14949 + Interview Questions in Maths in Class 11 Page 145 InterviewSolution

7201.	Differentiate the following w.r.t. x : sin (tan^(-1) e^(-x))
Answer» ANSWER :`(e ^(-X) cos (tan ^(-1) e ^(-x)))/( 1 + e ^(-2x))`

Discussion

7202.	Find the equation of line parallel to the Y- axis and drawn through the point of intersection of x-7+5 = 0 and 3x+ y -7=0.
Answer» ANSWER :`x-2 = 0`

Discussion

7203.	The sum of first three terms of a G.P. is (39)/(10)and their product is 1. Find the common ratio and the terms.
Answer» ANSWER :`(2)/(5) , 1,(5)/(2) "or " (5)/(2) , 1, (2)/(5)`

Discussion

7204.	The side BC of an equilateral angleABC is parallel to the x-axis. What are the slope of its sides?
Answer» ANSWER : `0, -SQRT(3), sqrt(3)`

Discussion

7205.	Using the substitution 2x + 1 = t^(2), show that int(6x)/(sqrt(2x + 1)) dx = 2(x - 1)sqrt(2x + 1 + c).
Answer» Answer :`2(X - 1)sqrt(2X + 1) + c`

Discussion

7206.	For all n in N , 3.5^(2n+1) + 2^(3n+1) is divisible by
Answer» 19 17 23 25 Answer :B::C

Discussion

7207.	Evaluate the following limits : Lim_( x to 0) (e^(ax)-e^(bx))/x
Answer» ANSWER :`-1/e`

Discussion

7208.	The straight line 2x+3y-1=0,3x+4y-6=0 and ax+by+1=0 are concurrent if the straight line 14x+9y+1=0 passes through the point
Answer» `(a,-B)` `(a,b)` `(-a,-b)` `(-a,b)` ANSWER :A

Discussion

7209.	d/(dx) [(e^(sinsqrt(x)) + e^(-sin sqrt(x)))/(e^(sin sqrt(x)) - e^(-sinsqrt(x)))] =
Answer» `(-2/(SQRT(x)) cos sqrt(x))/((e^(SIN sqrt(x)) - e^(-sin sqrt(x)))^2)` `(-2/(sqrt(x)) cos sqrt(x))/(e^(sin sqrt(x)))` `(-2 cossqrt(x))/(e^(sin sqrt(x)))` `(2 cossqrt(x))/(e^(sin sqrt(x)))` Answer :A

Discussion

7210.	Find value of sin 765^@
Answer» ANSWER :`(1)/(SQRT2)`

Discussion

7211.	There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?
Answer» ANSWER :`=(6)/(10)=(3)/(5)`

Discussion

7212.	If twice the square of the radius ofa circum circle to half the sum of the squares of the sides of inscribed triangle ABC, then sin^(2)A + sin^(2)B + sin^(2)C =
Answer» 1 2 4 8 Answer :A

Discussion

7213.	From the sets given below, select equal sets. A= {x : x in N, x lt 3} B= {1, 2} C= {3, 1} D= {x : x in N, x" is odd number " x lt 5} E= {2, 1} F= {1, 3}.
Answer» ANSWER :`A= B= E, C= D= F`

Discussion

7214.	The mean and standard deviation of 100 observation were calculated as 40 and 5.1, respectively by a student who took by mistake 50 instead of 40 for one observation . What are the correct mean standard deviation?
Answer» ANSWER :5

Discussion

7215.	The second term of a G.P. is 18 and the fifth term is 486. Find: (i) the first term, (ii) the common ratio
Answer» ANSWER :FIRST term=6 COMMON RATIO =3

Discussion

7216.	If cos h x = (5)/(2) then cos h(2x) =
Answer» `(5sqrt(21))/(2)` `(23)/(5sqrt(21))` `(23)/(2)` `(7)/(2)` ANSWER :C

Discussion

7217.	x^(2) + x/sqrt(2)+1=0
Answer» ANSWER :`(-1+-sqrt(7)i)/(2sqrt(2))`

Discussion

7218.	If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Answer» ANSWER :5,8,11

Discussion

7219.	"Cosh"3theta=99 if cosh theta=
Answer» 3 9 11 27 Answer :A

Discussion

7220.	Find the sum to n terms of the series in whose n^(th)terms is given by n(n+1)(n+4)
Answer» ANSWER :`(N(n+1))/(2) [(3n^(2) + 23n+ 34)/(6)]`

