14949 + Interview Questions in Maths in Class 11 Page 298 InterviewSolution

14851.	Let x be the length of one of the equal sides of an isosceles triangle, and let theta be the angle between them. If x is increasing at the rate (1/12) m/h/ and theta is increasing at the rate of pi//180 radians/h then the rate in m^(2)//h at which the area of the triangle whe x = 12m and theta = pi //4
Answer» `SQRT(3)((PI)/(5)+(1)/(2))` `sqrt(2)((pi)/(5)+(1)/(2))` `((pi)/(5)+(1)/(2))` `sqrt(2)((pi)/(5)+(1)/(5))` Answer :B

Discussion

14852.	Distance between to parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0is
Answer» `(3)/(2)` `(5)/(2)` `(7)/(2)` `(9)/(2)` Answer :C

Discussion

14853.	Write the negation of each of the following statements. Some students failed to qualify the entrance test.
Answer» Answer :No STUDENTS FAILED to QUALIFY the entrance TEST.

Discussion

14854.	AB is a variable lines sliding between the coordinate axes in such a way that A lies on x-axis and B lies on y-axis. The P is a variable point on AB such that PA=b, PB=a and AB=a+b, then the equation of the locus of P is
Answer» `X^(2)/a^(2)+y^2/b^2=1` `x^(2)/a^(2)-y^2/b^2=1` `x^2+y^2` `a^2+b^2` ANSWER :A

Discussion

14855.	Assertion (A) : tan 70^(@) - tan 20^(@) = 2 cot 40^(@) Reason (R ) : If A + B = 90^(@)then tan A. tan B = 1
Answer» A is true R is TURE and R is corect explanation of A A is true, R is true and R is not correct explanation of A A is true ,R is FALSE A is false, R is true Answer :A

Discussion

14856.	If 3x^(2)-11xy+10y^(2)-7x+13y+k=0denotes a pair of straight lines, then the point of intersection of the lines is
Answer» (1,3) (3,1) (-3,1) (1,-3) ANSWER :B

Discussion

14857.	Let A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}. Find A ∪ B.
Answer» Answer :`= {2, 4, 6, 8, 10, 12}`

Discussion

14858.	I : If180^(@) lt theta lt 270^@ , sin theta = -3//5 " then " cos theta //2 -=1//10. II : If630^(@) lt theta lt 720^(@) , \|tan theta \| =12//5 " then " tan theta//2= 2//3
Answer» Only I is TRUE Only II is true Both I and II are true NEITHER I nor II are true ANSWER :D

Discussion

14859.	The sides of a parallelogram are given by 6x^(2)+7xy+2y^(2)=0 and 6x^(2)+7xy+2y^(2)-5x-3y+1=0, then the equation of the diagonal not passing through the origin is
Answer» x-y=1 5x+3y-1=0 x+y+3=0 5x+3y+1=0 Answer :B

Discussion

14860.	If the pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the y-axis, then bc=
Answer» `G^(2)` `F^(2)` FG `2f^(2)` Answer :B

Discussion

14861.	Prove that the circles x^(2)+y^(2)+2ax+ay-3a^(2)=0andx^(2)+y^(2)-8ax-6ay+7a^(2)=0 touch each other.
Answer»

Discussion

14862.	Evaluate lim_(xto pi/2)(1-"sin"x)^2/((pi/2-x)^(2))
Answer» ANSWER :`1/8`

Discussion

14863.	Let a_(1), a_(2),…,a_(n) be fixed real numbers and define a function f(x)=(x-a_(1))(x-a_(2))…(x-a_(n)). What is lim_(xrarra_(1))f(x) ? For some a ne a_(1), a_(2), …..,a_(n), compute lim_(xrarra)(f(x).
Answer» Answer :`lim_(xrarra_(1))F(X)` EXISTS for all `ane 0`.

Discussion

14864.	Evaluate the following limits in lim_(xrarr0)(sinax+bx)/(ax+sinbx)a,b,a+b ne-
Answer» ANSWER :1

Discussion

14865.	If in DeltABC sides a,b,c are in A.P then
Answer» `B gt60^(@)` `B lt 60^(@)` `B LE 60^(@)` `B=\|A-C\|` ANSWER :C

Discussion

14866.	Identify the quantifier in the following statements. Atleast one natural number is not a prime number.
Answer» ANSWER :At LEAST

Discussion

14867.	Find equaiton of hyperbola satisfying given conditons Length of thelatus rectum is 8, eccentricity (3)/(sqrt(5)) and X - axis as major axis.
Answer» Answer :`(x^(2))/(25) - (y^(2))/(20) = 1`

