28278 + Interview Questions in Maths in Class 12

1.	The solution of the equation (3+2sqrt(2))^(x^(2)-8)+(3+2sqrt(2))^(8-x^2)=6 are
Answer» `3 pm 2 SQRT(2)` `pm 1` `pm 3sqrt(3), pm 2sqrt(2)` `SQRT7, pm(3)` ANSWER :D

Discussion

2.	int (sin^(8) x - cos ^(8) x)/( 1 - 2 sin^(2) x cos^(2) x) dxis
Answer» ANSWER :`-1/2sin2x+C`

Discussion

3.	Let Z be the set of all integers and let R be a relation on Z defined by a R b implies a ge b. then R is
Answer» SYMMETRIC and TRANSITIVE but not reflexive Reflexive and symmetric but transitive Reflexive and transitive but not symmetric An EQUIVALENCE relation Answer :C

Discussion

4.	The radius of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is
Answer» `2/3R` `SQRT(2/3)R` `3/4R` `sqrt(3/4)R` ANSWER :B

Discussion

5.	A line 'I' meets the circle x^2 + y^2 =61 in A, B and P(-5, 6) is such that PA = PB = 10. Then the equation of 'l' is
Answer» 5x+6y+11=0 5x-6y-11=0 5x-6y+11=0 5x-6y+12=0 Answer :C

Discussion

6.	If f , g , and h are functions having a cammon domain D and h(x) lef(x) leg(x), x in D and iflim_(x to a)h(x)=lim_(x to a)g(x)=l" "then" "lim_(x to a)f(x)=l The value of lim_(x to 0)(\|x\|)/(sqrt(x^(4)+4x^(2)+7))-
Answer» 1 0 `(1)/(2)` `-(1)/(2)` ANSWER :B

Discussion

7.	If f , g , and h are functions having a cammon domain D and h(x) lef(x) leg(x), x in D and iflim_(x to a)h(x)=lim_(x to a)g(x)=l" "then" lim_(x to 0)x^(4)sin((1)/(3sqrtx)) is
Answer» 0 1 `(1)/(3)` `-(1)/(3)` ANSWER :A

Discussion

8.	Primitive of root(3)((x)/((x^4-1)^(4)))w.r.t.X is :
Answer» `(3)/(4)(1+(1)/(x^4-1))^(1//3)+C` `-(3)/(4)(1+(1)/(x^4-1))^(1//3)+C` `(4)/(3)(1+(1)/(x^4-1))^(1//3)+C` `-(4)/(3)(1+(1)/(x^4-1))^(1//3)+C` ANSWER :B

Discussion

9.	If \|z_(1)+z_(2)\|=\|z_1\|+\|z_2\|,then arg z_(1)-arg z_(2)=
Answer» `PI` `(pi)/(2)` `0` `-pi` ANSWER :C

Discussion

10.	If the s.d. of -5, -4, -3, -2,-1,0,1,2,3,4,5 is sqrt(10) then find the standard deviation of 15, 16, 17,18,19,20,21,22,23,24,25
Answer» ANSWER :`SQRT(10)`

Discussion

11.	Find matrices X, if 2X-Y=[(6,-6,0),(-4,2,1)] and X+2Y=[(3,2,5),(-2,1,-7)].
Answer» `[(3,-2,-2),(-2,0,-1)]` `[(3,-2,2),(-2,1,-1)]` `[(3,-2,1),(-2,1,-1)]` None of these Answer :C

Discussion

12.	Differentiate the following w.r.t. x: sqrt(e^(sqrtx)), x gt 0
Answer» Answer :`(1)/(4) (e^(SQRTX))/(sqrt(XE^(sqrtx))),X GT 0`

Discussion

13.	Consider the system of equations ax + by + cz = 2 bx + cy + az = 2 cx + ay + bz = 2 where a,b,c are real numbers such that a + b + c = 0. Then the system
Answer» has two solutions in inconsistent has UNIQUE solution has INFINITELY MANY solutions Answer :B

Discussion

14.	From any point on the circle x^(2)+y^(2)=a^(2) tangent are drawn to the circle x^(2)+y^(2)=a^(2)sin^(2)theta. The angle between them is
Answer» `THETA//2` `theta` `2THETA` `4 theta` ANSWER :C

Discussion

15.	Evaluate the following (v) int_(0)^(5)[sqrt(x)]dx
Answer» ANSWER :5

Discussion

16.	The water is leaking from a conical funnel at a rate of 5cm^(3)//min. If the redius and height of the funnel are 5cm.and 10 cm respectively, find the rate of change of the surface of water in the funnel when height of water surface from the vertex is 7.5 cm.
Answer» ANSWER :`(-4)/(675 PI) cm//sec`

Discussion

17.	findthe areaof theregionboundedby thecurves y^2 = 9xand y= 3x.
Answer» ANSWER :`1/2` SEQ. UNITS

