14949 + Interview Questions in Maths in Class 11 Page 144 InterviewSolution

7151.	Consider a pendulum of length 50 cms If the tip of the pendulum describes an arc of length 10 cms find the angle (in radian) through which the pendulum swings.
Answer» SOLUTION :(1/5) RADIANS

Discussion

7152.	If g(f(x))= \|sinx \| and f(g(x))=(sin sqrt(x))^(2), then
Answer» `F(X)=sin^(2)x, g(x)=sqrt(x)` `f(x)=sin x, g(x)=\|x\|` `f(x)=x^(2), g(x)= sin sqrt(x)` f and g cannot be determined Answer :A

Discussion

7153.	If A and B are acute angles satisfying 3sin^(2)A+2sin^(2)B=1 and 3 sin2A=2sin2B then cos(A+2B)=
Answer» 0 1 `1//2` `1/4` ANSWER :A

Discussion

7154.	Let f(theta) = sin theta (sin theta + sin 3 theta). "Then" f(theta) is
Answer» `GE 0` only when `theta ge 0` `LE 0` for all real `theta` `ge 0` for all real `theta` `le 0` only when `theta le 0` ANSWER :C

Discussion

7155.	Express (cos theta - sin theta) as a cosine of an angle.
Answer» Answer :`sqrt(2) COS (THETA + (PI)/(4))`

Discussion

7156.	The range of alpha for which the points (alpha, alpha+2) and ((3alpha)/2,alpha^(2)) lie on opposite sides of the line 2x+3y-6=0.
Answer» ANSWER :`(0,1)`

Discussion

7157.	Draw the graph of the solution set of the inequation 2x -y ge 1
Answer» Solution :Consider the equation `,2x -y=1` The values of (x,y) satisfiying 2x -y =1ARE : Take a graph paper and plot the points A(2,3) and B (0,-1) Then line AB represents2x-y=1 This line divides the plane of the paper in two equal parts. Clearly , the points (0,0) does not lie on 2x-y=1 Also (0,0) does not satisfy`2x -y ge 1 ` LTBR GT So, we shade that part of the plane divided by line AB which does not contain (0,0) as SHOWN below . The shaded part of the plane togther with all points on the line AB condtitutes the SOLUTIONS set of the inequation `2x-y le 1 `

Discussion

7158.	Prove that cos^(2)x + cos^(2)(x + (pi)/(3)) + cos^(2) (x - (pi)/(3)) = (3)/(2)
Answer» ANSWER :`3/2=R.H.S.`

Discussion

7159.	How many four- letters words can be formed using the letters of the word 'INEFFECTIVE'?
Answer» ANSWER :` 1422`

Discussion

7160.	Express the following in the form a+bi, where a and b are real numbers (1+i)/(1-i)
Answer» ANSWER :`0+1i`

Discussion

7161.	Find the locus of the piont (acos^(3)theta,bsin^(3)theta)where theta is the parameter.
Answer» ANSWER :`a^(2/3)`

Discussion

7162.	Express the following in the form a+ bi (1+i)^(-3)
Answer» ANSWER :`(-1)/(4)-(1)/(4)i`

Discussion

7163.	Arrange the following in ascending order of magnitude (A) Area of parallelogram with adjacent sides I + 2j + 3k, 3i2j + k (B) Area of parallelogram with diagonals I + 2j 3k, 3i - 2j + k (C ) Area of parallelogram with diagonals are 3i + j - 2k, i - 3j + 4k (D) Area of parallelogram whose sides are 3i + j - 2k, i - 3j + 4k
Answer» B,A,C,D D,A,C,B D,C,A,B B,C,A,D Answer :D

Discussion

7164.	If theta is the angle between the line (x+1)/(3) = (y-1)/(2) = (z-2)/(4) and the plane 2x + y - 3z +4=0 then (8)/(29)(cosec ^(2) theta) =
Answer» ANSWER :7

