14949 + Interview Questions in Maths in Class 11 Page 203 InterviewSolution

10101.	If x = sin^(-1)t and y = log (1 - t^2) , then (d^2 y)/(dx^2)\|_(t=1//2) is
Answer» `(-8)/3` `8/3` `3/4` `(-3)/4` ANSWER :A

Discussion

10102.	Find the direciton cosines ofa line which is perpendicular to the lines whose direcition ratios are (1,-2,3) and (2,1,-1)
Answer» ANSWER :`((-1)/(SQRT(35)),(5)/(sqrt(35)),(3)/(sqrt(35)))`

Discussion

10103.	f(x) = sinx +cos2x (xgt0) has minima at x=
Answer» `(2n+1)(pi)/(2),AAn INZ` `(npi)/(2),.AAn in Z` `npi,AAn inZ` `(npi)/(2),AAn inZ` ANSWER :A

Discussion

10104.	log[(x-1)+sqrt(x^(2)-2x)], x ge 2, is equal to
Answer» `sinh^(-1)(X-1)` `cos h^(-1)(x-1)` `SIN h^(-1)(x + 1)` `cos h^(-1)(x + 1)` Answer :B

Discussion

10105.	(1)/(cos 290^(@)) + (1)/(sqrt(3)sin 250^(@)) = lambda "then" 3 lambda^(2) =
Answer» 16 4 `(4)/(SQRT(3))` `(16)/(3)` ANSWER :A

Discussion

10106.	Calculate the mean, variance and standard deviation for the following distribution :
Answer» ANSWER :14.18

Discussion

10107.	The parametric equations of the line are give by x=-2+r/(sqrt(10)) and y=1+(3r)/(sqrt(10)) then for the line
Answer» x-intercept is `7/3` inclination is `TAN^(-1)3` slope in `"tan"^(-1)1/3` y- intercept is 5 Answer :B

Discussion

10108.	A card is drawn from a pack of cards . Findthe probability that it is ace of spaded
Answer» ANSWER :`=(1)/(52)`.

Discussion

10109.	Find coordinates of the point which of the equidistance from O(0, 0, 0), A(l, 0, 0), B(0, m, 0) and C(0, 0, n).
Answer» ANSWER :`(l/2,m/2,n/2)`

Discussion

10110.	If \|vec(a)\|= \|vec(b)\| =1 and \|vec(a) xx vec(b)\|= vec(a).vec(b), then \|vec(a) + vec(b)\|^(2)=
Answer» `SQRT2` `2 + sqrt2` 2 1 Answer :B

Discussion

10111.	Find the domain of the function f(x)=(x^(2)+3x+5)/(x^(2)-5x+4)
Answer» ANSWER :`R- {1, 4}`

Discussion

10112.	If the sum of n terms of an A.P. isnP+1/2n(n-1)Q , where P and Q are constants, find the common difference.
Answer» ANSWER :d= Q

Discussion

10113.	If Cos^(-1)x+Cos^(-1)y+Cos^(-1)z=pi,"then "x^(2)+y^(2)+z^(2)+2xyz=
Answer» `X^(2)+y^(2)+Z^(2)+xyz=0` `x^(2)+y^(2)+z^(2)+2xyz=0` `x^(2)+y^(2)+z^(2)+xyz=1` `x^(2)+y^(2)+z^(2)+2xyz=1` ANSWER :D

Discussion

10114.	Let t_(1)=(sin^(-1)x)^(sin^(-1)x), t_(2)=(sin^(-1)x)^(cos^(-1)x), t_(3)=(cos^(-1)x)^(sin^(-1)x), t_(4)=(cos^(-1)x)cos^(-1)x Match the items of Column I with the items Column II {:("Column-I", "Column-II"), ("A) "x in (0,cos1),"p) "t_(1) gt t_(2) gt t_(4) gt t_(3)), ("B) "x in (cos1,1/sqrt(2)),"q) "t_(4) gt t_(3) gt t_(1) gt t_(2)), ("C) "x in (1/sqrt(2),sin1),"r) "t_(1) gt t_(2) gt t_(4) gt t_(3)), ("D) "x in (sin1","1),"s) "t_(3) gt t_(4) gt t_(1) gt t_(2)):}
Answer» ANSWER :A-q, B-s, C-r, D-p

Discussion

10115.	If lambda(2bar(i)-4bar(j)+4bar(k)) is a unit vector then lambda=
Answer» `pm1/4` `pm1/7` `pm1/5` `pm1/6` ANSWER :D

Discussion

10116.	If length of the side BC of a Delta ABCis 4cm and angle BAC = 120^(@) , then the distance between incentre & excentre of the circle touching the side BC internally is
Answer» 8 9 7 6 Answer :a

Discussion

10117.	If x+y =28 then the maximum value of x^(3)y^(4) is
Answer» `4^(3).24^(4)` `12^(3),16^(4)` `4321` `4321` ANSWER :B

Discussion

10118.	Find the distance between parallel lines(15x+8y-34=0), (15x+8y+31=0) ?
Answer» Answer :`(i) 65/17 ` UNITS, (II) `1/sqrt 2 \|(p + r)/L\|` units.

