C::D

Discussion

6.	Choose the correct answer intx^(2)e^(x^(3))dx equals
Answer» `1/3e^(X^(3))+C` `1/3e^(x^(2))+C` `1/2e^(x^(3))+C` `1/2e^(x^(2))+C` ANSWER :A

Discussion

7.	Sigma_(r=1)^(oo) 3^(r-1)(sin.(theta)/(3^(r)))^(3)is equal to
Answer» `theta - sin theta` `(1)/(2)(theta-sintheta)` `sin theta-theta` `(1)/(4)(theta-sintheta)` Solution :`((y-x)/(tan^(-1)y-tan^(-1)x))=(1)/(m)` `A(x, tan^(-1)x)` `B(y,tan^(-1)y)` `m="Slope of" AB =((tan^(-1)y-tan^(-1)x)/(y-x))` 'm' is minimum as A, Bboth tend to POINT with x-coordinate `(SQRT(3))` `implies m gt (d)/(dx) (tan^(-1)x)\|_(x=sqrt(3))` `implies m gt ((1)/(1+x^(2)))\|implies MGT(1)/(4)` `(1)/(m)lt4implies "MAXIMUM integral value of"((1)/(m)) "is" 3`.

Discussion

8.	Prove that the point on the parabola y^(2) = 4a ( a gt 0 nearest to the focus is its vertex.
Answer» ANSWER :which is NEAREST to the FOCUS is VERTEX `A(0,0)`.

Discussion

9.	Find the maximum and minimum values, if any, of the functions given by g(x) = x^(2) + 1
Answer»

Discussion

10.	Find the sum of first 16 terms of an A.P. a _(1), a _(2), a_(3)……….. If it is known that a _(1), + a _(4) + a _(7) + a _(10) + a _(13) + a _(16) = 147
Answer» ANSWER :392

Discussion

11.	Thetablebelowdetailsa recentcensusreportaboutthecommutinghabitsof U.S. Workers age16or over for theyears 2004, 2005 ,and 2006. The circlegraph(piechart) belowrepresents the2006means of transportationfor U.S. workersage 16or overforthefourtransportationtypeslisted. To the nearest degree , Whatis themeasureof thecentralanglefor the" Public"sector?
Answer» `8^(@)` `12 ^(@)` `20^(@)` `30^(@)` ANSWER :D

Discussion

12.	Ifint x^(2) c^(2x) dx = (e^(2))/(8) f(x) + c, then the sum of all the complex roots of f(x) = 1 is
Answer» `(1)/(2)` 3 1 2 Answer :A

Discussion

13.	Thetablebelowdetailsa recentcensusreportaboutthecommutinghabitsof U.S. Workers age16or over for theyears 2004, 2005 ,and 2006. Expressedin millionsof people, whatwasthe averagegrowthperyearfor femaleU.Sworkers age16or overfrom2004to 2006, rounded to thenearest0.1million ?
Answer» `0.5` `0.9` `1.3` `1.8` ANSWER :D

Discussion

14.	Three faces of a fair die are yellow, two faces are red and one face is blue. If the die is tossed 3 times, then the probability that thecolours yellow, red and blue appear is (need not be in that order)
Answer» `(1)/(36)` `(1)/(6)` `(5)/(6)` `(1)/(2)` Answer :B

Discussion

15.	Locate the position of the point P with respect to the circle S =0 when P(2,1) and S = x^(2)+ y ^(2) -2x -4y +3
Answer» ANSWER : INTERIOR

Discussion

16.	If the sum to first n terms of the A.P. 2, 4, 6, …. is 240, then the value of n is
Answer» 14 15 16 17 Answer :B

Discussion

17.	Person A speaks true in 75% and B speaks true in 80% then ....... is the probability that both contradict each other.
Answer» `(7)/(20)` `(13)/(20)` `(3)/(5)` `(2)/(5)` ANSWER :A

Discussion

18.	Two cards are drawn successfully with replacement from a well- shuffled pack of 52 cards. Find the probability distribution of number of aces.
Answer» ANSWER :`(##NCERT_KAN_MAT_XII_P2_C13_SLV_024_A01##)`