Discussion

7165.	f : R - {0} to R " given by " f(x) = (1)/(x) - (2)/(e^(2x)-1) can be made continuous at x = 0 by defining f(0) as
Answer» 1 2 -1 0 Answer :A

Discussion

7166.	Evaluate the following limits : Lim_(x to 0) (3 sin x^(@) - sin 3x^(@))/(x^(3))
Answer» Answer :` 4(pi/180)^(3)" " (x to 0 rArr (PIX)/(180) to 0 )`

Discussion

7167.	Write the additive inverse of the following -2+ 3i
Answer» ANSWER :`2-3i`

Discussion

7168.	Let PQR be a triangle of area Deltawitha = 2, b = 7//2 , " and " c = 5//2,where a, b, and c are the lengths of the sides of the triangle opposite to the angles at P, Q, and R, respectively. Then (2 sin P - sin 2P)/(2 sin P + sin 2P) equals
Answer» `3/(4Delta)` `(45)/(4 DELTA)` `(3/(4 Delta))^(2)` `(45/(4 Delta))^(2)` Answer :C

Discussion

7169.	Numberof integral values of b for which the equation (x^(3))/(3)-x=b has three distinct solution is ____
Answer» ANSWER :1

Discussion

7170.	If F(x)=x^(3)+bx^(2)+cx+dand0ltb^(2)ltc, then in (-oo,oo)
Answer» `f(x)` is a strictly INCREASING FUNCTION f(x)has a local maxima f(x) is strictly decreasing function f(x) is bounded Answer :C

Discussion

7171.	The line joining two points A(2,0), B(3,1) is rotated about A in anticlockwise direction through an angle 15^(@). If B goes to C then C=
Answer» `y = SQRT3 x-2` `y = sqrt3( x-2)` `y = sqrt3 (x+2)` `x-2 = sqrt3 y ` ANSWER :B

Discussion

7172.	How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
Answer» ANSWER :1440

Discussion

7173.	Three dice are thrown simultaneously. write the event that all the three dice show the same number as a set.
Answer» SOLUTION :{(1,1,1),(2,2,2),(6,6,6),(3,3,3),(4,4,4),(5,5,5),(6,6,6)}

Discussion

7174.	d/(dx)[cos^(-1)(xsqrtx-sqrt((1-x)(1-x^2)))] =
Answer» `1/(SQRT(1-x^2))-1/(2sqrt(x-x^2))` `(-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2))` `1/(sqrt(1-x^2))+1/(2sqrt(x-x^2))` `1/(sqrt(1-x^2))` ANSWER :B

Discussion

7175.	Complete the table using calculator and use the result to estimate the limit. lim_(xrarr0)(sinx)/x
Answer» ANSWER :1

Discussion

7176.	The values 'a' for which the function f(x)=(a+2)x^(3)=3ax^(2)+9ax-1 decreases for all real values of x, is
Answer» `alt-2` `agt-2` `alt-3` `-3ltalt-2` ANSWER :C

Discussion

7177.	Four cards are drawn from a full pack of cards . Find the probability thatall the four are spades , and one of them is a king , and
Answer» ANSWER :`=(44)/(54145)`.

Discussion

7178.	Evaluate the following limits : Lt_(xto0)(2^(x)-3^(x))/x
Answer» ANSWER :`LOG(2//3)`

Discussion

7179.	Ortho centreand centroid of any trinangle are A(-3,5) and (3,3) respectively. If C is cirsum centre of this triangle then radius of the circle whose diameter bar(AC) is ………
Answer» `SQRT(10)` `2sqrt(10)` `3sqrt((5)/(2)` `(3sqrt(5))/(2)` ANSWER :C

Discussion

7180.	If =\|(2a,x_(1),y_(1)),(2b,x_(2),y_(2)),(2c,x_(3),y_(3))\|=abc/2 ne 0then the area area of the triangle whose vertices are (x_(1)/a,y_(1)/a),(x_(2)/b,y_(2)/b),(x_(3)/c,y_(3)/c)is:
Answer» `(1)/(4)` `(1)/(4)` ABC `(1)/(8)` `(1)/(8)`abc Answer :A