Discussion

18.	Choose the correct answer int_(0)^(2/3)(dx)/(4+9x^(2)) equals
Answer» `pi/6` `pi/12` `pi/24` `pi/4` ANSWER :C

Discussion

19.	Find the second order derivatives of the functions given in Exercises 1 to 10. log x
Answer» ANSWER :`-(1)/(x^2)`

Discussion

20.	Find the values of the following correct to five decimals. sqrt(1.01)-sqrt(0.99)
Answer» SOLUTION :N/A

Discussion

21.	Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (sin x)^(x) + sin^(-1) sqrt(x)
Answer» Answer :`(SINX)^(x)(x COT x+log SIN x)+(1)/(2)(1)/(sqrt(x-x^(2)))`.

Discussion

22.	If lim_(n to infty)((n!)1/n)/n=L where n in N, then the absolute value of log_(e)(L) is
Answer» 1 `1/2` `1/3` 2 Solution :LN L`=lim_(n to infty) ln ((n!)/(n^(n))^(1/n))` `=lim_(n to infty) sum_(r=1)^(n) 1/n ln(r/n)` `=int_(0)^(1) (ln X)dx=-1`

Discussion

23.	Differentiate the functions with respect to x in Exerecises 1 to 8. sec (tan (sqrt(x)))
Answer» ANSWER :`(sec(tansqrt(X)).TAN(tansqrt(x)).sec^(2)SQRT(x))/(2sqrt(x))`

Discussion

24.	Find the area of the region bounded by y axis and the parabola x=5-4y-y^(2).
Answer» ANSWER :36

Discussion

25.	Find the number of terms in the expansion of (1+x)^n(1-x)^n.
Answer» SOLUTION :`(1+x)^n(1-x)^n= (1-x^2)^n` `THEREFORE` The number of TERMS in this EXPANSION is (n+1).

Discussion

26.	Evaluate the definite integrals . I=underset(1)overset(5)int (dx)/(sqrt(2x-1))
Answer» ANSWER :2

Discussion

27.	Find the value of lambda so that the vectors veca and vecb are perpendicular to each other. veca = 3hati+4hatj, vecb = -5hati+lambdahatj.
Answer» Solution :If `VECA` and `VECB` are perpendicular `veca.vecb = 0` `implies (3hati+4hatj).(-5hati+lambdahatj) = 0` `implies -15+4lambda = 0 implies LAMBDA = 15/4`

Discussion

28.	Evaluate: int_(0)^((pi)/(2)) log (sin x) dx
Answer» SOLUTION :N/A

Discussion

29.	Let y=f (x) and x/y (dy)/(dx) =(3x ^(2)-y)/(2y-x^(2)),f(1)=1 then the possible value of 1/3 f(3) equals :
Answer» 9 4 3 2 Answer :C

Discussion

30.	Differentiate w.r.t.x the function. (sin x- cos x)^( sin x - cos x), (pi)/(4) ltx lt (3pi)/(4).
Answer» ANSWER :`(sin X- cos x)^(sin x-cos x)(cos x+ sin x)(1+ log(sin x-cos x)); SINX GT cos x`

Discussion

31.	Which of the following statements is a contingency?
Answer» <P>`(~p ^^ ~q) ^^ (q ^^ R)` `( p to q) vv ( q to p)` `(p to ~q) to r ` `(q to r) vv (r to p)` ANSWER :C

Discussion

32.	IFA={1,2,3}then matchfollowingsubsetsofA xx Aproperly
Answer» `(I) to(B),(II) to(A),(III) to (C )` `(I)to (A) , (II) to (C ) ,(III) to(B) ` `(I ) to (C ) ,(II) to (B ), (III)to (A ) ` `(I)to (A) ,(II) to(B ), (III)to (C ) ` ANSWER :B

Discussion

33.	Lt_(ntooo){(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(3n)}=
Answer» LOG 2 log 3 log 4 log 5 Answer :B

Discussion

34.	Thevalueofcos^(-1) (-1) + tan^(-1) (oo ) + sin ^(-1)1=……
Answer» `-PI` `(3PI)/2` `30^(@)` `2pi` Answer :D

Discussion

35.	A :tan ( alpha - beta ) + tan ( beta - alpha ) + tan ( gamma - alpha ) = tan ( alpha - beta ) tan (beta - gamma ) tan (gamma - alpha ) R : In Delta ABC , sum tan A = Pi tan A
Answer» A is TRUE , R is true and R is correct explanation of A A is true , R is TRUEAND R is not correct explanation of A A is true , R is false A is false , R is true Answer :B

Discussion

36.	A die is thrown 6 times. If getting an odd number is success, What is the probability (a) 5 successes (b) at least 5 successes (c) at most 5 successes
Answer» ANSWER :(i) `(3)/(32)` (ii) `(7)/(64)` (III) `(63)/(64)`

