14949 + Interview Questions in Maths in Class 11 Page 243 InterviewSolution

12101.	Show that the coefficient of the middle term in the expansion of (1+x)^2n is equal to the sum of the coefficients of two middle terms in the expansion of (1 + x)^2n-1
Answer» ANSWER :`^2N`Cundersetn

Discussion

12102.	Evaluate : lim_(xto0) (1+ax)^(1//x)
Answer» ANSWER :` Lim_(xto0) (1+ax)^(1//ax)=E`

Discussion

12103.	What is the value of C_0+C_2+C_4+....?
Answer» SOLUTION :`2^(n-1)`

Discussion

12104.	The sum of n terms of two arithmetic progressions are in the ratio (3n + 8) : (7n + 15). Find the ratio of their 12^("th")terms.
Answer» ANSWER :`7/16`

Discussion

12105.	If A(3, 0) and B(-3, 0) are two points and PA+PB=10, then the locus of P where P is any point (x, y) is
Answer» `(X^(2))/(16)+(y^(2))/(7)=1` `(x^(2))/(16)-(y^(2))/(7)=1` `(x^(2))/(7)+(y^(2))/(16)=1` `(x^(2))/(25)+(y^(2))/(16)=1` Answer :4

Discussion

12106.	If x=sin^(-1)(a^(6)+1)+cos^(-1)(a^(4)+1)-tan^(-1)(a^(2)+1), a in R, then the value of sec^(2)x is
Answer» ANSWER :2

Discussion

12107.	If y= (x^2 +3)/( x^3 + 2x), find (dy)/( dx) at x=1.
Answer» ANSWER :(II) `(-14)/(9)`

Discussion

12108.	If sin theta, 1, cos 2 theta are in G.P., then general values of theta
Answer» `THETA = n PI + (-1)^(n) (pi)/(2), n in Z` `theta = n pi + (-1)^(n-1) (pi)/(2), n in Z` `theta = n pi + (-1)^(n) (pi)/(6), n in Z` `theta = n pi + (-1)^(n-1) (pi)/(6), n in Z` ANSWER :B

Discussion

12109.	Find the Cartesian equation of the locus whose parametric equations are x=acostheta,y=asintheta where theta is the parameter.
Answer» ANSWER :`a^(2)`

Discussion

12110.	Consider the experiment in which a coin is tossed repeatedly until a head comes up. Describe the sample space.
Answer» ANSWER :not A' = A {1, 4, 6}

Discussion

12111.	The quadrilateral formed by the lines sqrt(3)x+y=0,sqrt(3)y+x=0, sqrt(3)x+y=1,sqrt(3)y+x=1 is
Answer» a rectagle a square a rhombus parallelogram Answer :C

Discussion

12112.	The origin is translated to the point A. The point (3,4) is changed to (6,8), then A =
Answer» (3,4) (-3,-4) (9,12) (-9,-12) ANSWER :B

Discussion

12113.	If tan^(-1)(x^(2)+3abs(x)-4)+cot^(-1)(4pi+sin^(-1)sin14)=pi/2, then the value of sin^(-1)sin2x is
Answer» `6-2pi` `2pi-6` `pi-3` `3-pi` ANSWER :A::B

Discussion

12114.	Find the coordinates of the point which is three-fifths of the way from (3, 4, 5) to (-2,-1,0).
Answer» ANSWER :`(0,1,2)`

Discussion

12115.	Calculate the standard deviation from the following following set of observations: 8, 9, 15, 23, 5, 11, 19, 8, 10, 12
Answer» ANSWER :5.23

Discussion

12116.	Provethat cos2x=cos^2x-sin^2x.
Answer» ANSWER :`= cos^2 X - sin^2 x`.

Discussion

12117.	Let A= (1, 2, 3, 4, 6). Let R be the relation on A defined by {(a,b) a, b in A,b is exactly divisible by a] (i) Write R in roster form (ii) Find the domain of R (iii) Find the range of R.
Answer» Answer :(i) R={(1,1),(1,2),(1,3),(1,4),(1,6),(2,4),(2,6),(2,2),(4,4),(6,6),(3,3),(3,6)} (II) Domain of R={1,2,3,4,6} (III) RANGE of R={1,2,3,4,6}

Discussion

12118.	A wheel markes 360 revolutions in one minute. Through how many radians does it turn in one second ?
Answer» ANSWER :`12pi`

Discussion

12119.	tan["cos"^(-1)4/5+"tan"^(-1)2/3]=
Answer» `17/6` `7/16` `16/7` `6/17` ANSWER :A

