28278 + Interview Questions in Maths in Class 12

1.	Let x and y be positive real numbers such thaty^(3) + y le x -x^(3) . Then match the following list -I with List- II Where [.] is greatest integer function. {:( "List - I " , " List - II"), ( "(P)" [x^(1/x) - y^(1/y)], (1) -1),("(Q)" [ x^(1/x)-1], "(2) 0"),("(R) " [3-(1-x)^(2)], "(3) " 1), ("(s) " [ x^(2) -y^(2)+1] , "(4)" 2):}
Answer» ANSWER :B

Discussion

2.	Evaluation of definite integrals by subsitiution and properties of its : If f(a+b+1-x)=f(x)AAx where a and b are fixed positive real numbers, then (1)/(a+b)int_(a)^(b)x(f(x)+f(x+1)dx= is equal to
Answer» `int_(a-1)^(b-1)F(X)dx` `int_(a+1)^(b+1)f(x+1)dx` `int_(a-1)^(b-1)f(x+1)dx` `int_(a+1)^(b+1)f(x)dx` ANSWER :C

Discussion

3.	Let vecaandvecb be two unit vectors and theta is the angle between them Thenveca+vecb isa unit vector if
Answer» `THETA=(PI)/(4)` `theta=(pi)/(3)` `theta=(pi)/(2)` `theta=(2pi)/(3)` Answer :D

Discussion

4.	Let A and B any two events. Which one of the following statements is always true?
Answer» <P>`P(A'//B)=P(A//B)` `P(A//B)=P(B'//A)` `P(A'//B)=1-P(A//B)` `P(A'//B)=1-P(A//B')` ANSWER :C

Discussion

5.	IFx^2+P_1 x+q_1 =0, x^2 +p_2 x +q_2=0 , x^2 +p_3 x+q_3=0hasa coomonrootthenp_(1) ^2 +p_(2)^2 +P_3^2+4(q_1+q_2+q_3)=
Answer» `2(p_1p_2+p_2p_3+p_3 p_1` `(p_2p_1+q_2 q_3 + Q _3 p_1)` `2(q_1 p_2+q_2p_3 +p_3 q_1)` none Answer :A

Discussion

6.	Assertion (A ) :If 1,2,3aretherootsofax^3 +bx^2 + cx ++d =0thenrootsofax^3 + 2 bx^2 + 4 cx +8d =0are2,4,6 Reason (R ): Theequationwhoserootsare ktimesthe rootsof theequationf(x)=0Isf(x//k) =0thenthe truestatmentamongthe followingis :
Answer» bothA and RaretrueR ISTHE correctexplanationof A bothA andRare trueand Ris NOTTHE CORRECTEXPLANATION of A Ais trueand Risfalse A isfalseand Ristrue Answer :A

Discussion

7.	Integration by partial fraction : int(xdx)/(x^(4)+x^(2)+1)=......
Answer» `(1)/(3)TAN^(-1)((2X^(2)+1)/(3))` `(1)/(SQRT(3))tan^(-1)((2x^(2)+1)/(3))` `(1)/(sqrt(3))tan^(-1)((2x^(1)+1)` None of these Answer :B

Discussion

8.	A surveywas conducted among a randomly chosen sample of 250 single men and 250 single women about whether they owned any dogs or cats. The table below displays a summary of the survey results. According to the table, which of the following statements is most likely to be false?
Answer» The porability that a woman is a cat owner is GREATER than the probability that a cat owner is a woman The probability that a dog owner is male is greater than the probability that a randomly chosen person is a cat owner. The probability that a woman does not own a dog or cat is greater than the probability that a MAN owns at least ONE dog and one cat. The probability that a cat owner is a woman is greater than the probability that a MEN owns a dog. Answer :A

Discussion

9.	int_(0)^(1)(xSin^(-1)x)/(sqrt(1-x^(2)))dx=
Answer» 0 1 2 3 Answer :B

Discussion

10.	int_(0)^(3)xsqrt(1+x)dx=
Answer» `(116)/(15)` `(15)/(116)` 0 `(115)/(16)` ANSWER :A

