14949 + Interview Questions in Maths in Class 11 Page 224 InterviewSolution

11151.	Which is true
Answer» `tanabs(tan^(-1)X)=ABS(x)` `cotabs(cot^(-1)x)=x` `tan^(-1)abs(TANX)=abs(x)` `sinabs(sin^(-1)x)=abs(x)` Answer :A::B::C::D

Discussion

11152.	The parabola y^2=4px passes thrugh the point (3,-2). Obtain the length of the latus rectum and the coordinates of the focus.
Answer» ANSWER :`(4)/(3),(1/3,0)`

Discussion

11153.	If A_(i),B_(i),C_(i) are the cofactors of a_(i),b_(i),c_(i) respectively,i=1,2,3 in Delta =\|(a_(1),b_(2),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))\|show that \|(A_(1),B_(1),C_(1)),(A_(2),B_(2),C_(2)),(A_(3),B_(3),C_(3))\|=Delta^(0)
Answer» Answer :`\|(A_(1),B_(1),C_(1)),(A_(2),B_(2),C_(2)),(A_(3),B_(3),C_(3))\|=Delta^(0)`

Discussion

11154.	The sum of the sequence 5+55+555+… upto n terms is
Answer» `(5)/( 9) [ ( 10 (10^(n) -1) +n) /( 9) ]` `(5)/( 9) [ ( 10 (10^(n) -1) )/( 9) -n]` `(5)/( 9) [ ( 10(10^(n+1) -1)) /( 9) - n]` `(5)/( 9) [ (10(10^(n-1) -1)) /( 9) -n]` Answer :B

Discussion

11155.	If vec(p)= vec(a)-vec(b), vec(q)= vec(a) + vec(b), \|vec(a)\|= \|vec(b)\|=t " then " \|vec(p) xx vec(q)\|=
Answer» `2 SQRT(t^(2)-(VEC(a).vec(B))^(2))` `3 sqrt(t^(2)-(vec(a).vec(b))^(2))` `sqrt(t^(4) -(vec(a).vec(b))^(2))` `2 sqrt(t^(4)-(vec(a).vec(b))^(2))` Answer :D

Discussion

11156.	Let f:R-{1} rarr R-{2} defined by f(x)=(2x+3)/(x+1) be a bijection mark all the correct alternative w.r.t real solutions
Answer» the number of REAL solutions of `f(X)=f^(-1)(x)` is 2 `f(x)=f^(-1)(x), ` if `f(x)=x` `f(x)=f^(-1)(x)`, only if `f(x)=x` All the above are correct Answer :A::B::C::D

Discussion

11157.	If f : R rarr Rsatisfies \|f(x) - f(y)\| le \|x - y\|^3 and f(4) = 192 then (f(7))/24 is equal to
Answer»

Discussion

11158.	If one end a diameter of the circle x^(2) + y^(2) - 4x - 6y + 11 = 0 is (3,4), then find the cordinate of the other end of the diameter.
Answer» ANSWER :(1,2)

Discussion

11159.	A card is selected from a pack of 52 cards. Calculate the probability that the card is (i) an ace (ii) black card.
Answer» ANSWER :(i) `(1)/(13)`(II) 26

Discussion

11160.	Let f(x)=sqrtx and g(x)=x be two functions defined over the set of non-negative real numbers. Find (f+g) (x), (f-g), (fg) (x) and (f/g) (x).
Answer» ANSWER :`SQRTX - X`

Discussion

11161.	If f(x)= sqrtx and g(x)= x be two functions defined in the domain R^(+) uu {0}, then find the value of(f+g) (x).
Answer» ANSWER :`SQRTX + X`

Discussion

11162.	Find the equation of bisector of the obtuse angle between the lines x+y-5=0 and x-7y+7=0
Answer» ANSWER :3x-y-9=0

Discussion

11163.	For each of the following compound statements first identify the connecting words and then break it into component statements: The sand heats up quickly in the sun and does not cool down fast at night.
Answer» ANSWER : ''And''. the component STATEMENTS are: The SAND heats up quickily in the sun. The sand does not COOL down fast at night.

Discussion

11164.	For each of the following compound statements first identify the connecting words and then break it into component statements: x=2 and x=3 are the roots of the equation 3x^(2)-x-10=0.
Answer» Answer : ''And''. The COMPONENT STATEMENTS are: `X = 2` is a root of the EQUATION `3x^(2)- x - 10 = 0` `x = 3` is a root of the equation `3x^(2) - x - 10 = 0`

Discussion

11165.	For each of the following compound statements first identify the connecting words and then break it into component statements: Square of an integer is positive or negative.
Answer» Answer : ''Or''. The COMPONENT statements are: SQUARE of an INTEGER is positive. Square of an integer is NEGATIVE

Discussion

11166.	For each of the following compound statements first identify the connecting words and then break it into component statements: All rational numbers are real and all real numbers are not complex.
Answer» ANSWER : ''And''. The COMPONENT statements are: All RATIONAL NUMBERS are real. All real numbers are not COMPLEX.