Discussion

12120.	Determine 2nd term and 5'th term of an A.P. whose 6th term is 12 and 8th term is 22
Answer» ANSWER :`-8 , 5R 18

Discussion

12121.	Two students Anil and Ashima appeared is an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability qualify the examination is 0.02. Find the probability that (a) Bothe Anil and Ashima will not qualify the examination. (b) Atleast one of them will qualify the examination and (c) Only one of them will qualify the examination.
Answer» ANSWER :` = 1/6`

Discussion

12122.	IF (n + 2)! = 2550n! find n.
Answer» ANSWER :49

Discussion

12123.	For what value of lambda is the function defined by f (x)f(x)={{:(lambda (x^(2)-2x),if x le0),(4x+1,if x gt0):}is continuous at x = 3
Answer» ANSWER :x=3

Discussion

12124.	Three letters are dictated to three person and an envolopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
Answer» ANSWER :`2/3`

Discussion

12125.	Find three numbers in G.P. : (i) Whose sum is 30 and whose product is 216 (ii) Whose sumis 38 and whose product is 1728.
Answer» ANSWER :(i) `5/(2+sqrt(3)),6,6(2+sqrt(3))` or `6/(2-sqrt(3)),6,6(2-sqrt(3))` (II) 8,12,18

Discussion

12126.	A series are 2n observations. The half of them is a and the reamaining half is -a . If their standard deviation is 2 then \|a\| =………
Answer» 2 `SQRT2` `1/N` `(sqrt2)/(n)` ANSWER :A

Discussion

12127.	Tickets are numbered from 1 to 100 . Theyare wellshuffled and a ticketis drawn at random . What is the probability that the drawn ticket has a number which is greater than 75 ?
Answer» ANSWER :`=(1)/(4)`

Discussion

12128.	Tickets are numbered from 1 to 100 . Theyare wellshuffled and a ticketis drawn at random . What is the probability that the drawn ticket has a number which is a square ?
Answer» ANSWER :`=(1)/(10)`.

Discussion

12129.	Tickets are numbered from 1 to 100 . Theyare wellshuffled and a ticketis drawn at random . What is the probability that the drawn ticket has an number which is a multiple of 7?
Answer» ANSWER :`=(7)/(50)`

Discussion

12130.	Tickets are numbered from 1 to 100 . Theyare wellshuffled and a ticketis drawn at random . What is the probability that the drawn ticket has a number 5 or multiple of 5 ?
Answer» ANSWER :`=(1)/(5)`

Discussion

12131.	sqrt2 "cosec"20^@sec20^@ =
Answer» 2 `2sin20^@ "COSEC"40^@` 4 `4sin45^@ "cosec"40^@` ANSWER :D

Discussion

12132.	Four cards are drawn from a full pack of cards . Find the probability thatat least oneof the four cards is an ace.
Answer» ANSWER :`=(47659)/(54145)`.

Discussion

12133.	cos 20 thetain terms ofsin 5 theta .
Answer» Answer :`1 - 8 sin ^(2) 5 THETA + 8 sin ^(4) 5 theta `

Discussion

12134.	Evaluate the following limits : Lt_(xto0)(1+x)^(3)
Answer» ANSWER :1

Discussion

12135.	If 1, omega, omega^(2) are three cube roots of unity, show that (a + omega b+ omega^(2)c) (a + omega^(2)b+ omega c)= a^(2) + b^(2) + c^(2)- ab- bc - ca
Answer» Answer :`a^(2) + B^(2) + C^(2)- ab- bc - AC`

Discussion

12136.	How many 3-digit even numbers can be made using the digits 1,2,3,4, 6, 7, if no digit is repeated?
Answer» ANSWER :60

Discussion

12137.	Line l : 2x - 3y + 8= 0 intersect parabola y^(2) = 8x in point P and Q then, coordinates if midpoint of bar(PQ) …..
Answer» (5,6) (2, -3) (-3, 5) (-5, -6) Answer :C

Discussion

12138.	Numbers of proper subsets of the set having n elements are 2^(n+1) -2,(n gt 1 in N)
Answer» ANSWER :FALSE STATEMENT

Discussion

12139.	If tan(A+B) = m and tan (A - B) = n , find tan 2A and tan 2B in terms of m and n (mn != 1)
Answer» ANSWER :`(m+n)/(1-mn),(m-n)/(1+mn)`