Discussion

11.	The sum of the roots of the equation x^(2) + \|2x - 3\| + 4 = 0,is
Answer» 2 `-2` `SQRT(2)` `- sqrt(2)` ANSWER :C

Discussion

12.	Ifx sin ^3 theta +y cos^3 theta= sin theta cos theta andx sintheta =y cos thetathen x^2+y^2is
Answer» `5A^(2)` `4A^(2)` `3A^(2)` `a^(2)` ANSWER :D

Discussion

13.	Three dice are thrown at the sametime. Find the probability of getting three two's, if it is known that the sum of the numbers on the dice was six.
Answer» ANSWER :`(1)/(10)`

Discussion

14.	The shadow of a tower of height (1 +sqrt3 ) metre standing on the ground is found to be 2 metre longer when the sun's elevation is 30^(@), then when the sun's elevation was :
Answer» `30^(@)` `45^(@)` `60^(@)` `75^(@)` Solution :Let AB is a TOWER of HEIGHT `(1+sqrt3)` m, BC and BD and BD are its shadows. When the sun's elevation are `30^(@)` and `alpha` (say) respectively and CD = 2M. `therefore"In triangle ABC,"` `2+BD=(1+sqrt3)COT 30^(@)` `or 2+BD=(1+sqrt3)sqrt3` `or BD=(sqrt3+3)-2=sqrt3+1` Now, in triangle ABD `tan alpha=(AB)/(BD)=(1+sqrt3)/(sqrt3+1)=1=1 tan 45^(@)` `therefore alpha=45^(@)`

Discussion

15.	If A,B are symmetric matrices of sameorder , then AB - BA is a :
Answer» NULL MATRIX UNIT matrix SYMMETRIC matrix skew - symmetric matrix ANSWER :D

Discussion

16.	he flu shot for a flu seaons is created four strains of the flu virus, named Strain A,B,C and D, respectively. Medicalresearchers use the following data to determine the effectiveness of the vacine over the flu season. Table 1 shows the effectiveness of the vaccine against each of these strains individually. The graph below the table shows the prevalence of each of these strains during each month of the flu season, represented as a percentage of the overall cases of flu that month. For the strain against which the flu shot was the most effective. approximately how effective was the shot overall during the month that strain was least prevalent?
Answer» 0.13 0.2 0.27 0.48 Answer :D

Discussion

17.	If y ^(2) = a ^(2) cos ^(2) x + b b^(2) sin ^(2) x then y + y _(2)=
Answer» `a ^(2) B ^(2) ` `(a ^(2) b ^(2))/(y ^(3))` `y ^(3)` NONE ANSWER :B

Discussion

18.	Find the value of the following cot^(-1) (tan (-6))
Answer» ANSWER :`4pi-10`,

Discussion

19.	If (1 + isqrt2)^(x) = 3^(x) , then its only integral solution is
Answer» 2 0 3 4 Answer :B

Discussion

20.	Given p=3hat(i)+2hat(j)+4hat(k), a=hat(i)+hat(j), b=hat(j)+hat(k), c=hat(i)+hat(k) and p=x a +y b +z c, then x, y and z are respectively
Answer» `3/2, 1/2, 5/2` `1/2, 3/2, 5/2` `5/2, 3/2, 1/2` `1/2, 5/2, 3/2` Solution :`p=x a + yb +zc` `rArr""3hati+2hatj+4hatk=x(hati+hatj)+y(hatj+hatk)+z(hati+hatk)` `rArr""3hati+2hatj+4hatk=(x+z)hati+(x+y)hatj+(y+z)hatk` `x+z=3"...(i)"` `x+y=2"...(II)"` `x+z=4"...(iii)"` Now, subtracting EQ. (ii) from Eq. (i), we get `z-y=1"...(IV)"` From EQS. (iii) and (iv), we gt `z=5/2, y=3/2` From Eq. (ii) we get `x=1/2` HENCE, `x=1/2, y=3/2, z=5/2`

Discussion

21.	For a point P in the plane let d_(1)(P)and d_(2) be the distance of the point P from the lines x-y=0 R consisting of all points P lying in the first quadrant of the plane and satisfying 2 ge d_(1)(P)+d_(2)(P)ge 4, is
Answer»