Discussion

7181.	.......... is the foot of perpendicular from point (-2,3) to the line 2x-y-3=0.
Answer» `(-2,3)` `(2,1)` `(3,2)` `(1,2)` ANSWER :B

Discussion

7182.	A (-2, 2, 3) and (13, -3, 13) and L is a line through A Equation of a line L, pependicular to the line AB is
Answer» `(x+2)/(15)=(y-2)/(-5)=(z-3)/(10)` `(x-2)/(3)=(y+2)/(13)=(z+3)/(2)` `(x+2)/(3)=(y-2)/(13)=(z-3)/(2)` `(x-2)/(15)=(y+2)/(-5)=(z+3)/(10)` ANSWER :c

Discussion

7183.	Evaluate the following limits : Lim_(x to 0) (1- cos x)/(x^(2))
Answer» ANSWER :COS X

Discussion

7184.	Ifp_1 , p_2 , p_3are the altitudes drawn from the vertices A,B, C of triangles respectivelyshow that(1)/( p_1) +(1)/(p_2)-(1)/( p_3)= ( 2ab cos ^(2)C//2) / ( Delta (a+b+ c) )
Answer» ` (1)/( r_3) ` ` r_1+r_2` ` r_3` ` ( 1)/ (r_1 ) ` ANSWER :A

Discussion

7185.	Write each of the following statements in the form ''if-then'' The Bannana trees will bloom if it stays warm for a month.
Answer» Answer :If the BANANA tree stays WARM for a month, then it will BLOOM.

Discussion

7186.	Evaluate : lim_(xrarrinfty)[(3+x)^5 -3^5]/x
Answer» ANSWER :405

Discussion

7187.	Differentiate the following functions: 12. 8x^(3) - x^(2) + 5 - (2)/( x ) + (4)/( x^3).
Answer» ANSWER :`24X^(2) - 2X + (2)/(x^2) - (12)/( x^4)`

Discussion

7188.	Write the middle term or terms in the expansion of (3a - (a^3)/(6) )^9
Answer» ANSWER :`=- (21)/(16) a^(19)`.

Discussion

7189.	If a,bgt0 then the minimum value of y=(b^(2))/(a-x)+(a^(2))/(x),0ltxlta is
Answer» '((a+B)^(2))/(a)' 4b 2a 2b Answer :B

Discussion

7190.	If Delta =a^2-(b-c)^2, is the area of the triangle ABC, then tan A=
Answer» `(1)/(16)` `(8)/(15)` `(3)/(4)` `(4)/(3)` ANSWER :B

Discussion

7191.	Area of the largest rectangle that can be inscribed in the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1is
Answer» 2ab AB `SQRT(ab)` `a//b` ANSWER :A

Discussion

7192.	Evaluate the following limits : Lt_(xto0)((1+5x^(2))/(1+3x^(2)))^(1/x^(2))
Answer» ANSWER :`E^(2)`

Discussion

7193.	Which of the following expresses the circumference of a circle inscribed in a sector. OAB with radius R and AB = 2a ?
Answer» `2PI(RA)/(R+a)` `(2piR^(3))/(a)` `2pi(R-a)^(2)` `2pi(R)/(R-a)` ANSWER :A

Discussion

7194.	(d)/(dx) [(x +1)(x^2+1)(x ^(4) + 1) (x ^(8) +1)]=(15 x ^(p) -16x^q+1) (x-1) ^(-2) implies (p,q)=
Answer» `(12,11)` `(15,14)` `(16,14)` `(16,15)` ANSWER :D