Discussion

11167.	The sides of a triangle are the consecutive natural number and its largest angle is twice the smallest one. The sides of the triangle are
Answer» `2, 3, 4` `3, 4, 5 ` `4, 5, 6` `5, 6 ` Answer :C

Discussion

11168.	Find the value of sin^(-1)(sin2011^(0))+cos^(-1)(cos2011^(0))+tan^(-1)(tan2011^(0))
Answer» 1 `-1` 2 0 Answer :B

Discussion

11169.	Show that following lines forms an equilateral triangle and find its area x^(2)-4xy^(2)=0, x+y-3=0
Answer» ANSWER :`(3sqrt(3))/(2)` SQ. UNITS

Discussion

11170.	If the vertex of the parabola is the point (-3, 0) and the directrix is the line x + 5 = 0, then its equation is ……
Answer» `y^(2) = 8(x + 3)` `(x^(2) = 8 (y + 3)` `(y^(2) = -8(x + 3)` `y^(2) = 8(x + 5)` Answer :A

Discussion

11171.	Find the point on the curve y^2=4x which is nearst to the point (2,1)
Answer» (4,4) (1,2) (9,6) (4,6) ANSWER :B

Discussion

11172.	If the system of equations (a+2)^(3)x+(1+7)^(3)y+(a+15)^(3)z=0 (a+2)x+(a+7)y+(a+15)z=0 x+y+z=0 possesses a non - trivial solution, find a.
Answer» ANSWER :`a=-8`

Discussion

11173.	If the sum of n terms of an AP is given by S_(n) = 3n+ 2n^(2), then the common difference of the AP is
Answer» 3 2 6 4 Answer :D

Discussion

11174.	Logical from of p and negation q is pvee(~q) .
Answer» ANSWER :FALSE STATEMENT

Discussion

11175.	If A=[a_(ij)]_(mxxn) is a matrix of rank r then
Answer» `R="min"{m,N}` `r LT "min "{m,n}` `r le" min"{m,n}` none Answer :C

Discussion

11176.	If cos y =x cos (a + y)then (dy)/(dx)=
Answer» `(COS^2(a+y))/(SINA)` `(cos^2(a+y))/(COSA)` `(cosa)/(sin^2(a+y))` `(cos(a+y))/(sina)` ANSWER :A

Discussion

11177.	sin alpha + sin beta = 1/4 and cos alpha + cos beta = 1/3 The value of cos ( alpha + beta) is
Answer» `12/25` `25/12` `25/13` `24/7` ANSWER :B

Discussion

11178.	Coefficient of x^(2)in (x^(2) + 1/x)^(6) is 1 (ii)1,4, 7 are in H.P(iii) -log(1-x)=x + x^(2)/2 + x^(2)/3 +…(iv)The Geometric mean between a and b is sqrt(ab).State which two are correct
Answer» (i) and (IV) are TRUE (III) and (iv) are true (i) and (II) are true (ii) and (iii) are true Answer :B

Discussion

11179.	Let f(x) be a real valued function defined by f(x)=x^(2)-2\|x\| an g(x)
Answer» ANSWER :A-q;B-ps;C-qrs;D-t

Discussion

11180.	Expand the following expressions : (1-x+x^(2))^(4)
Answer» ANSWER :`1-4x+10X^(2)-16x^(3)+19x^(4)-16x^(5)+10x^(6)-4x^(7)+x^(8)`

Discussion

11181.	Find the slope of a line parallel to the which passes through the following points: (-1, 3) and (4, 7)
Answer» ANSWER : `4/(5)`

Discussion

11182.	Which term of the following sequences: (1)/(3), (1)/(9), (1)/(27),….is (1)/(19683) ?
Answer» ANSWER :`9^(TH)`

Discussion

11183.	If alpha, beta, gamma, delta are the solutions of the equation tan(theta + (pi)/(4)) = 3 tan 3 theta, no two of which have equal tangents. The value of (1)/(tan alpha) + (1)/(tan beta) + (1)/(tan gamma) + (1)/(tandelta) is
Answer» -8 8 `2//3` `1//3` ANSWER :B

Discussion

11184.	If y =Sin ^(-1) (2x sqrt (1- x ^(2))), find (dy)/(dx).
Answer» ANSWER :`LT 1`

Discussion

11185.	If cos(sin^(-1)sqrt(13/17))=sin(tan^(-1)x) then x=
Answer» `4/17` `2/sqrt(13)` `3/2` `17/4` ANSWER :B

Discussion

11186.	If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) and (y, -2, -5) respectively and if they are collinear, then (x, y) =
Answer» (2, -3) (-2, 3) (-2, -3) (2, 3) ANSWER :A