Discussion

22.	The tangent at the point P (x_(1),y_(1)) to the parabola y^(2)=4ax meets the parabola y^(2)=4a(x+b) at Q and R then the midpoint of QR is
Answer» (2,4) (4,2) (7,9) none Answer :A

Discussion

23.	A brick manufacturer has two depots A and B with stocks of 30000 and 20000 bricksrespectively. He receives orders from three builders P, Q and R for 15000, 20000 and 15000 bricks respectively. The cost of transporting 1000 bricks to the builders from the depots (in rupees) are given below: How should the manufacturer fulfil the order so as to keep the cost of transportation minimum? What is the minimum cost?
Answer» SOLUTION :N/A

Discussion

24.	cos 2x- 3 cos x + 1=(1)/((cot 2 x - cot x)sin (x-pi)) holds , if
Answer» COS X =0 cos x =1 `cos x=(5)/(2)` for no value of x Answer :A

Discussion

25.	What can you say about the set, A,B,ifA Delta B =phi
Answer» SOLUTION :`A DELTA B = PHI IMPLIES A=B`

Discussion

26.	Form, a cosmetic shop containing perfumes and does, a pair is selected at random. The probability that the selected pair will consist of one perfume and one deo is 16/31. Find the maximum number of perfumes and does the shop can contain ?
Answer» ANSWER :32

Discussion

27.	The P(u,v,q) is a point whose distance from the line x=y=z is twice its distance from the plane x+y+z=1 and uv+vw+wu=0 then u^(2)+v^(2)+w^(2)-4(u+v+w) is equal to
Answer» `-2` 0 2 4 Answer :A

Discussion

28.	The variance of the following frequency distribution is {:("Class Interval",0-4,4-8,8-12,12-16,16-20),("Frequency",2,4,6,3,1):}
Answer» `(295)/(16)` `(304)/(16)` `(37)/(4)` `(97)/(4)` Answer :A

Discussion

29.	Choose the correct answer from the bracket The line y=x+1 is a tangent to the curve y^2=4x at the point.
Answer» (1,2) (2,1) `(1,-2)` `(-1,2)` ANSWER :A

Discussion

30.	For a loaded die, the probabilities of outcomes are given as under : P(1) = P(2) = 0.2, P(3) = P(5) = P(6) = 0.1 and P(4) = 0.3. The die is thrown two times. Let A and B be the events, 'same number each time', and 'a total score is 10 or more', respectively. Determine whether or not A and B are independent.
Answer» ANSWER :A and B are not INDEPENDENT.

Discussion

31.	Let 0 lt A_(i) pi for i = 1,2,"……"n. Use mathematical induction to prove that sin A_(1) + sin A_(2)+ "….." + sin A_(n) le n sin ((A_(1) + A_(2) + "……" + A_(n))/(n))where n ge 1 is a natural number. [You may use the fact thatp sin x + (1-p) sin y le sin [px+(1-p)y], where 0 le p le 1 and 0 le x , y le pi.
Answer» Solution :For `n = 1`,the inequality becomes `sinA_(1)lesin A_(1)`,which is clearlytrue. Let us assume that the inequility holds for `n = K` where k is some positive integer. Then `sinA_(1) + sinA_(2) + "……"+sinA_(n) le k SIN ((A_(1) + A_(2) +"....." + A_(k))/(k))"......"(1)` Adding `sin A_(k+1)` on bothsides, we GET `sin A_(1) + sin A_(2) + "......" +sin A_(k) +suin A_(k+1) le k sin((A_(1) + A_(2) +"......."+A_(k))/(k)) + sin A_(k+1)` Now, `k sin ((A_(1) + A_(2) + "......." + A_(k))/(k))+ sin A_(k+1)` `= (k+1)[(k)/(k+1)sin alpha+(1)/(k+1) sin A_(k+1)]`, where `alpha = (A_(1) + A_(2) + "......" + A_(g))/(k)` ` le (k + 1 )sin{(1+(1)/(k+1)) alpha + (1)/(k+1) A_(k+1)}` {Using `p sin x+ (1-p) sinyle sin[px + (1-p)y]}` `= (k+1)sin((A_(1)+A_(2)+"......."A_(k+1))/(k+1))` Thus, the inequality hold for `n= k +1`. Hence, by the PRINCIPLE of mathematicalinduction, the inequality holds for all `n in N`.