Discussion

7221.	If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements, how many elements does X ∩ Y have ?
Answer» ANSWER :`= 10`

Discussion

7222.	Let O be a point inside Delta ABCsuch that angle OAB = angle OBC = angle OCA = theta cosec^(2) A + cosec^(2)B + cosec^(2)C is equal to
Answer» `cot^(2) THETA` `COSEC^(2)theta ` `TAN^(2) theta` `sec^(2) theta ` ANSWER :B

Discussion

7223.	If A and B are two sets, then (AuuB')'nn(A'uuB)' is(i) null set(ii) universal set(iii) A'(iv) B'
Answer» NULL SET universal set `A'` `B'` ANSWER :A

Discussion

7224.	Are the following pairs of statements negations of each other: The number x is a rational number. The number x is an irrational number.
Answer» Answer :The NEGATION of the first statement is ''X is an irrational NUMBER'' which is the same as the second statement. Therefore, the pairs are NEGATIONS of each other.

Discussion

7225.	Which of the following is not a negation of A natural number is greater than zero.
Answer» A NATURAL NUMBER is not GREATER than zero It is false that a natural number is greater than zero. It is false that a natural number is not greater than zero None of the above Answer :C

Discussion

7226.	If 3i^(3)-2ai^(2)+(1-a)i+5 is real then find the value of a.
Answer» ANSWER :`-2`

Discussion

7227.	((1+Tan33^(@))(1+Tan12^(@)))/((1+Tan18^(@))(1+Tan27^(@)))=
Answer» 1 2 3 `SQRT(3)` ANSWER :A

Discussion

7228.	By multiplying each term by non zero constant we get geometric sequence .
Answer» ANSWER :FALSE STATEMENT

Discussion

7229.	Sin 40^(@) 25^(1) 19^(@)35^(1) + Cos40^(@) 25^(1).Sin19^(@) 35^(1)=
Answer» 1 `(SQRT(3))/(2)` 0 -1 Answer :B

Discussion

7230.	AA n in N, 5^(2n+2) - 24n - 25 is divisible by
Answer» 576 25 24 50 Answer :A

Discussion

7231.	If the dirction cosines of a line are ((1)/(2) ,0,n) and n lt 0, then find n.
Answer» ANSWER :`(-SQRT(3))/(2)`

Discussion

7232.	cos (pi/7) cos ((2pi)/(7) ) cos ( (4pi )/(7) ) =
Answer» `1//8` `-1//8` `1//4` `-1//4` ANSWER :B

Discussion

7233.	Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (B – C)′
Answer» ANSWER :`{ 1, 3, 4, 5, 6, 7, 9 }`

Discussion

7234.	The mid point of the sides of a triangle are (2,3,4),(1,5,-1) and (0,4,-2). Find the coordinates of the centroidof the triangle.
Answer» ANSWER :`(1,4,(1)/(3))`

Discussion

7235.	"If "\|a\|lt1,\|b\|lt1, then find the sum to infinity of the following series : (i) (a+b )+(a^(2)+ab+b^(2))+(a^(3)+a^(2)b+ab^(2)+b^(3))+...oo (ii) 1+(1+a)b+(1+a+a^(2))cdotb^(2)+...oo
Answer» SOLUTION :N/a

Discussion

7236.	For 0lt, y lt pi , the number of ordered pairs (x,y) satisfying the system of equations cot^(2)(x'-y)-(1+sqrt(3))cot(x-y)=sqrt(3)=0 and cosy=(sqrt(3))/2 is
Answer» 0 1 2 3 Answer :C