Discussion

19.	A farmer sells strawberries at a market in both pint-sized containers and quart-sized containers. The farmer charges $5 for each pint, $5 for each quart, is always paid on the day of purchase, and sells no other goods. On a recent day , the farmer sold as many pint containers as quart containers and received $120 in sales. How many pints of strawberries did the farmer sell ?
Answer» 12 15 24 40 Answer :B

Discussion

20.	Evaluate the definite integral in exercise overset(1)underset(0) int (dx)/(sqrt(1-x^(2)))
Answer» ANSWER :`(PI)/(2)`

Discussion

21.	If on Q defined by ab = a - b. Identity element is
Answer» 0 1 a - B Does not EXISTS ANSWER :D

Discussion

22.	State with reason, "Collection of all possible sets " is set or not ?
Answer» SOLUTION :It is a SET, as it is WELL DEFINED.

Discussion

23.	If the ellipse (x^(2))/( 4) + y^(2) =1 meets the ellipsex^(2)+(y^(2))/( a^(2)) =1 in four distinct points anda= b ^(2) - 5b+7,then b does not lie in
Answer» ` [4,5 ]` `( infty ,2 )UU( 3, infty ) ` ` (-infty ,0) ` ` [2,3]` Answer :D

Discussion

24.	Let M be the foot of the perpendicular from a point P on the parabola y^(2) = 8(x-3) on to its directrix and let S be the focal of the parabola. If DeltaSPM is an equalateral triangle, then P =
Answer» `(4sqrt(3),8)` `(8,4sqrt(3))` `(9,4sqrt(3))` `(4sqrt(3),9)` ANSWER :C

Discussion

25.	Form the differential equation of the family of ellipse having foci ony - axis and centre at origin.
Answer» ANSWER :`xyy" + X(y')^(2) - yy' = 0`

Discussion

26.	If int_(0)^(pi//4) sec^(2)theta sin theta d theta=int_(0)^(lambda)(dx)/(sqrtx+sqrt(x+lambda)), then lambda=
Answer» `(9)/(16)` `(9)/(25)` `(16)/(25)` `(25)/(16)` ANSWER :A

Discussion

27.	Thetablebelowdetailsa recentcensusreportaboutthecommutinghabitsof U.S. Workers age16or over for theyears 2004, 2005 ,and 2006. The thenearestpercent, whatpercentof allU.Sworkersage16oroverin 2004 wasfemale ?
Answer» `50%` `48%` `46%` `44%` ANSWER :C

Discussion

28.	If int (x sqrt(x) -1)/(sqrt(x) -1)dx =ax^(2) + bx^(3//2)+cx + d then ascending order of a, b, c, is
Answer» a, B, c b,c,a c,a,b d, b, a ANSWER :A

Discussion

29.	The incentre of the triangle ABC where A(-36, 7) B (20,7) and C (0,-8) is
Answer» `((sqrt(105))/(3))` `(2)/(3)` `((sqrt(211))/(3))` `((sqrt(205))/(3))` ANSWER :D

Discussion

30.	Find the vector equation of the line which is parallel to the vector 3hati-2hatj+6hatk and which passes through the point (1, -2, 3).Hint for solution : Vector equation of line passes from point bara and parallel to vector barb isbarr=bara+lambda barb.
Answer» ANSWER :`=(1+3lambda)BARI+(-2-2lambda)BARJ+(3+6lambda)BARK`

Discussion

31.	the valueofsec^2 theta+ cosec^2 thetaisequal to
Answer» ` tan ^2 THETA+ cot ^2 theta ` `SEC ^2 thetacosec ^2 theta ` `sec thetacosec theta ` ` sin^2thetacos^2 theta ` Answer :B

Discussion

32.	A triangle ABC is placed so that the mid-points of the sides are on the x, y, z axes. Lengths of the intercept made by the plane containing the triangle on these axes are respectively alpha,beta,gamma. Coordinates of the centroid of the trianlge ABC are
Answer» `(-alpha//3,beta//3,gamma//3)` `(alpha//3,-beta//3,gamma//3)` `(alpha//3,beta//3,-gamma//3)` `(alpha//3,beta//3,gamma//3)` ANSWER :D