Discussion

32.	Let f(x) be a function defined by f(x) =(ab -a^2-2)x -underset(0)overset(x)(cos^4 t + sin^2t-2)dtIf (x) is a decreasing function for all x in Randa in R where a is independent of x, then
Answer» `be in (1,OO)` `b in(-1,1)` `b in (-oo,]` non of these Solution :We have `f(X)=(ab-a^2-2)x-underset

Discussion

33.	If PQ is a double ordinate of the hyperbola such that OPQ is an equilateral triangle,being the centre of the hyperbola, then eccentricity e of the hyperbola satisfies
Answer» `E=(2)/SQRT(3)` `e=sqrt(3)/(2)` `EGT(2)/sqrt(3)` `1ltelt(2)/sqrt(3)` Answer :C

Discussion

34.	Determine whether a*b ="min" {a,b} "on" N operations as defined by are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.
Answer» SOLUTION :`a,b in N IMPLIES "min" {a,b} in N ` `:.ab in N` ` implies ` is a BINARY OPERATION on N

Discussion

35.	i. Show that the points A(-2,3,5),B(1,2,3),C(7,0,-1) are collinear. ii. Find the ratio in which B divides line segment AC.
Answer» ANSWER :(i) A,B,and C are COLLINEAR (II)`1:2`

Discussion

36.	If M is the skew symmetric matrix of order nxxn then ,
Answer» DET (M-1) =det(M+1) Det ( M-1) =-det (M+1) if n is odd Det(M-1) =det (M+1) if n is even Det (M) = 0 for all POSITIVE integral values of 'n' ANSWER :B::C

Discussion

37.	Evaluation of definite integrals by subsitiution and properties of its : int_(1)^(5)[x-3]dx=......... where [.] is maximum integer function.
Answer» 1 2 4 8 Answer :B

Discussion

38.	If x(dy)/(dx) = y (log y- log x +1),then the solution of the equation is
Answer» `y log (X//y) = CX` `x log (y//x) = cy` `log (y//x) = cx` `log (x//y) = cy` ANSWER :C

Discussion

39.	Differentiate the following w.r.t. x : sqrt((3)^(sqrt(x))),x gt 0.
Answer» Answer :`(e^(SQRT(X)))/(4sqrt(xe^(sqrt(x)))), x GT 0`

Discussion

40.	If 3x+2y=15 and x +y=10, what is the value of y ?
Answer» `-15` `-5` 5 15 Solution :Isolate x in the second equation, then substitute the result into the first equation: `x =10-y` ` 3 (10-y)+2y=15` `30-3y+2y=15` ` -y =-15` `y =15` If you NEEDED to KNOW the value of x as well, you COULD now substitute 15 for y into either equation to FIND that `c =-5.` The correct answer is (D).

Discussion

41.	A die is loaded so that six turns up twice as often as one and three times as often as any other face. Find the probability of getting an even number on the die if the die is rolled once.
Answer» ANSWER :`(10)/(17)`

Discussion

42.	Giventhe integral int_(0)^(1) sqrt(1 - x^(2))dx. Made the substitution x = sin t . It is possible to take the number pi and pi //2 as thelimits for t ?
Answer» ANSWER :It is POSSIBLE

Discussion

43.	The value of underset(x to pi/2)limsqrt(("tan"x-"sin"("tan"^(-1)("tan" x)))/("tan" x+"cos"^2("tan" x))) is
Answer» -1 0 1 None of these Answer :C