Discussion

7237.	Write downthe slope of the lineperpendicular to the line joining B(2, -3) and S(-4, 1).
Answer» ANSWER : `3/(2)`

Discussion

7238.	0 le a le 3, 0 le b le 3and the equation x^(2) + 4+ 3 cos ( a x + b) = 2 xhas atleast one solution then the value of a + b
Answer» `PI//2` `pi//4` `pi//3` `pi` ANSWER :D

Discussion

7239.	If sin^(-1)(a//x)+sin^(-1)(b//x)=pi//2 then x=
Answer» `AB` `SQRT(ab)` `sqrt(a^(2)+b^(2))` `a^(2)+b^(2)` Answer :C

Discussion

7240.	Find the Cartesian equation of the plane passing through the point (-2,1,3) and perpendicular to the vector 3bar(i) + bar(j) + 5bar(k).
Answer» ANSWER :`3x+y=5z=10`

Discussion

7241.	Express sin3A and cos2A in terms of sine function
Answer» SOLUTION :sinA=3sinA-`4sin^3A` ,`cos2A=1-2sin^2A`

Discussion

7242.	Compute the following limits. Lt_(xtooo)(2x+3)/(5x-1)
Answer» ANSWER :2/5

Discussion

7243.	The sum up to n terms of the series (1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))+(1)/(sqrt(5)+sqrt(7))+……. is …………….
Answer» `SQRT(2n+1)` `(sqrt(2n+1))/(2)` `sqrt(2n+1)-1` `(sqrt(2n+1)-1)/(2)` ANSWER :D

Discussion

7244.	Write the conjugate of (3+4i)^(2)
Answer» ANSWER :`-7-24i`

Discussion

7245.	Find the equation of a line drawn perpendicular to the line (x)/(4) + (y)/(6)=1 through the point, where it meets the Y-axis.
Answer» ANSWER :`2x-3y+18=0` is the EQUATION of a REQUIRED LINE.

Discussion

7246.	Reduce the equation of the line sqrt(3)x + y-8 = 0 into normal form. Find the values of p and omega.
Answer» <P> ANSWER :`p= 4 " and " OMEGA= 30^(@)`

Discussion

7247.	Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 0. . .A
Answer» ANSWER :`in`

Discussion

7248.	Let f: R to Rbe a function such that for somep gt 0, f(x+p)= (f(x)- 5)/( f(x) - 3)for allx in R. Then period of f is
Answer» 2p 4p 3p 5p Answer :B

Discussion

7249.	What are the points on the y-axis whose distance from the line (x)/(3)+(y)/(4)=1 is 4 units.
Answer» ANSWER :`(0, - 8/3), (0, 32/3)`

Discussion

7250.	Find the sum to n terms of each of the series in1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + ...
Answer» ANSWER :`(N(n+1)^2(n+2))/12`

Discussion

Explore topic-wise InterviewSolutions in .

Differentiate the following w.r.t. x : sin (tan^(-1) e^(-x))

Find the equation of line parallel to the Y- axis and drawn through the point of intersection of x-7+5 = 0 and 3x+ y -7=0.

The sum of first three terms of a G.P. is (39)/(10)and their product is 1. Find the common ratio and the terms.

The side BC of an equilateral angleABC is parallel to the x-axis. What are the slope of its sides?

Using the substitution 2x + 1 = t^(2), show that int(6x)/(sqrt(2x + 1)) dx = 2(x - 1)sqrt(2x + 1 + c).

For all n in N , 3.5^(2n+1) + 2^(3n+1) is divisible by

Evaluate the following limits : Lim_( x to 0) (e^(ax)-e^(bx))/x

The straight line 2x+3y-1=0,3x+4y-6=0 and ax+by+1=0 are concurrent if the straight line 14x+9y+1=0 passes through the point

d/(dx) [(e^(sinsqrt(x)) + e^(-sin sqrt(x)))/(e^(sin sqrt(x)) - e^(-sinsqrt(x)))] =

Find value of sin 765^@

There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?

If twice the square of the radius ofa circum circle to half the sum of the squares of the sides of inscribed triangle ABC, then sin^(2)A + sin^(2)B + sin^(2)C =

From the sets given below, select equal sets. A= {x : x in N, x lt 3} B= {1, 2} C= {3, 1} D= {x : x in N, x" is odd number " x lt 5} E= {2, 1} F= {1, 3}.