Discussion

37.	Let V_(1)= variance of {13, 16, 19…………103} and V_(2)=" variance of "{20, 26, 32…………..200}. Then V_(1):V_(2) is
Answer» `1:2` `1:1` `4:9` `1:4` ANSWER :D

Discussion

38.	int _(0)^(pi//2) (sin^(3) x cos x dx ) /(sin^(4) x + cos^(4) x )=
Answer» `PI` `pi/2` `pi/4` `pi/8` ANSWER :D

Discussion

39.	From the top of a building of height h, a tower standing on the ground is observed to make an angle theta. If the horizontal distance between the building and the tower is h, the height of the tower is
Answer» `(2 h cos theta)/(SIN theta + cos theta)` `(2H)/(1+cot theta)` `(2h)/(1+tan theta)` `(2h)/(sin theta + cos theta)` ANSWER :B

Discussion

40.	For any complex number z, maximum value of \|z\|-\|z-1\| is
Answer» 0 1 `1//2` `3//2` ANSWER :C

Discussion

41.	Find the equation of the circle passing through(-2,3) (4,5)and whose centre lies on x-axis
Answer» Answer :` 3(X^(2) +y^(2)) -14X -67 =0`

Discussion

42.	Solve the differential equation dy/dx+2y tan x=sin x,y=0 when x=pi/3
Answer» ANSWER :`:. y SEC^(2)x=sec x-2`

Discussion

43.	Find all pairs of consecutive even positive intetegers, both of which are larger than 5such that their sum is less than 23.
Answer» ANSWER :The POSSIBLE PAIRS are (6,8)(8,10) and (10, 12)

Discussion

44.	If vec(a) and vec(b) are two vectors such that \|vec(a)\|= 2, \|vec(b)\| = 3 and vec(a)*vec(b)=4 then find the value of \|vec(a)-vec(b)\|
Answer» ANSWER :`SQRT(5)`

Discussion

45.	Out of 30 consecutive integers, three integers are drawn at random. Find the probability that their sum is (i) an odd number (ii) an even number
Answer» ANSWER :`(i) (13)/(116)` `(II) (103)/(116)`

Discussion

46.	Find the mean deviation about the meanfor the following data (##VIK_MAT_IIA_QB_C08_SLV_005_Q01.png" width="80%">
Answer» ANSWER :`10.4`

Discussion

47.	Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 are
Answer» 216 375 400 720 Answer :D

Discussion

48.	Integrate the function 1/(sqrt((x-1)(x-2)))
Answer» ANSWER :`logabs(X-3/2+sqrt(x^(2)-3x+2))+C`

Discussion

49.	Show that 2 sin x + than x ge 3x all x in (0, pi/20).
Answer» SOLUTION :Let `F(x) = 2 sin x + tan x - 3x` Then `f.(x) = 2 cos x + sec^2 x - 3` Now `f.(x) GT 0 for all x in (0,pi/2)`. Thus `f.(x) is INCREASING in (0,pi/2). But `F(0) = 0` Thus `f(x) ge 0 for all x in (0, pi/2)` `rArr 2 sin x + tan x - 3x ge 0 for all x in (0, pi/2)cdot . `2 sin x + tan x ge 3x for all x in (0,pi/2).

Discussion

50.	Two vertical lamp posts of equal heights stand on either side of a road 50 meters wide. At a point on the road, between the two lamp posts, the angles of elevation of the tops of the lamp posts are 60^(@)and 30^(@) Then the highest of each post and the position of the point from one pole are :
Answer» `21 - 65 m, 12-5 ` `21.65 m, 20 m` `23 m, 12.5m ` NONE of these. Answer :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The solution of the equation (3+2sqrt(2))^(x^(2)-8)+(3+2sqrt(2))^(8-x^2)=6 are

int (sin^(8) x - cos ^(8) x)/( 1 - 2 sin^(2) x cos^(2) x) dxis

Let Z be the set of all integers and let R be a relation on Z defined by a R b implies a ge b. then R is

The radius of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is

A line 'I' meets the circle x^2 + y^2 =61 in A, B and P(-5, 6) is such that PA = PB = 10. Then the equation of 'l' is

If f , g , and h are functions having a cammon domain D and h(x) lef(x) leg(x), x in D and iflim_(x to a)h(x)=lim_(x to a)g(x)=l" "then" "lim_(x to a)f(x)=l The value of lim_(x to 0)(|x|)/(sqrt(x^(4)+4x^(2)+7))-

If f , g , and h are functions having a cammon domain D and h(x) lef(x) leg(x), x in D and iflim_(x to a)h(x)=lim_(x to a)g(x)=l" "then" lim_(x to 0)x^(4)sin((1)/(3sqrtx)) is

Primitive of root(3)((x)/((x^4-1)^(4)))w.r.t.X is :

If |z_(1)+z_(2)|=|z_1|+|z_2|,then arg z_(1)-arg z_(2)=

If the s.d. of -5, -4, -3, -2,-1,0,1,2,3,4,5 is sqrt(10) then find the standard deviation of 15, 16, 17,18,19,20,21,22,23,24,25

Find matrices X, if 2X-Y=[(6,-6,0),(-4,2,1)] and X+2Y=[(3,2,5),(-2,1,-7)].