Discussion

12140.	Find Lt_(x to a) ((x sin a - a sin x)/(x -a))
Answer» ANSWER :`sina-acosa`

Discussion

12141.	If a polynomial functions f(x)satisfies f(f(f(x))) = 8x + 21 , where p and q are real numbers , then p+q is equal to ………………….
Answer» ANSWER :5

Discussion

12142.	Evaluate Lt_(x to0)(sqrt(1+x)-1)/(x)
Answer» ANSWER :`1/2`

Discussion

12143.	If r. a = r.b = r.c = 0 where a,b,c are noncoplannar, then
Answer» `VEC(R )= vec(a)` `vec(r )=vec(b)` `vec(r )= vec(0)` `vec(r )= vec(C )` ANSWER :C

Discussion

12144.	If each side of length 'a' of an equilateral triangle substends an angle of 60^(@) at the top of a tower h metrs heigh situated at the centre of the triangle then
Answer» `3A^(2)=2h^(2)` `2a^(2)=3H^(2)` `a^(2)=3h^(2)` `3a^(2)=h^(2)` ANSWER :B

Discussion

12145.	If 2 cot ""( B)/(2) = cot ""(A) /( 2) + cot "" ( C )/(2)then a,b,c are in
Answer» <P>` A.G. P ` ` G.P ` ` A.P ` ` H. P ` ANSWER :C

Discussion

12146.	If angle thetabetween the line (x+1)/(1) = (y-1)/(2) = (z-2)/(2) and the plane 2x - y + sqrt lamda z + 4 =0 is such that sin theta = 1/3, the value of lamdais
Answer» `5/3` `(-3)/(5)` `3/4` `(-4)/(3)` ANSWER :A

Discussion

12147.	If the slope of one of the line given by 6x^2+2hxy+72y^2=0 " is four times the other, value of " h^2-4045 is
Answer» 0 5 10 15 Answer :B

Discussion

12148.	Find the degree measures corresponding to the following radian measures. (Use pi=(22)/(7)) -4
Answer» ANSWER :` (i) 39^(@) 22' 30''` (ii) `-229^(@)5'27''` (III)` 3000 ^(@)` (IV) `210^(@)`

Discussion

12149.	A function f is defined by f(x)= {{:((sin (a + 1) x + sinx)/(x)" if " x lt 0),(c "if " x = 0),(((x + bx^(2))^(1/2)- x^(1/2))/(bx^(3/2)) " if" x gt 0 ):} It f(x) is continuous at x = 0 , find the values of a,b and c .
Answer» `a = (-3)/(2) , c = (1)/(2) , b NE 0 ` ` a = b = (1)/(2) , c = 0 ` ` a = b = c = (1)/(2)` `a = (1)/(2) BNE 0 c = 1 ` ANSWER :A

Discussion

12150.	Evaluate underset(k=1)overset(11)Sigma (2 + 3^(k))
Answer» Answer :`22 + (3)/(2) (3^(11)-1)`

Discussion

Explore topic-wise InterviewSolutions in .

Show that the coefficient of the middle term in the expansion of (1+x)^2n is equal to the sum of the coefficients of two middle terms in the expansion of (1 + x)^2n-1

Evaluate : lim_(xto0) (1+ax)^(1//x)

What is the value of C_0+C_2+C_4+....?

The sum of n terms of two arithmetic progressions are in the ratio (3n + 8) : (7n + 15). Find the ratio of their 12^("th")terms.

If A(3, 0) and B(-3, 0) are two points and PA+PB=10, then the locus of P where P is any point (x, y) is

If x=sin^(-1)(a^(6)+1)+cos^(-1)(a^(4)+1)-tan^(-1)(a^(2)+1), a in R, then the value of sec^(2)x is

If y= (x^2 +3)/( x^3 + 2x), find (dy)/( dx) at x=1.

If sin theta, 1, cos 2 theta are in G.P., then general values of theta

Find the Cartesian equation of the locus whose parametric equations are x=acostheta,y=asintheta where theta is the parameter.

Consider the experiment in which a coin is tossed repeatedly until a head comes up. Describe the sample space.

The quadrilateral formed by the lines sqrt(3)x+y=0,sqrt(3)y+x=0, sqrt(3)x+y=1,sqrt(3)y+x=1 is

The origin is translated to the point A. The point (3,4) is changed to (6,8), then A =

If tan^(-1)(x^(2)+3abs(x)-4)+cot^(-1)(4pi+sin^(-1)sin14)=pi/2, then the value of sin^(-1)sin2x is

Find the coordinates of the point which is three-fifths of the way from (3, 4, 5) to (-2,-1,0).