Discussion

33.	Find the range of f(x) =x^(2) -5x + 6
Answer» ANSWER :`[-1/4,INFTY)`

Discussion

34.	Let f: R rarr Rbe defined by f(x) = 3x^(2) - 5 and g : R rarr R, g(x) = x/(x^(2)+1)Then gof is ...........
Answer» `(3X^(2)-5)/(9x^(4)-30x^(2)+26)` `(3x^(2)-5)/(9x^(4)-6x^(2)+26)` `(3x^(2))/(x^(4)+2x^(2)-4)` `(3x^(2))/(9x^(4)+30x^(2)-2)` SOLUTION :N/A

Discussion

35.	Let S_(n) the area of the figure enclosed by a curve y = x^(3) (1 - x^(3)). 0 le x le 1 and the x-axis. The value of underset(n to oo)("lim") S_(n) is
Answer» .1/2 .1/3 .1/4 1 Answer :C

Discussion

36.	If I_(m c) = int e^(mx). X^(n)dx, then I_(mn) + (n)/(m)I_(m, n-1) =
Answer» `x^(N).E^(MX) + C` `(X^(n)e^(mx))/(n) + C` `(X^(n).e^(mx))/(m) + C` `(-X^(n).e^(mx))/(m) + C` ANSWER :C

Discussion

37.	If A and B are two events then show that (i) (P(AnnB^(c)))=P(A)-P(AnnB) (ii) The probability that exactly one of them occurs is given by P(A)+P(B)-2P(AnnB)
Answer» ANSWER :`(i) 0.5` `(II) 0.4)`

Discussion

38.	If a line intersect a hyperbola at (-2, -6) " and " (4, 2) and one of the asymptote at (1, -2) , then the centre of the hyperbola is
Answer» `(7, 6)` `(1, -2)` `(10, 10)` `(-5, -10)` Solution :N/A

Discussion

39.	The solution of the differential equation (dy)/(dx)-2ytan2x=e^(x)sec2x is
Answer» `ysin2x=e^(X)+C` `ycos2x=e^(x)+c` `y=e^(x)cos2x+c` `ycos2x+e^(x)=c` ANSWER :B

Discussion

40.	Which list has a greater standard deviation ? {:("List A:",{3, 4, 5, 6, 7},"List B:",{3, 3, 5, 7, 7}):}
Answer» ANSWER :DATASET B

Discussion

41.	Which of the following pairs of reaction occurs most frquently in the blood surrounding alveoli ?
Answer» `Hb + O_(2) rarr HbO_(2) and HHb rarr Hb + H^(+)` `HbO_(2) rarr Hb + O_(2)and Hb + H^(+) rarr HHb` `H^(+) + Hb rarr HHb and H_(2)CO_(3) rarrHCO_(3) + H^(+)` `CO_(2) + H_(2)O rarr H_(2)CO_(3) and H_(2)CO_(3) rarr HCO_(3) + H^(+)` ANSWER :A

Discussion

42.	If a, b and c are three non-collinear points and ka+2b+3c is a point in the plane of a, b, c then k=
Answer» 4 5 `-5` `-4` ANSWER :C

Discussion

43.	If f(x)= {4 - (x-7)^(3)}, then find f^(-1)(x)=
Answer» `(4-x)^(1/3)+7` `(4-x)^((1)/(3))-7` `(4+x)^(3)+7` NONE of these SOLUTION :N/A

Discussion

44.	If A and B are the points of intersection of y=f(x) and y=f^(-1)(x), then
Answer» A and B NECESSARITY LIE on the LINE y=x A and B must be coincident slope of line AB may be -1 None of these above Answer :C

Discussion

45.	Using elementary row transformations , find the inverse of [{:(3,1),(5,2):}]
Answer» ANSWER :`thereforeA^(-1)=[{:(2,-1),(-5,3):}]`