Discussion

7195.	If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) are direction cosines of two lines which inculude an angle 120^(@), then the direction cosines of the line which bisects the angle between them is
Answer» `(l_(1)+l_(2)),(m_(1)+m_(2)),(n_(1)+n_(2))` ` ((l_(1)-l_(2))/(sqrt(3)),(m_(1)-m_(2))/(sqrt(3)),(n_(1)-n_(2))/(sqrt(3)))` ` ((l_(1)-l_(2))/(2),(m_(1)-m_(2))/(2),(n_(1)-n_(2))/(2))` ` ((l_(1)-l_(2))/(sqrt(2)),(m_(1)-m_(2))/(sqrt(2)),(n_(1)-n_(2))/(SQRT2))` Answer :B

Discussion

7196.	IF Delta ABC,if a tan A+b tan B=(a+b) tan ((A+B)/2), then the triangle is
Answer» Right-angled scalene isosceles Equailateral Answer :C

Discussion

7197.	Co-efficient of variance of one data is 45% and mean is 12 then S.D. is 5.4
Answer» ANSWER :TRUE STATEMENT

Discussion

7198.	A manufacturer uses 4 raw materials A, B, C, D in the production of a certain commodity. Masses of raw materials used in manufacturing are in the ratio 2 : 3 : 4: 1. The prices, in Rs, of the materials per kilogram in the years 1978, 1980 are given in the following table: Calculate the index number for the total cost of the raw materials used for the manufacture of the commodity in, 1980, using 1978 as the base year. If the commodity is sold for Rs.5.75 in 1978, calculate the selling price in 1980, on the assumption that selling prices are directly proportional to the cost of raw material.
Answer» ANSWER :`114.9` RS. `6.61`

Discussion

7199.	Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2),(3,3) , (1,2), (2,3)} is reflexive but neither symmetric nor transitive.
Answer» ANSWER :but `(1,3) cancelinR rArr R ` is not transitive . R is REFLEXIVE but NEITHER symmetric nor transitive .

Discussion

7200.	Find the maximum or minimum values of the following functions. x^(3) - 6x^(2) + 9x + 1
Answer» Answer :At X = 1, maximum VALUE = 5; at x = 3 MINIMUM value = 1

Discussion

Explore topic-wise InterviewSolutions in .

Consider a pendulum of length 50 cms If the tip of the pendulum describes an arc of length 10 cms find the angle (in radian) through which the pendulum swings.

If g(f(x))= |sinx | and f(g(x))=(sin sqrt(x))^(2), then

If A and B are acute angles satisfying 3sin^(2)A+2sin^(2)B=1 and 3 sin2A=2sin2B then cos(A+2B)=

Let f(theta) = sin theta (sin theta + sin 3 theta). "Then" f(theta) is

Express (cos theta - sin theta) as a cosine of an angle.

The range of alpha for which the points (alpha, alpha+2) and ((3alpha)/2,alpha^(2)) lie on opposite sides of the line 2x+3y-6=0.

Draw the graph of the solution set of the inequation 2x -y ge 1

Prove that cos^(2)x + cos^(2)(x + (pi)/(3)) + cos^(2) (x - (pi)/(3)) = (3)/(2)

How many four- letters words can be formed using the letters of the word 'INEFFECTIVE'?

Express the following in the form a+bi, where a and b are real numbers (1+i)/(1-i)

Find the locus of the piont (acos^(3)theta,bsin^(3)theta)where theta is the parameter.

Express the following in the form a+ bi (1+i)^(-3)

If theta is the angle between the line (x+1)/(3) = (y-1)/(2) = (z-2)/(4) and the plane 2x + y - 3z +4=0 then (8)/(29)(cosec ^(2) theta) =

f : R - {0} to R " given by " f(x) = (1)/(x) - (2)/(e^(2x)-1) can be made continuous at x = 0 by defining f(0) as

Evaluate the following limits : Lim_(x to 0) (3 sin x^(@) - sin 3x^(@))/(x^(3))

Write the additive inverse of the following -2+ 3i

Let PQR be a triangle of area Deltawitha = 2, b = 7//2 , " and " c = 5//2,where a, b, and c are the lengths of the sides of the triangle opposite to the angles at P, Q, and R, respectively. Then (2 sin P - sin 2P)/(2 sin P + sin 2P) equals