Discussion

14868.	Evaluate :lim_(xrarr0)[sqrt(x+4)-2]/x by filling the table.
Answer» ANSWER :`0.25`

Discussion

14869.	Find the roots of x^(2) + x/sqrt(2)+1=0
Answer» ANSWER :`(-1+-sqrt(7)i)/(2sqrt(2))`

Discussion

14870.	If (1- tan2^(@) cot 62^(@))/( tan 152^(@) - cot88^(@))=ksqrt(3) , then value of k is
Answer» -1 `-(1)/(2)` 1 `(1)/(2)` ANSWER :A

Discussion

14871.	A tower subtends angles alpha,2 alpha, 3 alpha respectively at points A,B and C all lying on a horizontal line through the foot of the tower, Then (AB)/(BC)=
Answer» `(sin3alpha)/(sin2alpha)` `1+2cos2alpha` `2+2cos2alpha` `(sin2alpha)/(SINALPHA)` ANSWER :B

Discussion

14872.	Let O be a point inside Delta ABCsuch that angle OAB = angle OBC = angle OCA = theta Area of Delta ABC is equal to
Answer» `((a^(2)+B^(2)+C^(2))/4) tan THETA ` `((a^(2)+b^(2)+c^(2))/4)cot theta` `((a^(2)+b^(2)+c^(2))/2) tan theta ` `((a^(2)+b^(2)+c^(2))/2) cot theta` ANSWER :A

Discussion

14873.	An electric current 'C' is measured by tangent galvanometer. The relative error in the current corresponding to an error deltatheta in its angle of deflection is
Answer» `sectheta.deltatheta` `cosectheta.deltatheta` `tantheta.deltatheta` `sectheta.cosectheta.deltatheta` ANSWER :D

Discussion

14874.	Find the derivative of f(x)=(1)/(x)
Answer» ANSWER :`-(1)/(X^(2))`

Discussion

14875.	If 3sin beta = sin(2alpha + beta), then tan(alpha + beta)-2tan alpha is:
Answer» independent of `ALPHA ` independent of `BETA` dependent of both `alpha and beta` independent of both `alpha and beta` Answer :A::B::D

Discussion

14876.	If Tan A = (17)/(18), TanB = (1)/(35) then Cos (A+B) =
Answer» 1 `SQRT(2)` -1 `(1)/(sqrt(2))` ANSWER :D

Discussion

14877.	If y= tan^(-1)sqrt((1-x)/(1+x)) then dy/dx at
Answer» `(-1)/(2\|x\|sqrt(x^2-1))` `(-1)/(2xsqrt(x^2-1))` `(1)/(2xsqrt(x^2-1))` `(1)/(2xsqrt(x^2+1))` ANSWER :A

Discussion

14878.	Solve : 7 sin^(2) theta + 3 cos^(2) theta = 4.
Answer» ANSWER :`THETA = N PI +- (pi)/(3), n in I`

Discussion

14879.	If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E ?
Answer» ANSWER :907200

Discussion

14880.	If (2,k,-1) is the centroid of the triangle with vertices (2,-1,2)(1,-3,-4) and (3,k,-1), then k=
Answer» `4/3` 12 -4 -2 Answer :D

Discussion

14881.	The range of the function f(x)= log _e (2 (2- log _( sqrt2) (16 sin ^(2) x+1) ) )
Answer» `[0, 1]` `(-OO, 1]` `[-1, 1]` `(-oo, oo)` ANSWER :B

Discussion

14882.	Prove that sqrt3 csc 20 ^(@)- sec 20^(@)=4
Answer» 1 2 3 4 Answer :D

Discussion

14883.	If A = {x in R : 0 lt x lt 4} and B = {x in R : 1 le x le 7} then find A Delta B.
Answer» Answer :`{x in R, 0 lt x lt 1 or 4 LE x le 7}`

Discussion

14884.	If tan alpha = (1)/(sqrt(x(x^(2)+x+1))), tan beta = (sqrt(x))/(sqrt(x^(2)+x+1)) and tan gamma = sqrt(x^(-3)+x^(-2)+x^(-1)) then alpha+beta =
Answer» `GAMMA` `2gamma` `-gamma` `gamma//2` ANSWER :A

Discussion

14885.	Iftan 20^(@) = lambda , " then " (tan 250^@ + tan 340^(@))/(tan 200^(@) - tan 110^(@))=
Answer» `(1+lambda^(2))/(1-lambda^(2))` `(1-lambda^(2))/(1+lambda^(2))` `(1+lambda^(2))/(2lambda)` `(1-lambda^(2))/(2lambda)` ANSWER :B

Discussion

14886.	Let A (0,4,1), B(2,3,-1) and C(4,5,0) be the vertices of a DeltaABC. Find AB,BC and AC
Answer» SOLUTION :`3,3, ROOT(3)(2)`