Discussion

10119.	Let bar(b)=bar(i)-2bar(j)+3bar(k), bar(a)=2bar(i)+3bar(j)-bar(k) and bar(c)=lambdabar(i)+bar(j)+(2lambda-1)bar(k)." If "bar(c) parallel to the plane containing bar(a), bar(b)" then "lambda=
Answer» 0 1 -1 2 Answer :A

Discussion

10120.	Fnd the equation of the tangent to the ellipse (x ^(2))/(16) + (y ^(2))/(9) =1 which makes an angle of 30^(@) with the x-axis.
Answer» ANSWER :`sqrt43`

Discussion

10121.	For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If x in [-1, -1/2), then the value of a+bpi is
Answer» `2PI` `3PI` `PI` `-2pi` ANSWER :C

Discussion

10122.	ax+b(sec(tan^(-1)x))=c and ay+b(sec(tan^(-1)y))=c The value of (x+y)/(1-xy) is
Answer» `(2ab)/(a^(2)-b^(2))` `(2AC)/(a^(2)-c^(2))` `(c^(2)-b^(2))/(a^(2)+b^(2))` NONE of these Answer :B

Discussion

10123.	On which point we shift origin so that new transformed form of the equation y^(2) + 4y + 8x-2 =0 does not contain constant term and term does not contain y ?
Answer» ANSWER :`((3)/(4) , -2)`

Discussion

10124.	When 2^( 301)is divided by 5, the least +ve remainder is
Answer» 4 8 2 6 Answer :C

Discussion

10125.	Which of the following sentences are statements? Justify 15+8gt23
Answer» ANSWER :It is STATEMENT.

Discussion

10126.	If cot^(-1)""n/pi gt pi/6, n in N, then the maximum value of n is
Answer» 6 7 5 none of these Answer :C

Discussion

10127.	A person stading on the bank of a river observerves that the angle of elevation of the top of the tree on the opposite bank of the river is 60^(@) and when he retires 40 metersaway from the tree the angle of elevation becomes 30^(@). The breadth of the river is
Answer» `20M` `60M` `40M` `30M` ANSWER :A

Discussion

10128.	How many numbers greater than 1000000 can be formed by using the digits 1, 2,0, 2, 4, 2,4?
Answer» ANSWER :360

Discussion

10129.	A ticket is drawn from two hundred tickets numbered from 1 to 200. Find the probility that the number is divisible by 2 or 3 or 5.
Answer» ANSWER :`=(73)/(100)`.

Discussion

10130.	Find the sum to n terms of the series (1.2.3) + (2.3.4) + (3.4.5) ...
Answer» ANSWER :`(N(n+1)(n+2)(n+3))/(4)`

Discussion

10131.	4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade ?
Answer» Answer :`(""^(13)C_(3).""^(13)C_(1))/(""^(52)C_(4))`

Discussion

10132.	2tan^(-1)(-2) equal to
Answer» `-cos^(-1)((-3)/5)` `-PI+"cos"^(-1)3/5` `-(pi)/2+tan^(-1)(-3/4)` `-pi+cot^(-1)(-3/4)` Answer :A::B::C::D

Discussion

10133.	If \|vec(a)\|=2, \|vec(b)\|=4, then (\|vec(a) xx vec(b)\|^(2))/(1-cos^(2)(vec(a), vec(b)))=
Answer» 8 2 64 32 Answer :C

Discussion

10134.	Use the second derivative test to find local extrema of the function f(x) = x^(3) - 9x^(2) - 48x + 72 on R
Answer» ANSWER :LOCAL minimum x = -376, local maximum = 124

Discussion

10135.	Findlimit of the following if it exists: lim_(xto0)(e^(4x)-1)/(x)
Answer» ANSWER :4

Discussion

10136.	Find the condition that one root of ax^(2)+bx+c=0 may be four times the other.
Answer» ANSWER :25 AC, Which is the CONDITION REQUIRED.