Discussion

11187.	Let f(x){:{(2x+a",",x ge -1),(bx^(2)+3,x lt -1):} and g(x)={:{(x+4",",0 le x le 4),(-3x-2,-2 lt x lt 0):} If a=2 and b=3, then the range of g(f(x)) is
Answer» `(-2, 8]` `(0, 8]` `[4, 8]` `[-1, 8]` ANSWER :C

Discussion

11188.	Cosh(0) =
Answer» 0 1 e not DEFINED ANSWER :B

Discussion

11189.	Represent the complex number z=1+isqrt(3) in the polar form.
Answer» ANSWER :the COMPLEX NUMBER is `z=2(COS pi/3 + I SIN pi/3)`

Discussion

11190.	Prove that cos ((pi)/(4) + x) + cos ((pi)/(4) -x) = sqrt2 cos x
Answer» ANSWER :`SQRT2 COS X = R.H.S.`

Discussion

11191.	Find the points of local maximum or local minimum for the following sin2x-x" in "[-pi/2,pi/2]
Answer» ANSWER :MINIMUM VALUE `=-sqrt3/2+pi/6" at "x=-pi/6` MAXIMUM value `sqrt3/2-pi/6" at "x=pi/6`

Discussion

11192.	Eccentricity of x^2-4y^2=1 is ...........
Answer» ANSWER :`sqrt5/2`

Discussion

11193.	If a makes an angle of pi//4 with the positive direction of each of x-axis and y - axis, then the angle that the line makes with the positive direction of the z-axis is
Answer» `pi//2` `pi//6` `pi//3` `pi//4` ANSWER :A

Discussion

11194.	If A and B are two events such that P(AcupB)=0.07,P(AcapB)=0.02, and P(B)=0.05,then show that A and B are independent.
Answer» ANSWER :`:.`A and B are INDEPENDENT.

Discussion

11195.	If two dice are thrown simultaneously, find the probability of getting a sum of 7 or 11.
Answer» ANSWER :`(2)/(9)`

Discussion

11196.	Using binomial theorem , Evaluate the following : (0.99)^(5)
Answer» ANSWER :`0.951`

Discussion

11197.	For each of the following statements, determine whether an inclusive Or or exclusive or is used. Give reasons for your answer: The school is closed if it is a holiday or a Sunday.
Answer» ANSWER :INCLUSIVE SENSE

Discussion

11198.	If cos(A+B+C)=cos A cos B cos C, then (8sin(B+C)sin(C+A)sin(A+B))/(sin2A sin 2B sin 2C)=
Answer» 1 `-1` `(1)/(2)` `-(1)/(2)` ANSWER :B

Discussion

11199.	Explain briefly, what is meant by a "weighted average". Calculate a cost of living index from the following table of prices and weights.
Answer» ANSWER :`104.4`

Discussion

11200.	Show that the line y =x + sqrt7 touches the hyperbola 9x ^(2) - 16 y ^(2) = 144.
Answer» Answer :`(y ^(2) )/(69) - (X ^(2))/(100) =1`

Discussion

Explore topic-wise InterviewSolutions in .

Which is true

The parabola y^2=4px passes thrugh the point (3,-2). Obtain the length of the latus rectum and the coordinates of the focus.

If A_(i),B_(i),C_(i) are the cofactors of a_(i),b_(i),c_(i) respectively,i=1,2,3 in Delta =|(a_(1),b_(2),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))|show that |(A_(1),B_(1),C_(1)),(A_(2),B_(2),C_(2)),(A_(3),B_(3),C_(3))|=Delta^(0)

The sum of the sequence 5+55+555+… upto n terms is

If vec(p)= vec(a)-vec(b), vec(q)= vec(a) + vec(b), |vec(a)|= |vec(b)|=t " then " |vec(p) xx vec(q)|=

Let f:R-{1} rarr R-{2} defined by f(x)=(2x+3)/(x+1) be a bijection mark all the correct alternative w.r.t real solutions

If f : R rarr Rsatisfies |f(x) - f(y)| le |x - y|^3 and f(4) = 192 then (f(7))/24 is equal to

If one end a diameter of the circle x^(2) + y^(2) - 4x - 6y + 11 = 0 is (3,4), then find the cordinate of the other end of the diameter.

A card is selected from a pack of 52 cards. Calculate the probability that the card is (i) an ace (ii) black card.

Let f(x)=sqrtx and g(x)=x be two functions defined over the set of non-negative real numbers. Find (f+g) (x), (f-g), (fg) (x) and (f/g) (x).