Discussion

14887.	State which of the following sets are finite or infinite : {x : x in N" and "2x-1 =0}
Answer» ANSWER :FINITE

Discussion

14888.	Through the point (2,3) ,a straight line is drawn making, positive intercept on the coordinate axes, . The area of the triangle thus formed is leastwhen the ratio of the intercepts on the x and y axes is
Answer» `2:3` `3:2` `4:9` `9:4` ANSWER :A

Discussion

14889.	If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets : D = { f, g, h, a}
Answer» ANSWER :`={B, C, d, E}`

Discussion

14890.	Which of the following statements are true and which are false? In each case give a valid reason for saying so. t : sqrt(11) is a rational number.
Answer» Answer :FALSE. Since 11 is a PRIME NUMBER, therefore `SQRT(11)` is IRRATIONAL.

Discussion

14891.	Which of the following statements are true and which are false? In each case give a valid reason for saying so. s: If x and y are integers such that x gt y, then -x lt -y.
Answer» ANSWER :TRUE, by the RULE of INEQUALITY

Discussion

14892.	Which of the following statements are true and which are false? In each case give a valid reason for saying so. r: Circle is a particular case of an ellipse.
Answer» Answer :True. In the EQUATION of an ellipse if we PUT a = b, then it is a CIRCLE (Direct Method)

Discussion

14893.	Which of the following statements are true and which are false? In each case give a valid reason for saying so. q: The centre of a circle bisects each chord of the circle
Answer» ANSWER :FALSE. This can be shown by GIVING a COUNTER EXAMPLE. A chord which is not a dimaeter gives the counter example.

Discussion

14894.	The value of ((cos A + coa B)/( sin A - sin B)) ^(2015) + ((sin A + sin B)/( cos A - cos B)) ^(2015) =
Answer» 0 `COT ^(2015) ((A +B)/( 2))` `cot ^(2015) ((A-B)/(2))` `2 tan ^(2015) ((A+B)/(2))` ANSWER :A

Discussion

14895.	Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that (a) you both enter the same section? (b) you both enter the different sections?
Answer» ANSWER :(a) `17/33` (B) `16/33`

Discussion

14896.	The point in which the YZ plane divides the line joining the points (3, 5, -7) and (-2, 1, 8) is (x, y, z). Then the value of x+5y+z is
Answer» 10 15 12 20 Answer :B

Discussion

14897.	If the sum of two unit vectors is an unit vector, the magnitude of their difference is
Answer» `SQRT2` `sqrt3` 1 `sqrt5` ANSWER :B

Discussion

14898.	Assertion (A) : For all +ve, integral values of 'n', 3^(2n) + 7 isdivisible by 8 Reason (R) : G.C.F. of 16 and 88 is 8
Answer» A true, R true and R is the correct EXPLANATION of A A true,R true and R is not a correct explanation of A A true, R false A false, R true Answer :A

Discussion

14899.	{:("List - I " ,"List - II " ),("A) The general solution of " sec^(2) x = sqrt(2) ( t - tan ^(2) x),"p) " (2 n + 1) pi//2),("B) If " sin ^(6) x = 1 + cos ^(4) 3 x" then " x = ,"q) " x = n pi pm (pi)/(3) ),("C) The general solution of sin " 2 alpha = 4 sin (x + alpha ) sin (x - alpha ) is ,"r) " n pi pm pi//8 ):}
Answer» ANSWER :A - R; B - p; C - Q

Discussion

14900.	If A is the point bar(a)+2bar(b), P is the point bar(a) and P devides AB in 2 : 3 then the P.V. of B is
Answer» `BAR(a)+3bar(B)` `bar(a)-2bar(b)` `bar(a)-3bar(b)` `3bar(a)-bar(b)` Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

Distance between to parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0is

Write the negation of each of the following statements. Some students failed to qualify the entrance test.

AB is a variable lines sliding between the coordinate axes in such a way that A lies on x-axis and B lies on y-axis. The P is a variable point on AB such that PA=b, PB=a and AB=a+b, then the equation of the locus of P is

Assertion (A) : tan 70^(@) - tan 20^(@) = 2 cot 40^(@) Reason (R ) : If A + B = 90^(@)then tan A. tan B = 1

If 3x^(2)-11xy+10y^(2)-7x+13y+k=0denotes a pair of straight lines, then the point of intersection of the lines is

Let A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}. Find A ∪ B.

I : If180^(@) lt theta lt 270^@ , sin theta = -3//5 " then " cos theta //2 -=1//10. II : If630^(@) lt theta lt 720^(@) , |tan theta | =12//5 " then " tan theta//2= 2//3

The sides of a parallelogram are given by 6x^(2)+7xy+2y^(2)=0 and 6x^(2)+7xy+2y^(2)-5x-3y+1=0, then the equation of the diagonal not passing through the origin is

If the pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the y-axis, then bc=

Prove that the circles x^(2)+y^(2)+2ax+ay-3a^(2)=0andx^(2)+y^(2)-8ax-6ay+7a^(2)=0 touch each other.