Discussion

44.	Range off(x) = sin^(-1) log [x] + log ( sin^(-1)[x]), where[]denotes GIF is
Answer» 1 2 0 `{LOG . Pi/2}` ANSWER :D

Discussion

45.	int_(-pi//4)^(n pi - pi/4) \| sin x + cos x \| dx ( n in N)is :
Answer» 0 2n `2sqrt2n` None of these Solution :`int_(-pi//4)^(npi -pi/4) \|sinx+cosx\| = sqrt2 int_(-pi//4)^(npi -pi/4) \|sin (x+pi/4)\|DX` ` x + pi/4=t rArr dx = dt` `= sqrt2 int_0^(N pi)\|sin t\|dx = n sqrt2 int_0^pi sin t dt` ` = n sqrt2 (-COS t)_0^pi = n sqrt2(1-(-1))` ` = 2SQRT2 n`

Discussion

46.	Let O be the circumcentre of acute angled Delta ABC and let r _(1) ,r _(2) and r _(3) be the radil of the circles drawn on the altitudes OD, OE, and OFof triangle OBC, OCA and OAB as diameter then minimum value of (a ^(2))/(r _(1) ^(2)) + (b ^(2))/(r _(2)^(2)) + (c ^(2))/(r _(3)^(2)) is "_______"
Answer» ANSWER :`144.00`

Discussion

47.	Examine the continuity of the function f(x)= {((2x^(2)-3x-2)/(x-2)",","if " x ne 2),(5",","if " x =2):} at x= 2
Answer» ANSWER :x=2

Discussion

48.	Select the correct answer :Degree of differential equationx^2(dy/DX)^2-y(d^2y/(dx^2))=0
Answer» `1` `0` `2` `3` ANSWER :A

Discussion

49.	Find the angle between the vector 2hati-3hatj+hatk and hati+hatj-2hatk.
Answer» ANSWER :`COS^(-1)((3)/(sqrt(84)))`

Discussion

50.	If : f(x,y)={:[(cosx,sinx,0),(-sinx,cosx,0),(0,0,e^(y))]:} then : [f(x,-y)]^(-1)=
Answer» `F(X,-y)` f(-x,-y) f(-x,y) NONE of these Answer :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Evaluation of definite integrals by subsitiution and properties of its : If f(a+b+1-x)=f(x)AAx where a and b are fixed positive real numbers, then (1)/(a+b)int_(a)^(b)x(f(x)+f(x+1)dx= is equal to

Let vecaandvecb be two unit vectors and theta is the angle between them Thenveca+vecb isa unit vector if

Let A and B any two events. Which one of the following statements is always true?

IFx^2+P_1 x+q_1 =0, x^2 +p_2 x +q_2=0 , x^2 +p_3 x+q_3=0hasa coomonrootthenp_(1) ^2 +p_(2)^2 +P_3^2+4(q_1+q_2+q_3)=

Assertion (A ) :If 1,2,3aretherootsofax^3 +bx^2 + cx ++d =0thenrootsofax^3 + 2 bx^2 + 4 cx +8d =0are2,4,6 Reason (R ): Theequationwhoserootsare ktimesthe rootsof theequationf(x)=0Isf(x//k) =0thenthe truestatmentamongthe followingis :

Integration by partial fraction : int(xdx)/(x^(4)+x^(2)+1)=......

A surveywas conducted among a randomly chosen sample of 250 single men and 250 single women about whether they owned any dogs or cats. The table below displays a summary of the survey results. According to the table, which of the following statements is most likely to be false?

int_(0)^(1)(xSin^(-1)x)/(sqrt(1-x^(2)))dx=

int_(0)^(3)xsqrt(1+x)dx=

The sum of the roots of the equation x^(2) + |2x - 3| + 4 = 0,is

Ifx sin ^3 theta +y cos^3 theta= sin theta cos theta andx sintheta =y cos thetathen x^2+y^2is

Three dice are thrown at the sametime. Find the probability of getting three two's, if it is known that the sum of the numbers on the dice was six.