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

Consider the system of equations ax + by + cz = 2 bx + cy + az = 2 cx + ay + bz = 2 where a,b,c are real numbers such that a + b + c = 0. Then the system

From any point on the circle x^(2)+y^(2)=a^(2) tangent are drawn to the circle x^(2)+y^(2)=a^(2)sin^(2)theta. The angle between them is

Evaluate the following (v) int_(0)^(5)[sqrt(x)]dx

The water is leaking from a conical funnel at a rate of 5cm^(3)//min. If the redius and height of the funnel are 5cm.and 10 cm respectively, find the rate of change of the surface of water in the funnel when height of water surface from the vertex is 7.5 cm.

findthe areaof theregionboundedby thecurves y^2 = 9xand y= 3x.

Choose the correct answer int_(0)^(2/3)(dx)/(4+9x^(2)) equals

Find the second order derivatives of the functions given in Exercises 1 to 10. log x

Find the values of the following correct to five decimals. sqrt(1.01)-sqrt(0.99)

Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (sin x)^(x) + sin^(-1) sqrt(x)

If lim_(n to infty)((n!)1/n)/n=L where n in N, then the absolute value of log_(e)(L) is

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

Find the area of the region bounded by y axis and the parabola x=5-4y-y^(2).

Find the number of terms in the expansion of (1+x)^n(1-x)^n.

Evaluate the definite integrals . I=underset(1)overset(5)int (dx)/(sqrt(2x-1))

Find the value of lambda so that the vectors veca and vecb are perpendicular to each other. veca = 3hati+4hatj, vecb = -5hati+lambdahatj.

Evaluate: int_(0)^((pi)/(2)) log (sin x) dx

Let y=f (x) and x/y (dy)/(dx) =(3x ^(2)-y)/(2y-x^(2)),f(1)=1 then the possible value of 1/3 f(3) equals :

Differentiate w.r.t.x the function. (sin x- cos x)^( sin x - cos x), (pi)/(4) ltx lt (3pi)/(4).

Which of the following statements is a contingency?

IFA={1,2,3}then matchfollowingsubsetsofA xx Aproperly

Lt_(ntooo){(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(3n)}=

Thevalueofcos^(-1) (-1) + tan^(-1) (oo ) + sin ^(-1)1=……

A :tan ( alpha - beta ) + tan ( beta - alpha ) + tan ( gamma - alpha ) = tan ( alpha - beta ) tan (beta - gamma ) tan (gamma - alpha ) R : In Delta ABC , sum tan A = Pi tan A

A die is thrown 6 times. If getting an odd number is success, What is the probability (a) 5 successes (b) at least 5 successes (c) at most 5 successes

Let V_(1)= variance of {13, 16, 19…………103} and V_(2)=" variance of "{20, 26, 32…………..200}. Then V_(1):V_(2) is

int _(0)^(pi//2) (sin^(3) x cos x dx ) /(sin^(4) x + cos^(4) x )=

From the top of a building of height h, a tower standing on the ground is observed to make an angle theta. If the horizontal distance between the building and the tower is h, the height of the tower is

For any complex number z, maximum value of |z|-|z-1| is

Find the equation of the circle passing through(-2,3) (4,5)and whose centre lies on x-axis

Solve the differential equation dy/dx+2y tan x=sin x,y=0 when x=pi/3

Find all pairs of consecutive even positive intetegers, both of which are larger than 5such that their sum is less than 23.

If vec(a) and vec(b) are two vectors such that |vec(a)|= 2, |vec(b)| = 3 and vec(a)*vec(b)=4 then find the value of |vec(a)-vec(b)|

Out of 30 consecutive integers, three integers are drawn at random. Find the probability that their sum is (i) an odd number (ii) an even number

Find the mean deviation about the meanfor the following data (##VIK_MAT_IIA_QB_C08_SLV_005_Q01.png" width="80%">

Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 are

Integrate the function 1/(sqrt((x-1)(x-2)))

Show that 2 sin x + than x ge 3x all x in (0, pi/20).

Two vertical lamp posts of equal heights stand on either side of a road 50 meters wide. At a point on the road, between the two lamp posts, the angles of elevation of the tops of the lamp posts are 60^(@)and 30^(@) Then the highest of each post and the position of the point from one pole are :