Discussion

46.	Given F(x)={{:(0,xle1),(x-1/4,1lexle5),(1,xgt5):} is cumulative distrubution of X find P(2ltxlt4)
Answer» `-1/4` 0 `1/2` `1/3` ANSWER :C

Discussion

47.	The rate at which the population of a city increases at any times is proportional to the population anticipated after 3 more years .
Answer» ANSWER :` 4,26,680`

Discussion

48.	{:("Column I " " ", " Column II") , ("(A) The number of the distinct real roots of the equation "" " (x+1)^(5) = 2(x^(5) +1) "is" , "(p)" 16),("(B) The absolute maximum value of the function " f(x) = ((x+1)^(4))/(x^(4)-x^(3) + x^(2) -x+1) " " "is", "(q)" 2), ("(C) Let f(x)= ab sin x " + sqrt(1-a)^(2) " cos x + c where \|a\|
Answer» 4,1,3,2 2,1,4,3 1,3,2,4 1,3,4,2 Answer :A::B::C::D

Discussion

49.	Let A and B be two sets , then (A uu B)^c uu (A^c nn B) equals :
Answer» `A^c` `B^c` A None of these ANSWER :A

Discussion

50.	Which of the following holds for a right angle triangle ABC?
Answer» Diameter of one of the ex-circles equals to the PERIMETER of the triangle. Diameter of the circle circumscribing `DeltaABC` equals to one of the sides of triangle. `r:b+c:a=2:17:13` Diameter of incircle equals to LENGTH of the SHORTEST tangent DRAWN from the vertices to the incircle Solution :(A) `Let""2r_(1)=2s` `s TAN((A)/(2))=simpliesA=(pi)/(2)` (B) `Let""2R=aimpliessinA=1impliesA=(pi)/(2)` (C )`Let" "r=2k,b+c=17k,a=13k` `s=15k,r=(s-a)"tan"(A)/(2)implies(A)/(2)=(pi)/(4)` `A-(pi)/(2)` (D) `2r=s-aimplies"tan"(A)/(2)=(1)/(2)"":.Ane(pi)/(2)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find underset(-a)overset(a)int(x^(2)+sqrt(a^(2)-x^(2)))dx

A binomial distribution has mean 5 and variance 4. Find the number of trials.

If the normal at any point P on the ellipse meets the axes in G and g respectively. Find the ratio PG : Pg.

If the absolute term (independent of x ) in the expansion of (sqrtx-k//x^2)^10 is 405 then k=

Which of the followingstatements are true where phi(x) is a polynomial.

Choose the correct answer intx^(2)e^(x^(3))dx equals

Sigma_(r=1)^(oo) 3^(r-1)(sin.(theta)/(3^(r)))^(3)is equal to

Prove that the point on the parabola y^(2) = 4a ( a gt 0 nearest to the focus is its vertex.

Find the maximum and minimum values, if any, of the functions given by g(x) = x^(2) + 1

Find the sum of first 16 terms of an A.P. a _(1), a _(2), a_(3)……….. If it is known that a _(1), + a _(4) + a _(7) + a _(10) + a _(13) + a _(16) = 147

Ifint x^(2) c^(2x) dx = (e^(2))/(8) f(x) + c, then the sum of all the complex roots of f(x) = 1 is

Thetablebelowdetailsa recentcensusreportaboutthecommutinghabitsof U.S. Workers age16or over for theyears 2004, 2005 ,and 2006. Expressedin millionsof people, whatwasthe averagegrowthperyearfor femaleU.Sworkers age16or overfrom2004to 2006, rounded to thenearest0.1million ?

Three faces of a fair die are yellow, two faces are red and one face is blue. If the die is tossed 3 times, then the probability that thecolours yellow, red and blue appear is (need not be in that order)

Locate the position of the point P with respect to the circle S =0 when P(2,1) and S = x^(2)+ y ^(2) -2x -4y +3

If the sum to first n terms of the A.P. 2, 4, 6, …. is 240, then the value of n is

Person A speaks true in 75% and B speaks true in 80% then ....... is the probability that both contradict each other.

Two cards are drawn successfully with replacement from a well- shuffled pack of 52 cards. Find the probability distribution of number of aces.