The shadow of a tower of height (1 +sqrt3 ) metre standing on the ground is found to be 2 metre longer when the sun's elevation is 30^(@), then when the sun's elevation was :

If A,B are symmetric matrices of sameorder , then AB - BA is a :

If y ^(2) = a ^(2) cos ^(2) x + b b^(2) sin ^(2) x then y + y _(2)=

Find the value of the following cot^(-1) (tan (-6))

If (1 + isqrt2)^(x) = 3^(x) , then its only integral solution is

Given p=3hat(i)+2hat(j)+4hat(k), a=hat(i)+hat(j), b=hat(j)+hat(k), c=hat(i)+hat(k) and p=x a +y b +z c, then x, y and z are respectively

For a point P in the plane let d_(1)(P)and d_(2) be the distance of the point P from the lines x-y=0 R consisting of all points P lying in the first quadrant of the plane and satisfying 2 ge d_(1)(P)+d_(2)(P)ge 4, is

The tangent at the point P (x_(1),y_(1)) to the parabola y^(2)=4ax meets the parabola y^(2)=4a(x+b) at Q and R then the midpoint of QR is

cos 2x- 3 cos x + 1=(1)/((cot 2 x - cot x)sin (x-pi)) holds , if

What can you say about the set, A,B,ifA Delta B =phi

Form, a cosmetic shop containing perfumes and does, a pair is selected at random. The probability that the selected pair will consist of one perfume and one deo is 16/31. Find the maximum number of perfumes and does the shop can contain ?

The P(u,v,q) is a point whose distance from the line x=y=z is twice its distance from the plane x+y+z=1 and uv+vw+wu=0 then u^(2)+v^(2)+w^(2)-4(u+v+w) is equal to

The variance of the following frequency distribution is {:("Class Interval",0-4,4-8,8-12,12-16,16-20),("Frequency",2,4,6,3,1):}

Choose the correct answer from the bracket The line y=x+1 is a tangent to the curve y^2=4x at the point.

Let f(x) be a function defined by f(x) =(ab -a^2-2)x -underset(0)overset(x)(cos^4 t + sin^2t-2)dtIf (x) is a decreasing function for all x in Randa in R where a is independent of x, then

If PQ is a double ordinate of the hyperbola such that OPQ is an equilateral triangle,being the centre of the hyperbola, then eccentricity e of the hyperbola satisfies

Determine whether a**b ="min" {a,b} "on" N operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

i. Show that the points A(-2,3,5),B(1,2,3),C(7,0,-1) are collinear. ii. Find the ratio in which B divides line segment AC.

If M is the skew symmetric matrix of order nxxn then ,

Evaluation of definite integrals by subsitiution and properties of its : int_(1)^(5)[x-3]dx=......... where [.] is maximum integer function.

If x(dy)/(dx) = y (log y- log x +1),then the solution of the equation is

Differentiate the following w.r.t. x : sqrt((3)^(sqrt(x))),x gt 0.

If 3x+2y=15 and x +y=10, what is the value of y ?

A die is loaded so that six turns up twice as often as one and three times as often as any other face. Find the probability of getting an even number on the die if the die is rolled once.

Giventhe integral int_(0)^(1) sqrt(1 - x^(2))dx. Made the substitution x = sin t . It is possible to take the number pi and pi //2 as thelimits for t ?

The value of underset(x to pi/2)limsqrt(("tan"x-"sin"("tan"^(-1)("tan" x)))/("tan" x+"cos"^2("tan" x))) is

Range off(x) = sin^(-1) log [x] + log ( sin^(-1)[x]), where[]denotes GIF is

int_(-pi//4)^(n pi - pi/4) | sin x + cos x | dx ( n in N)is :

Let O be the circumcentre of acute angled Delta ABC and let r _(1) ,r _(2) and r _(3) be the radil of the circles drawn on the altitudes OD, OE, and OFof triangle OBC, OCA and OAB as diameter then minimum value of (a ^(2))/(r _(1) ^(2)) + (b ^(2))/(r _(2)^(2)) + (c ^(2))/(r _(3)^(2)) is "_______"

Examine the continuity of the function f(x)= {((2x^(2)-3x-2)/(x-2)",","if " x ne 2),(5",","if " x =2):} at x= 2

Select the correct answer :Degree of differential equationx^2(dy/DX)^2-y(d^2y/(dx^2))=0

Find the angle between the vector 2hati-3hatj+hatk and hati+hatj-2hatk.

If : f(x,y)={:[(cosx,sinx,0),(-sinx,cosx,0),(0,0,e^(y))]:} then : [f(x,-y)]^(-1)=