Evaluate lim_(xto pi/2)(1-"sin"x)^2/((pi/2-x)^(2))

Let a_(1), a_(2),…,a_(n) be fixed real numbers and define a function f(x)=(x-a_(1))(x-a_(2))…(x-a_(n)). What is lim_(xrarra_(1))f(x) ? For some a ne a_(1), a_(2), …..,a_(n), compute lim_(xrarra)(f(x).

Evaluate the following limits in lim_(xrarr0)(sinax+bx)/(ax+sinbx)a,b,a+b ne-

If in DeltABC sides a,b,c are in A.P then

Identify the quantifier in the following statements. Atleast one natural number is not a prime number.

Find equaiton of hyperbola satisfying given conditons Length of thelatus rectum is 8, eccentricity (3)/(sqrt(5)) and X - axis as major axis.

Evaluate :lim_(xrarr0)[sqrt(x+4)-2]/x by filling the table.

Find the roots of x^(2) + x/sqrt(2)+1=0

If (1- tan2^(@) cot 62^(@))/( tan 152^(@) - cot88^(@))=ksqrt(3) , then value of k is

A tower subtends angles alpha,2 alpha, 3 alpha respectively at points A,B and C all lying on a horizontal line through the foot of the tower, Then (AB)/(BC)=

Let O be a point inside Delta ABCsuch that angle OAB = angle OBC = angle OCA = theta Area of Delta ABC is equal to

An electric current 'C' is measured by tangent galvanometer. The relative error in the current corresponding to an error deltatheta in its angle of deflection is

Find the derivative of f(x)=(1)/(x)

If 3sin beta = sin(2alpha + beta), then tan(alpha + beta)-2tan alpha is:

If Tan A = (17)/(18), TanB = (1)/(35) then Cos (A+B) =

If y= tan^(-1)sqrt((1-x)/(1+x)) then dy/dx at

Solve : 7 sin^(2) theta + 3 cos^(2) theta = 4.

If the different permutations of all the letter of the word EXAMINATION are﻿ listed as in a dictionary, how many words are there in this list before the first﻿ word starting with E ?

If (2,k,-1) is the centroid of the triangle with vertices (2,-1,2)(1,-3,-4) and (3,k,-1), then k=

The range of the function f(x)= log _e (2 (2- log _( sqrt2) (16 sin ^(2) x+1) ) )

Prove that sqrt3 csc 20 ^(@)- sec 20^(@)=4

If A = {x in R : 0 lt x lt 4} and B = {x in R : 1 le x le 7} then find A Delta B.

If tan alpha = (1)/(sqrt(x(x^(2)+x+1))), tan beta = (sqrt(x))/(sqrt(x^(2)+x+1)) and tan gamma = sqrt(x^(-3)+x^(-2)+x^(-1)) then alpha+beta =

Iftan 20^(@) = lambda , " then " (tan 250^@ + tan 340^(@))/(tan 200^(@) - tan 110^(@))=

Let A (0,4,1), B(2,3,-1) and C(4,5,0) be the vertices of a DeltaABC. Find AB,BC and AC

State which of the following sets are finite or infinite : {x : x in N" and "2x-1 =0}

Through the point (2,3) ,a straight line is drawn making, positive intercept on the coordinate axes, . The area of the triangle thus formed is leastwhen the ratio of the intercepts on the x and y axes is

If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets : D = { f, g, h, a}

Which of the following statements are true and which are false? In each case give a valid reason for saying so. t : sqrt(11) is a rational number.

Which of the following statements are true and which are false? In each case give a valid reason for saying so. s: If x and y are integers such that x gt y, then -x lt -y.

Which of the following statements are true and which are false? In each case give a valid reason for saying so. r: Circle is a particular case of an ellipse.

Which of the following statements are true and which are false? In each case give a valid reason for saying so. q: The centre of a circle bisects each chord of the circle

The value of ((cos A + coa B)/( sin A - sin B)) ^(2015) + ((sin A + sin B)/( cos A - cos B)) ^(2015) =

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that (a) you both enter the same section? (b) you both enter the different sections?

The point in which the YZ plane divides the line joining the points (3, 5, -7) and (-2, 1, 8) is (x, y, z). Then the value of x+5y+z is

If the sum of two unit vectors is an unit vector, the magnitude of their difference is

Assertion (A) : For all +ve, integral values of 'n', 3^(2n) + 7 isdivisible by 8 Reason (R) : G.C.F. of 16 and 88 is 8

If A is the point bar(a)+2bar(b), P is the point bar(a) and P devides AB in 2 : 3 then the P.V. of B is

If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E ?