14949 + Interview Questions in Maths in Class 11 Page 262 InterviewSolution

13051.	Write the converse of each of the following statements, In which cases is the converse true ? If Mr. Saxena is elected to office, then all our problems are over.,
Answer» Answer :If all our problems are over, then Mr. SAXENA is ELECTED to OFFICE.

Discussion

13052.	If (cos x)/(cos y)=2 and cos(x-y) = sqrt(3)/2, then tan y=
Answer» `sqrt(3)+4` `sqrt(3)+1` `sqrt(3)-4` `sqrt(3)-1` ANSWER :C

Discussion

13053.	Find the pairs of equal sets, if any, give reasons: A = {0}, B = {x : x > 15 and x < 5}, C = {x : x – 5 = 0 }, D = {x: x^(2) = 25}, E = {x : x is an integral positive root of the equation x^(2) – 2x –15 = 0}.
Answer» ANSWER :C, E

Discussion

13054.	If f(theta) = sin(tan^(-1)(("sin theta)/(sqrt(cos 2 theta)))), where -pi/4 lt theta lt pi/4, then the value of d/(d(tan theta)) f(theta) is
Answer» `1` `-1` `0` `sqrt(2)` ANSWER :B

Discussion

13055.	Equation of a line is 3x - 4y + 10 = 0 . Find its (i) slope , (ii) x - and y - intercepts.
Answer» ANSWER :`B = 5/2`

Discussion

13056.	Write the contrapositive of the inverse of p implies q .
Answer» <P> ANSWER :Q => p

Discussion

13057.	InDelta ABC , if (1- (r_1)/(r_2)) (1- ( r_1)/( r_3))= 2, then the triangle is
Answer» isosceles Equilateral RIGHT ANGLED Scalene Answer :C

Discussion

13058.	Find {:(" Lt"),(xrarr0):}(sin(a+bx)-sin(a-bx))/(x)
Answer» ANSWER :`2bcosa`

Discussion

13059.	The perpendicular distance of any point vec(a) on to the line vec(r )= vec(b) + t vec(c ) is
Answer» `(\|(VEC(a)-vec(B))XX vec(C )\|)/(\|vec(b)\|)` `(\|(vec(a)-vec(b))xx vec(c)\|)/(\|vec(c)\|)` `(\|vec(a)-vec(b)\|)/(\|vec(c)\|)` `(\|(vec(a)-vec(b))xx vec(c )\|)/(\|vec(a)\|)` ANSWER :B

Discussion

13060.	A=(2,3,5), B(-1,3,2), C=(lambda,5,mu) are the vertices of a triangle. If the median AM is equally inclined to the coordinate axes, then (lambda,mu)=
Answer» ANSWER :4

Discussion

13061.	A straight line L with direction cosines l, m, n is parallel to 3x-4y+2z+8=0 where
Answer» `3l-4m+2n=0` `(L)/(3)=(m)/(-4)=(n)/(2)` `l+m+n-8=0` `3l-4m+2n+8=0` ANSWER :A

Discussion

13062.	Expand (X^2+3/x)^4, x != 0
Answer» ANSWER :4

Discussion

13063.	For what values of A in the first quardrant, the expression (cot^(3)A-3 cotA)/(3cot^(2)A-1) is positive?
Answer» ANSWER :`0ltAltpi/6,pi/3ltAltpi/2`

Discussion

13064.	Iffrom the top of a tower of 60 meter height, the angles of depression of the top and floor of a house are alpha and beta " respectively and if the height of the house is " (60sin(beta-alpha))/x, then x =
Answer» `SINALPHASINBETA` `cosalphacosbeta` `sinalphacosbeta` `cos ALPHA SIN BETA` Answer :D

Discussion

13065.	The range of cosh((x)/(2)) is
Answer» `(-ALPHA, alpha)` `(0, alpha)` `(0, 1)` `[2, alpha)` ANSWER :D

Discussion

13066.	If a, b are the roots of equation x^(2)-3x + p =0 and c, d are the roots of x^(2) - 12x + q = 0 and a, b, c, d are in G.P., then prove that : p : q =1 : 16
Answer» SOLUTION :N/a

Discussion

13067.	Simplify: i^(28)
Answer» ANSWER :1

Discussion

13068.	If x=tanh^(-1)(y), then log_(e )((1+y)/(1-y))=
Answer» X 4X 2x 3X Answer :C

Discussion

13069.	Convert into factorial7,8,9,10,11, 12, 13, 14, 15.
Answer» ANSWER :` (15!)/( 6!) `

Discussion

13070.	What universal set(s) would you propose for each of the following : The set of right triangles.
Answer» ANSWER :UNIVERSAL SET : The set of TRIANGLES in the PLANE.