Discussion

10137.	Find (dy)/(dx) if y ^(x) = x ^(sin y)
Answer» ANSWER :`(y (SIN y - X LOG y))/( x ( x -y COS y log x))`

Discussion

10138.	Evaluate the following limits. Lt_(xtoa)(x^(2)-a^(2))/(x-a)
Answer» ANSWER :2A

Discussion

10139.	A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. A - (B - C)
Answer» ANSWER :`={1, 2, 3, 4}`

Discussion

10140.	Evalute 7Lt_(xto pi/2)(cotx-cosx)/((pi/2-x)^(3))
Answer» ANSWER :`1/2`

Discussion

10141.	If (3-tan^2""(pi)/7)/(1-tan^(2)""(pi)/7)=kcos""(pi)/7then the value of k is
Answer» 1 2 3 4 Answer :D

Discussion

10142.	The number of values of theta in the interval (-(pi)/(2),(pi)/(2)) satisfying the equation (sqrt(3))^(sec^(2_(theta))=tan^(4) theta = 2 tan^(2) thetais
Answer» 2 4 0 1 Answer :D

Discussion

10143.	If A and B be the points (3, 4, 5) and (-1, 3, -7) respectively, find the equation of the set of points P such that PA^(2)+PB^(2)=k^(2), where k is a constant.
Answer» Answer :`X^(2)+y^(2)+z^(2)-2x-7y+2z=(K^(2)-109)/(2)`

Discussion

10144.	If f(x)=sinx" then " 2f(x).f(90-x)=.... .
Answer» ANSWER :`F(2X)`

Discussion

10145.	If the equation 2hxy + 2gx + 2fy + c = 0 represents two straight lines, show that they form a rectangle of area (\|fg\|)/(h^2) with the co-ordinate axes.
Answer» `(\|f\|)/(g^(2))` `(\|FH\|)/(g^(2))` `(\|fg\|)/(H^(2))` `(\|GH\|)/(f^(2))` Answer :C

Discussion

10146.	If(x/3+1,y-2/3)=(5/3,1/3)" then "x+y=....... .
Answer» ANSWER :3

Discussion

10147.	If the liney = x +k touches theellipse 9x^(2) + 16y^(2) = 144, then (i) k = 5 only (ii) k = - 5 only (iii) k = 5, - 5 (iv) none of these
Answer» K = 5 only k = - 5 only k = 5, - 5 NONE of these ANSWER :C

Discussion

10148.	Which of the following quantities are rational ?
Answer» `sin((11pi)/12)sin((5pi)/12)` `"COSEC"((9pi)/10)SEC((4pi)/5)` `sin^4((pi)/8)cos^4((pi)/8)` `(1+cos""(2PI)/9)(1+cos""(4pi)/9)(1+cos""(8pi)/9)` Answer :A::B::C::D

Discussion

10149.	The maximum value of cos x ((cos x )/( 1- sin x) + (1- sin x)/( cos x) ) is
Answer» 4 3 2 1 Answer :C

Discussion

10150.	If 'a' and 'b'are natural numbers such that a^(2) - b^(2) is prime number then a^(2) - b^(2) equals
Answer» `a+b` `a-b` `AB` `1` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

If x = sin^(-1)t and y = log (1 - t^2) , then (d^2 y)/(dx^2)|_(t=1//2) is

Find the direciton cosines ofa line which is perpendicular to the lines whose direcition ratios are (1,-2,3) and (2,1,-1)

f(x) = sinx +cos2x (xgt0) has minima at x=

log[(x-1)+sqrt(x^(2)-2x)], x ge 2, is equal to

(1)/(cos 290^(@)) + (1)/(sqrt(3)sin 250^(@)) = lambda "then" 3 lambda^(2) =

Calculate the mean, variance and standard deviation for the following distribution :

The parametric equations of the line are give by x=-2+r/(sqrt(10)) and y=1+(3r)/(sqrt(10)) then for the line

A card is drawn from a pack of cards . Findthe probability that it is ace of spaded

Find coordinates of the point which of the equidistance from O(0, 0, 0), A(l, 0, 0), B(0, m, 0) and C(0, 0, n).

If |vec(a)|= |vec(b)| =1 and |vec(a) xx vec(b)|= vec(a).vec(b), then |vec(a) + vec(b)|^(2)=

Find the domain of the function f(x)=(x^(2)+3x+5)/(x^(2)-5x+4)

If the sum of n terms of an A.P. isnP+1/2n(n-1)Q , where P and Q are constants, find the common difference.