Calculate the standard deviation from the following following set of observations: 8, 9, 15, 23, 5, 11, 19, 8, 10, 12

Provethat cos2x=cos^2x-sin^2x.

Let A= (1, 2, 3, 4, 6). Let R be the relation on A defined by {(a,b) a, b in A,b is exactly divisible by a] (i) Write R in roster form (ii) Find the domain of R (iii) Find the range of R.

A wheel markes 360 revolutions in one minute. Through how many radians does it turn in one second ?

tan["cos"^(-1)4/5+"tan"^(-1)2/3]=

Determine 2nd term and 5'th term of an A.P. whose 6th term is 12 and 8th term is 22

IF (n + 2)! = 2550n! find n.

For what value of lambda is the function defined by f (x)f(x)={{:(lambda (x^(2)-2x),if x le0),(4x+1,if x gt0):}is continuous at x = 3

Three letters are dictated to three person and an envolopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

Find three numbers in G.P. : (i) Whose sum is 30 and whose product is 216 (ii) Whose sumis 38 and whose product is 1728.

A series are 2n observations. The half of them is a and the reamaining half is -a . If their standard deviation is 2 then |a| =………

Tickets are numbered from 1 to 100 . Theyare wellshuffled and a ticketis drawn at random . What is the probability that the drawn ticket has a number which is greater than 75 ?

Tickets are numbered from 1 to 100 . Theyare wellshuffled and a ticketis drawn at random . What is the probability that the drawn ticket has a number which is a square ?

Tickets are numbered from 1 to 100 . Theyare wellshuffled and a ticketis drawn at random . What is the probability that the drawn ticket has an number which is a multiple of 7?

Tickets are numbered from 1 to 100 . Theyare wellshuffled and a ticketis drawn at random . What is the probability that the drawn ticket has a number 5 or multiple of 5 ?

sqrt2 "cosec"20^@sec20^@ =

Four cards are drawn from a full pack of cards . Find the probability thatat least oneof the four cards is an ace.

cos 20 thetain terms ofsin 5 theta .

Evaluate the following limits : Lt_(xto0)(1+x)^(3)

If 1, omega, omega^(2) are three cube roots of unity, show that (a + omega b+ omega^(2)c) (a + omega^(2)b+ omega c)= a^(2) + b^(2) + c^(2)- ab- bc - ca

How many 3-digit even numbers can be made using the digits﻿ 1,2,3,4, 6, 7, if no digit is repeated?﻿

Line l : 2x - 3y + 8= 0 intersect parabola y^(2) = 8x in point P and Q then, coordinates if midpoint of bar(PQ) …..

Numbers of proper subsets of the set having n elements are 2^(n+1) -2,(n gt 1 in N)

If tan(A+B) = m and tan (A - B) = n , find tan 2A and tan 2B in terms of m and n (mn != 1)

Find Lt_(x to a) ((x sin a - a sin x)/(x -a))

If a polynomial functions f(x)satisfies f(f(f(x))) = 8x + 21 , where p and q are real numbers , then p+q is equal to ………………….

Evaluate Lt_(x to0)(sqrt(1+x)-1)/(x)

If r. a = r.b = r.c = 0 where a,b,c are noncoplannar, then

If each side of length 'a' of an equilateral triangle substends an angle of 60^(@) at the top of a tower h metrs heigh situated at the centre of the triangle then

If 2 cot ""( B)/(2) = cot ""(A) /( 2) + cot "" ( C )/(2)then a,b,c are in

If angle thetabetween the line (x+1)/(1) = (y-1)/(2) = (z-2)/(2) and the plane 2x - y + sqrt lamda z + 4 =0 is such that sin theta = 1/3, the value of lamdais

If the slope of one of the line given by 6x^2+2hxy+72y^2=0 " is four times the other, value of " h^2-4045 is

Find the degree measures corresponding to the following radian measures. (Use pi=(22)/(7)) -4

A function f is defined by f(x)= {{:((sin (a + 1) x + sinx)/(x)" if " x lt 0),(c "if " x = 0),(((x + bx^(2))^(1/2)- x^(1/2))/(bx^(3/2)) " if" x gt 0 ):} It f(x) is continuous at x = 0 , find the values of a,b and c .

Evaluate underset(k=1)overset(11)Sigma (2 + 3^(k))

How many 3-digit even numbers can be made using the digits 1,2,3,4, 6, 7, if no digit is repeated?