Discussion

13071.	If 2,3,6 are exradiiof triangle, then itsinradiusis
Answer» `1` ` 2` ` 4` ` 6` ANSWER :A

Discussion

13072.	Show that Lt_(xto-2)((x^(5)+2x^(4)+x^(2)+3x+2)/(x^(4)+2x^(3)+3x^(2)-5x-22))=-3/5
Answer» ANSWER :`-3/5`

Discussion

13073.	If A+B+C= 2S , " then " sin (S-A) sin(S-B) + sinS sin(S-C)=
Answer» `4 COS ""A/2 .cos ""B/2.cos""C/2` `4cos ""A/2.cos""B/2.sin""C/2` `4cos ""A/2.sin""B/2 .sin"C/2` `4 sin ""A/2. sin ""B/2. sin""C/2` Answer :B

Discussion

13074.	Which of the following statements is true I Ina DeltaABC if 4s(s-a)(s-b)(s-c)=a^(2)b^(2) then it is right angled triangle II in a DeltaABC the expression sinA+sinB+sinC is maximum then the triangle is equilateral
Answer» onlyI only II both I and II neither I nor II Answer :C

Discussion

13075.	f(x) = (1 - cos (4x))/(x^(2)) ,x in 0, f (0) = 8 , at x =0 fis
Answer» continuous DISCONTINUOUS not determined NONE ANSWER :C

Discussion

13076.	Express each of the complex number given in the form of a+ib (1/3 + 3i)^(3)
Answer» ANSWER :`-242/27 - 26 i`

Discussion

13077.	Solve sin 3 theta+ sin theta = sin 2 theta, 0 le theta le 2pi. Given the general solution.
Answer»

Discussion

13078.	The straight roads intersect at angle of 60^@. A bus on one road is 2km. Away from the intersection and a car on the other road is 3 km. away from the intersection. Then the direct distance between the two vehicles is
Answer» 1 KM `sqrt(2) km` 4 km `sqrt(7) km` Answer :D

Discussion

13079.	Observe the following statements: Assertion (A): If "sinh"^(-1) sqrt(3)=log_(e )(sec theta+tan theta), then theta=(pi)/(3) Reason (R ) : If tan theta=sqrt(3), sec theta =2 rArr theta =(pi)/(3) Then the true statement among the following is :
Answer» A is true, R is false A is true, R is true, R `RARR` A A is false, R is true A is false, R is false ANSWER :B

Discussion

13080.	The transformed equation of 5x^(2) + 4xy + 8y^(2) - 12x - 12y =0 when the axes are translated to the point (1,1//2) is
Answer» ANSWER :`RARR 5X^(2) + 4XY + 8Y^(2) = 9`

Discussion

13081.	Measure of an angle of the regular polygon having ten sides is .........radian.
Answer» ANSWER :`(4PI)/5` RADIAN

Discussion

13082.	Does x^(2)+y^(2)=0 represent a pair of straight lines
Answer» ANSWER :no

Discussion

13083.	The Spearman's rank correlation coefficient = (9)/(11), givensum d^(2)= 30. Find the number of observation.
Answer» ANSWER :10

Discussion

13084.	Examine the continuity of the following: x^2 cos x
Answer» ANSWER :` F(X) = x^(2) cos x ` is continuous for all x ` in RR ` .

Discussion

13085.	The volume of the tetrahedron having the edges barI+2barj-bark,bari+barj+bark,bari-barj+lamdabark as coterminous, is 2/3 cubic untis. Then lamda =
Answer» 1 2 3 4 Answer :A

Discussion

13086.	Consider the fuunctionh_2( x) =f(\|g\|) and h_2( x) = \|f( g(x))\| Which of the following is not true about h_2(x)?
Answer» The DOMAIN is R It is periodic with period `2PI` The range is [0, 1] NONE of these Answer :A

Discussion

13087.	If O is the origin and Q is a variable, point on x^(2)=4y, find the locus of the mid-point of OQ.
Answer» ANSWER : `X^(2)=2Y`

Discussion

13088.	Find the angle between the X-axis and the line joining the points (3,-1) and (4,-2).
Answer» ANSWER :`135^@`

Discussion

13089.	Differentiate the following functions w.r.t. x: (sec ( ax-b) )/( x^(2) -2)
Answer» ANSWER :`(a (x^2 -2) sec (AX - b) tan (ax -b) -2X sec (ax -b) )/( (x^2 -2)^2)`