Numberof integral values of b for which the equation (x^(3))/(3)-x=b has three distinct solution is ____

If F(x)=x^(3)+bx^(2)+cx+dand0ltb^(2)ltc, then in (-oo,oo)

The line joining two points A(2,0), B(3,1) is rotated about A in anticlockwise direction through an angle 15^(@). If B goes to C then C=

How many words, with or without meaning, can be formed using all the letters of﻿ the word EQUATION at a time so that the vowels and consonants occur together?﻿

Three dice are thrown simultaneously. write the event that all the three dice show the same number as a set.

d/(dx)[cos^(-1)(xsqrtx-sqrt((1-x)(1-x^2)))] =

Complete the table using calculator and use the result to estimate the limit. lim_(xrarr0)(sinx)/x

The values 'a' for which the function f(x)=(a+2)x^(3)=3ax^(2)+9ax-1 decreases for all real values of x, is

Four cards are drawn from a full pack of cards . Find the probability thatall the four are spades , and one of them is a king , and

Evaluate the following limits : Lt_(xto0)(2^(x)-3^(x))/x

Ortho centreand centroid of any trinangle are A(-3,5) and (3,3) respectively. If C is cirsum centre of this triangle then radius of the circle whose diameter bar(AC) is ………

If =|(2a,x_(1),y_(1)),(2b,x_(2),y_(2)),(2c,x_(3),y_(3))|=abc/2 ne 0then the area area of the triangle whose vertices are (x_(1)/a,y_(1)/a),(x_(2)/b,y_(2)/b),(x_(3)/c,y_(3)/c)is:

.......... is the foot of perpendicular from point (-2,3) to the line 2x-y-3=0.

A (-2, 2, 3) and (13, -3, 13) and L is a line through A Equation of a line L, pependicular to the line AB is

Evaluate the following limits : Lim_(x to 0) (1- cos x)/(x^(2))

Ifp_1 , p_2 , p_3are the altitudes drawn from the vertices A,B, C of triangles respectivelyshow that(1)/( p_1) +(1)/(p_2)-(1)/( p_3)= ( 2ab cos ^(2)C//2) / ( Delta (a+b+ c) )

Write each of the following statements in the form ''if-then'' The Bannana trees will bloom if it stays warm for a month.

Evaluate : lim_(xrarrinfty)[(3+x)^5 -3^5]/x

Differentiate the following functions: 12. 8x^(3) - x^(2) + 5 - (2)/( x ) + (4)/( x^3).

Write the middle term or terms in the expansion of (3a - (a^3)/(6) )^9

If a,bgt0 then the minimum value of y=(b^(2))/(a-x)+(a^(2))/(x),0ltxlta is

If Delta =a^2-(b-c)^2, is the area of the triangle ABC, then tan A=

Area of the largest rectangle that can be inscribed in the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1is

Evaluate the following limits : Lt_(xto0)((1+5x^(2))/(1+3x^(2)))^(1/x^(2))

Which of the following expresses the circumference of a circle inscribed in a sector. OAB with radius R and AB = 2a ?

(d)/(dx) [(x +1)(x^2+1)(x ^(4) + 1) (x ^(8) +1)]=(15 x ^(p) -16x^q+1) (x-1) ^(-2) implies (p,q)=

If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) are direction cosines of two lines which inculude an angle 120^(@), then the direction cosines of the line which bisects the angle between them is

IF Delta ABC,if a tan A+b tan B=(a+b) tan ((A+B)/2), then the triangle is

Co-efficient of variance of one data is 45% and mean is 12 then S.D. is 5.4

Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2),(3,3) , (1,2), (2,3)} is reflexive but neither symmetric nor transitive.

Find the maximum or minimum values of the following functions. x^(3) - 6x^(2) + 9x + 1

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?