If f(x)= sqrtx and g(x)= x be two functions defined in the domain R^(+) uu {0}, then find the value of(f+g) (x).

Find the equation of bisector of the obtuse angle between the lines x+y-5=0 and x-7y+7=0

For each of the following compound statements first identify the connecting words and then break it into component statements: The sand heats up quickly in the sun and does not cool down fast at night.

For each of the following compound statements first identify the connecting words and then break it into component statements: x=2 and x=3 are the roots of the equation 3x^(2)-x-10=0.

For each of the following compound statements first identify the connecting words and then break it into component statements: Square of an integer is positive or negative.

For each of the following compound statements first identify the connecting words and then break it into component statements: All rational numbers are real and all real numbers are not complex.

The sides of a triangle are the consecutive natural number and its largest angle is twice the smallest one. The sides of the triangle are

Find the value of sin^(-1)(sin2011^(0))+cos^(-1)(cos2011^(0))+tan^(-1)(tan2011^(0))

Show that following lines forms an equilateral triangle and find its area x^(2)-4xy^(2)=0, x+y-3=0

If the vertex of the parabola is the point (-3, 0) and the directrix is the line x + 5 = 0, then its equation is ……

Find the point on the curve y^2=4x which is nearst to the point (2,1)

If the system of equations (a+2)^(3)x+(1+7)^(3)y+(a+15)^(3)z=0 (a+2)x+(a+7)y+(a+15)z=0 x+y+z=0 possesses a non - trivial solution, find a.

If the sum of n terms of an AP is given by S_(n) = 3n+ 2n^(2), then the common difference of the AP is

Logical from of p and negation q is pvee(~q) .

If A=[a_(ij)]_(mxxn) is a matrix of rank r then

If cos y =x cos (a + y)then (dy)/(dx)=

sin alpha + sin beta = 1/4 and cos alpha + cos beta = 1/3 The value of cos ( alpha + beta) is

Coefficient of x^(2)in (x^(2) + 1/x)^(6) is 1 (ii)1,4, 7 are in H.P(iii) -log(1-x)=x + x^(2)/2 + x^(2)/3 +…(iv)The Geometric mean between a and b is sqrt(ab).State which two are correct

Let f(x) be a real valued function defined by f(x)=x^(2)-2|x| an g(x)

Expand the following expressions : (1-x+x^(2))^(4)

Find the slope of a line parallel to the which passes through the following points: (-1, 3) and (4, 7)

Which term of the following sequences: (1)/(3), (1)/(9), (1)/(27),….is (1)/(19683) ?

If alpha, beta, gamma, delta are the solutions of the equation tan(theta + (pi)/(4)) = 3 tan 3 theta, no two of which have equal tangents. The value of (1)/(tan alpha) + (1)/(tan beta) + (1)/(tan gamma) + (1)/(tandelta) is

If y =Sin ^(-1) (2x sqrt (1- x ^(2))), find (dy)/(dx).

If cos(sin^(-1)sqrt(13/17))=sin(tan^(-1)x) then x=

If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) and (y, -2, -5) respectively and if they are collinear, then (x, y) =

Let f(x){:{(2x+a",",x ge -1),(bx^(2)+3,x lt -1):} and g(x)={:{(x+4",",0 le x le 4),(-3x-2,-2 lt x lt 0):} If a=2 and b=3, then the range of g(f(x)) is

Cosh(0) =

Represent the complex number z=1+isqrt(3) in the polar form.

Prove that cos ((pi)/(4) + x) + cos ((pi)/(4) -x) = sqrt2 cos x

Find the points of local maximum or local minimum for the following sin2x-x" in "[-pi/2,pi/2]

Eccentricity of x^2-4y^2=1 is ...........

If a makes an angle of pi//4 with the positive direction of each of x-axis and y - axis, then the angle that the line makes with the positive direction of the z-axis is

If A and B are two events such that P(AcupB)=0.07,P(AcapB)=0.02, and P(B)=0.05,then show that A and B are independent.

If two dice are thrown simultaneously, find the probability of getting a sum of 7 or 11.

Using binomial theorem , Evaluate the following : (0.99)^(5)

For each of the following statements, determine whether an inclusive Or or exclusive or is used. Give reasons for your answer: The school is closed if it is a holiday or a Sunday.

If cos(A+B+C)=cos A cos B cos C, then (8sin(B+C)sin(C+A)sin(A+B))/(sin2A sin 2B sin 2C)=

Explain briefly, what is meant by a "weighted average". Calculate a cost of living index from the following table of prices and weights.

Show that the line y =x + sqrt7 touches the hyperbola 9x ^(2) - 16 y ^(2) = 144.