Discussion

13090.	The mathematical aptitude score of 10 computer programmers with their job performance is given below : Calculate the Spearman's coefficient of rank correlation and interpret the result.
Answer» ANSWER :`0.71`

Discussion

13091.	A given right cone has volume p, and the largest right circular cylinder that can be inscribed in the cone has volume q . Thenp:q is
Answer» `9 : 4` `8 : 3` `7 : 2` `4: 9` ANSWER :A

Discussion

13092.	Evaluate the following limits : Lim_(x to pi) (sin x )/(x - pi)
Answer» ANSWER :`-1`

Discussion

13093.	Given that the points A(2,3,4),B(-1,2,-3) and C(-4,1,-10) are collinear. Then the ratio in which C divides AB is
Answer» `1:2` `2:1` INTERNALLY `1:2` EXTERNALLY `2:1` externally ANSWER :D

Discussion

13094.	While defining inverse trigonometric functions, a new system is followed where domains and ranges have been redefined as follows: The minimum of (sin^(-1)x)^(3)-(cos^(-1)x)^(3) is equal to
Answer» `-63/8 PI^(3)` `63/8 pi^(3)` `(125pi^(3))/32` `(125^(3))/32` ANSWER :A

Discussion

13095.	While defining inverse trigonometric functions, a new system is followed where domains and ranges have been redefined as follows: If f(x)=3sin^(-1)x-2cos^(-1)x then f(x) is
Answer» EVEN function ODD function Neither even nor odd even as WELL as odd function Answer :B

Discussion

13096.	While defining inverse trigonometric functions, a new system is followed where domains and ranges have been redefined as follows: sin^(-1)(-x) is equal to
Answer» `-SIN^(-1)X` `pi+sin^(-1)x` `2pi-sin^(-1)x` `3pi-cos^(-1)sqrt(1-x^(2)),XGT0` Answer :C

Discussion

13097.	I : Ifx cos theta = y cos (120^@ + theta ) = z cos ( theta + 240^(@))thenxy+ yz+ zx=1 II :cos alpha + cos (120^(@) + alpha ) + cos (120^@ - alpha ) =0
Answer» Only I Only II Both I & II Neither I nor II Answer :B

Discussion

13098.	A circle is inscribed in an equilateral triangle of side a, The area of the square inscribed in the circle,in sq.units is
Answer» `a^(2)/12` `a^(2)/6` `a^(2)/8` NONE ANSWER :B

Discussion

13099.	Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and phi
Answer» Answer :`U= {0, 1, 2, 3, 4, 5, 6, 8}`

Discussion

13100.	Let the palanes, P _(1) : 2x - y + z =2 and P _(2) : x + 2y -z =3 are given, On the bases of the above information, Answer the following questions The equation of the bisector of angle of the planes P _(1) and P_(2) which is not containing origin, is
Answer» `X - 3y + 2 Z + 1=0` `x + 3y =5` `x + 3y + 2Z + 2=0` `3X + y=5` Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

Write the converse of each of the following statements, In which cases is the converse true ? If Mr. Saxena is elected to office, then all our problems are over.,

If (cos x)/(cos y)=2 and cos(x-y) = sqrt(3)/2, then tan y=

Find the pairs of equal sets, if any, give reasons: A = {0}, B = {x : x > 15 and x < 5}, C = {x : x – 5 = 0 }, D = {x: x^(2) = 25}, E = {x : x is an integral positive root of the equation x^(2) – 2x –15 = 0}.

If f(theta) = sin(tan^(-1)(("sin theta)/(sqrt(cos 2 theta)))), where -pi/4 lt theta lt pi/4, then the value of d/(d(tan theta)) f(theta) is

Equation of a line is 3x - 4y + 10 = 0 . Find its (i) slope , (ii) x - and y - intercepts.

Write the contrapositive of the inverse of p implies q .

InDelta ABC , if (1- (r_1)/(r_2)) (1- ( r_1)/( r_3))= 2, then the triangle is

Find {:(" Lt"),(xrarr0):}(sin(a+bx)-sin(a-bx))/(x)

The perpendicular distance of any point vec(a) on to the line vec(r )= vec(b) + t vec(c ) is

A=(2,3,5), B(-1,3,2), C=(lambda,5,mu) are the vertices of a triangle. If the median AM is equally inclined to the coordinate axes, then (lambda,mu)=

A straight line L with direction cosines l, m, n is parallel to 3x-4y+2z+8=0 where

Expand (X^2+3/x)^4, x != 0

For what values of A in the first quardrant, the expression (cot^(3)A-3 cotA)/(3cot^(2)A-1) is positive?