If Cos^(-1)x+Cos^(-1)y+Cos^(-1)z=pi,"then "x^(2)+y^(2)+z^(2)+2xyz=

If lambda(2bar(i)-4bar(j)+4bar(k)) is a unit vector then lambda=

If length of the side BC of a Delta ABCis 4cm and angle BAC = 120^(@) , then the distance between incentre & excentre of the circle touching the side BC internally is

If x+y =28 then the maximum value of x^(3)y^(4) is

Find the distance between parallel lines(15x+8y-34=0), (15x+8y+31=0) ?

Let bar(b)=bar(i)-2bar(j)+3bar(k), bar(a)=2bar(i)+3bar(j)-bar(k) and bar(c)=lambdabar(i)+bar(j)+(2lambda-1)bar(k)." If "bar(c) parallel to the plane containing bar(a), bar(b)" then "lambda=

Fnd the equation of the tangent to the ellipse (x ^(2))/(16) + (y ^(2))/(9) =1 which makes an angle of 30^(@) with the x-axis.

For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If x in [-1, -1/2), then the value of a+bpi is

ax+b(sec(tan^(-1)x))=c and ay+b(sec(tan^(-1)y))=c The value of (x+y)/(1-xy) is

On which point we shift origin so that new transformed form of the equation y^(2) + 4y + 8x-2 =0 does not contain constant term and term does not contain y ?

When 2^( 301)is divided by 5, the least +ve remainder is

Which of the following sentences are statements? Justify 15+8gt23

If cot^(-1)""n/pi gt pi/6, n in N, then the maximum value of n is

A person stading on the bank of a river observerves that the angle of elevation of the top of the tree on the opposite bank of the river is 60^(@) and when he retires 40 metersaway from the tree the angle of elevation becomes 30^(@). The breadth of the river is

How many numbers greater than 1000000 can be formed by using the﻿ digits 1, 2,0, 2, 4, 2,4?﻿

A ticket is drawn from two hundred tickets numbered from 1 to 200. Find the probility that the number is divisible by 2 or 3 or 5.

Find the sum to n terms of the series (1.2.3) + (2.3.4) + (3.4.5) ...

4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade ?

2tan^(-1)(-2) equal to

If |vec(a)|=2, |vec(b)|=4, then (|vec(a) xx vec(b)|^(2))/(1-cos^(2)(vec(a), vec(b)))=

Use the second derivative test to find local extrema of the function f(x) = x^(3) - 9x^(2) - 48x + 72 on R

Findlimit of the following if it exists: lim_(xto0)(e^(4x)-1)/(x)

Find the condition that one root of ax^(2)+bx+c=0 may be four times the other.

Find (dy)/(dx) if y ^(x) = x ^(sin y)

Evaluate the following limits. Lt_(xtoa)(x^(2)-a^(2))/(x-a)

A= {1, 2, 3, 4, 5}, B= {1, 3, 5, 6}, C= {1, 2, 3}, then find the following sets. A - (B - C)

Evalute 7Lt_(xto pi/2)(cotx-cosx)/((pi/2-x)^(3))

If (3-tan^2""(pi)/7)/(1-tan^(2)""(pi)/7)=kcos""(pi)/7then the value of k is

The number of values of theta in the interval (-(pi)/(2),(pi)/(2)) satisfying the equation (sqrt(3))^(sec^(2_(theta))=tan^(4) theta = 2 tan^(2) thetais

If A and B be the points (3, 4, 5) and (-1, 3, -7) respectively, find the equation of the set of points P such that PA^(2)+PB^(2)=k^(2), where k is a constant.

If f(x)=sinx" then " 2f(x).f(90-x)=.... .

If the equation 2hxy + 2gx + 2fy + c = 0 represents two straight lines, show that they form a rectangle of area (|fg|)/(h^2) with the co-ordinate axes.

If(x/3+1,y-2/3)=(5/3,1/3)" then "x+y=....... .

If the liney = x +k touches theellipse 9x^(2) + 16y^(2) = 144, then (i) k = 5 only (ii) k = - 5 only (iii) k = 5, - 5 (iv) none of these

Which of the following quantities are rational ?

The maximum value of cos x ((cos x )/( 1- sin x) + (1- sin x)/( cos x) ) is

If 'a' and 'b'are natural numbers such that a^(2) - b^(2) is prime number then a^(2) - b^(2) equals

How many numbers greater than 1000000 can be formed by using the digits 1, 2,0, 2, 4, 2,4?