The mean and standard deviation of 100 observation were calculated as 40 and 5.1, respectively by a student who took by mistake 50 instead of 40 for one observation . What are the correct mean standard deviation?

The second term of a G.P. is 18 and the fifth term is 486. Find: (i) the first term, (ii) the common ratio

If cos h x = (5)/(2) then cos h(2x) =

x^(2) + x/sqrt(2)+1=0

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

"Cosh"3theta=99 if cosh theta=

Find the sum to n terms of the series in whose n^(th)terms is given by n(n+1)(n+4)

If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements, how many elements does X ∩ Y have ?

Let O be a point inside Delta ABCsuch that angle OAB = angle OBC = angle OCA = theta cosec^(2) A + cosec^(2)B + cosec^(2)C is equal to

If A and B are two sets, then (AuuB')'nn(A'uuB)' is(i) null set(ii) universal set(iii) A'(iv) B'

Are the following pairs of statements negations of each other: The number x is a rational number. The number x is an irrational number.

Which of the following is not a negation of A natural number is greater than zero.

If 3i^(3)-2ai^(2)+(1-a)i+5 is real then find the value of a.

((1+Tan33^(@))(1+Tan12^(@)))/((1+Tan18^(@))(1+Tan27^(@)))=

By multiplying each term by non zero constant we get geometric sequence .

Sin 40^(@) 25^(1) 19^(@)35^(1) + Cos40^(@) 25^(1).Sin19^(@) 35^(1)=

AA n in N, 5^(2n+2) - 24n - 25 is divisible by

If the dirction cosines of a line are ((1)/(2) ,0,n) and n lt 0, then find n.

cos (pi/7) cos ((2pi)/(7) ) cos ( (4pi )/(7) ) =

Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (B – C)′

The mid point of the sides of a triangle are (2,3,4),(1,5,-1) and (0,4,-2). Find the coordinates of the centroidof the triangle.

"If "|a|lt1,|b|lt1, then find the sum to infinity of the following series : (i) (a+b )+(a^(2)+ab+b^(2))+(a^(3)+a^(2)b+ab^(2)+b^(3))+...oo (ii) 1+(1+a)b+(1+a+a^(2))cdotb^(2)+...oo

For 0lt, y lt pi , the number of ordered pairs (x,y) satisfying the system of equations cot^(2)(x'-y)-(1+sqrt(3))cot(x-y)=sqrt(3)=0 and cosy=(sqrt(3))/2 is

Write downthe slope of the lineperpendicular to the line joining B(2, -3) and S(-4, 1).

0 le a le 3, 0 le b le 3and the equation x^(2) + 4+ 3 cos ( a x + b) = 2 xhas atleast one solution then the value of a + b

If sin^(-1)(a//x)+sin^(-1)(b//x)=pi//2 then x=

Find the Cartesian equation of the plane passing through the point (-2,1,3) and perpendicular to the vector 3bar(i) + bar(j) + 5bar(k).

Express sin3A and cos2A in terms of sine function

Compute the following limits. Lt_(xtooo)(2x+3)/(5x-1)

The sum up to n terms of the series (1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))+(1)/(sqrt(5)+sqrt(7))+……. is …………….

Write the conjugate of (3+4i)^(2)

Find the equation of a line drawn perpendicular to the line (x)/(4) + (y)/(6)=1 through the point, where it meets the Y-axis.

Reduce the equation of the line sqrt(3)x + y-8 = 0 into normal form.﻿ Find the values of p and omega.

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 0. . .A

Let f: R to Rbe a function such that for somep gt 0, f(x+p)= (f(x)- 5)/( f(x) - 3)for allx in R. Then period of f is

What are the points on the y-axis whose distance from the line﻿ (x)/(3)+(y)/(4)=1 is 4 units.

Find the sum to n terms of each of the series in1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + ...

Reduce the equation of the line sqrt(3)x + y-8 = 0 into normal form. Find the values of p and omega.

What are the points on the y-axis whose distance from the line (x)/(3)+(y)/(4)=1 is 4 units.