Iffrom the top of a tower of 60 meter height, the angles of depression of the top and floor of a house are alpha and beta " respectively and if the height of the house is " (60sin(beta-alpha))/x, then x =

The range of cosh((x)/(2)) is

If a, b are the roots of equation x^(2)-3x + p =0 and c, d are the roots of x^(2) - 12x + q = 0 and a, b, c, d are in G.P., then prove that : p : q =1 : 16

Simplify: i^(28)

If x=tanh^(-1)(y), then log_(e )((1+y)/(1-y))=

Convert into factorial7,8,9,10,11, 12, 13, 14, 15.

What universal set(s) would you propose for each of the following : The set of right triangles.

If 2,3,6 are exradiiof triangle, then itsinradiusis

Show that Lt_(xto-2)((x^(5)+2x^(4)+x^(2)+3x+2)/(x^(4)+2x^(3)+3x^(2)-5x-22))=-3/5

If A+B+C= 2S , " then " sin (S-A) sin(S-B) + sinS sin(S-C)=

Which of the following statements is true I Ina DeltaABC if 4s(s-a)(s-b)(s-c)=a^(2)b^(2) then it is right angled triangle II in a DeltaABC the expression sinA+sinB+sinC is maximum then the triangle is equilateral

f(x) = (1 - cos (4x))/(x^(2)) ,x in 0, f (0) = 8 , at x =0 fis

Express each of the complex number given in the form of a+ib (1/3 + 3i)^(3)

Solve sin 3 theta+ sin theta = sin 2 theta, 0 le theta le 2pi. Given the general solution.

The straight roads intersect at angle of 60^@. A bus on one road is 2km. Away from the intersection and a car on the other road is 3 km. away from the intersection. Then the direct distance between the two vehicles is

Observe the following statements: Assertion (A): If "sinh"^(-1) sqrt(3)=log_(e )(sec theta+tan theta), then theta=(pi)/(3) Reason (R ) : If tan theta=sqrt(3), sec theta =2 rArr theta =(pi)/(3) Then the true statement among the following is :

The transformed equation of 5x^(2) + 4xy + 8y^(2) - 12x - 12y =0 when the axes are translated to the point (1,1//2) is

Measure of an angle of the regular polygon having ten sides is .........radian.

Does x^(2)+y^(2)=0 represent a pair of straight lines

The Spearman's rank correlation coefficient = (9)/(11), givensum d^(2)= 30. Find the number of observation.

Examine the continuity of the following: x^2 cos x

The volume of the tetrahedron having the edges barI+2barj-bark,bari+barj+bark,bari-barj+lamdabark as coterminous, is 2/3 cubic untis. Then lamda =

Consider the fuunctionh_2( x) =f(|g|) and h_2( x) = |f( g(x))| Which of the following is not true about h_2(x)?

If O is the origin and Q is a variable, point on x^(2)=4y, find the locus of the mid-point of OQ.

Find the angle between the X-axis and the line joining the points (3,-1) and (4,-2).

Differentiate the following functions w.r.t. x: (sec ( ax-b) )/( x^(2) -2)

The mathematical aptitude score of 10 computer programmers with their job performance is given below : Calculate the Spearman's coefficient of rank correlation and interpret the result.

A given right cone has volume p, and the largest right circular cylinder that can be inscribed in the cone has volume q . Thenp:q is

Evaluate the following limits : Lim_(x to pi) (sin x )/(x - pi)

Given that the points A(2,3,4),B(-1,2,-3) and C(-4,1,-10) are collinear. Then the ratio in which C divides AB is

While defining inverse trigonometric functions, a new system is followed where domains and ranges have been redefined as follows: The minimum of (sin^(-1)x)^(3)-(cos^(-1)x)^(3) is equal to

While defining inverse trigonometric functions, a new system is followed where domains and ranges have been redefined as follows: If f(x)=3sin^(-1)x-2cos^(-1)x then f(x) is

While defining inverse trigonometric functions, a new system is followed where domains and ranges have been redefined as follows: sin^(-1)(-x) is equal to

I : Ifx cos theta = y cos (120^@ + theta ) = z cos ( theta + 240^(@))thenxy+ yz+ zx=1 II :cos alpha + cos (120^(@) + alpha ) + cos (120^@ - alpha ) =0

A circle is inscribed in an equilateral triangle of side a, The area of the square inscribed in the circle,in sq.units is

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and phi

Let the palanes, P _(1) : 2x - y + z =2 and P _(2) : x + 2y -z =3 are given, On the bases of the above information, Answer the following questions The equation of the bisector of angle of the planes P _(1) and P_(2) which is not containing origin, is