Evaluate the definite integral in exercise overset(1)underset(0) int (dx)/(sqrt(1-x^(2)))

If **on Q defined by a**b = a - b. Identity element is

State with reason, "Collection of all possible sets " is set or not ?

If the ellipse (x^(2))/( 4) + y^(2) =1 meets the ellipsex^(2)+(y^(2))/( a^(2)) =1 in four distinct points anda= b ^(2) - 5b+7,then b does not lie in

Let M be the foot of the perpendicular from a point P on the parabola y^(2) = 8(x-3) on to its directrix and let S be the focal of the parabola. If DeltaSPM is an equalateral triangle, then P =

Form the differential equation of the family of ellipse having foci ony - axis and centre at origin.

If int_(0)^(pi//4) sec^(2)theta sin theta d theta=int_(0)^(lambda)(dx)/(sqrtx+sqrt(x+lambda)), then lambda=

Thetablebelowdetailsa recentcensusreportaboutthecommutinghabitsof U.S. Workers age16or over for theyears 2004, 2005 ,and 2006. The thenearestpercent, whatpercentof allU.Sworkersage16oroverin 2004 wasfemale ?

If int (x sqrt(x) -1)/(sqrt(x) -1)dx =ax^(2) + bx^(3//2)+cx + d then ascending order of a, b, c, is

The incentre of the triangle ABC where﻿ A(-36, 7) B (20,7) and C (0,-8) is﻿

Find the vector equation of the line which is parallel to the vector 3hati-2hatj+6hatk and which passes through the point (1, -2, 3).Hint for solution : Vector equation of line passes from point bara and parallel to vector barb isbarr=bara+lambda barb.

the valueofsec^2 theta+ cosec^2 thetaisequal to

A triangle ABC is placed so that the mid-points of the sides are on the x, y, z axes. Lengths of the intercept made by the plane containing the triangle on these axes are respectively alpha,beta,gamma. Coordinates of the centroid of the trianlge ABC are

Find the range of f(x) =x^(2) -5x + 6

Let f: R rarr Rbe defined by f(x) = 3x^(2) - 5 and g : R rarr R, g(x) = x/(x^(2)+1)Then gof is ...........

Let S_(n) the area of the figure enclosed by a curve y = x^(3) (1 - x^(3)). 0 le x le 1 and the x-axis. The value of underset(n to oo)("lim") S_(n) is

If I_(m c) = int e^(mx). X^(n)dx, then I_(mn) + (n)/(m)I_(m, n-1) =

If A and B are two events then show that (i) (P(AnnB^(c)))=P(A)-P(AnnB) (ii) The probability that exactly one of them occurs is given by P(A)+P(B)-2P(AnnB)

If a line intersect a hyperbola at (-2, -6) " and " (4, 2) and one of the asymptote at (1, -2) , then the centre of the hyperbola is

The solution of the differential equation (dy)/(dx)-2ytan2x=e^(x)sec2x is

Which list has a greater standard deviation ? {:("List A:",{3, 4, 5, 6, 7},"List B:",{3, 3, 5, 7, 7}):}

Which of the following pairs of reaction occurs most frquently in the blood surrounding alveoli ?

If a, b and c are three non-collinear points and ka+2b+3c is a point in the plane of a, b, c then k=

If f(x)= {4 - (x-7)^(3)}, then find f^(-1)(x)=

If A and B are the points of intersection of y=f(x) and y=f^(-1)(x), then

Using elementary row transformations , find the inverse of [{:(3,1),(5,2):}]

Given F(x)={{:(0,xle1),(x-1/4,1lexle5),(1,xgt5):} is cumulative distrubution of X find P(2ltxlt4)

The rate at which the population of a city increases at any times is proportional to the population anticipated after 3 more years .

Let A and B be two sets , then (A uu B)^c uu (A^c nn B) equals :

Which of the following holds for a right angle triangle ABC?

If on Q defined by ab = a - b. Identity element is

The incentre of the triangle ABC where A(-36, 7) B (20,7) and C (0,-8) is