14949 + Interview Questions in Maths in Class 11 Page 187 InterviewSolution

9301.	Without solving, find the nature of the roots of the following equations: (i) 3x^(2)-7x+5=0. (ii) 4x^(2)+4x+1=0. (iii) 3x^(2)+7x+2=0. (iv) x^(2)+px-q^(2)=0.
Answer» Answer :(i) IMAGINARY (ii) Real and equal (iii) Real and UNEQUAL and rational. (IV) Real and unequal if `pne0,QNE0`; Real and equal if p=q=0.

Discussion

9302.	A box contains 1 red and 3 identical white balls. Two balls are draw at random in succession without replacement. Write the sample space for this experiment.
Answer» ANSWER :{RW, WR, WW}

Discussion

9303.	The range of alpha for which the equation sin^(4)x+cos^(4)x+sin2x+alpha=0 has solution
Answer» ANSWER :`[(-3)/(2),(1)/(2)]`

Discussion

9304.	The function f:(-oo, -1) to (0, e^(5)] defined by f(x)=e^(x^(3)-3x+2) is
Answer» many-one and onto many-one and into one-one and onto one-one and into Answer :D

Discussion

9305.	Evaluate the following limits in lim_(xrarr0)(sinax)/(bx)
Answer» ANSWER :`(a)/(B)`

Discussion

9306.	If \|(alpha,x,x,x),(x,beta,x,x),(x,x,gamma,x),(x,x,x,delta)\| = f(x) - x f' (x) then f(x) is equal to
Answer» `(X - alpha) (x - beta) (x - GAMMA) (x - DELTA)` `(x + alpha) (x + beta) (x + gamma) (x + delta)` `2(x - alpha) (x - beta) (x - gamma) (x - delta)` NONE of these Answer :A

Discussion

9307.	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

9308.	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

9309.	The contrapositive of p implies q is …….
Answer» <P> ANSWER :`(~p) OR (-Q)`

Discussion

9310.	Solve the equations: Q. sqrt(x^(2)-3x)=4x^(2)-12x-3.
Answer» ANSWER :`(3pmsqrt(13))/(2),(6pm3sqrt(5))/(4)`.

Discussion

9311.	If the sum of reciprocals of x-and y-inercepts of a line is a constant k then theline passes through the fixed point whose co-ordinates are
Answer» (K,k) `((1)/(k),(1)/(k))` (k,-k) (-k,-k) ANSWER :B

Discussion

9312.	An the following statement, identify the connecting word and break it in to components ''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

9313.	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

9314.	Find distance between following pair of points : (2, 3, 5) and (4, 3, 1)
Answer» ANSWER :`2SQRT5` UNIT

Discussion

9315.	If a,b,c are in A.P. thentan ""( A)/(2) tan "" ( C) /(2) =
Answer» `1//4` ` 1//3` ` 3` `4` ANSWER :B

Discussion

9316.	IF the angles of triangle are in the ratio 1:1:4 then the ratio of the perimeter of the triangle to its largest side is
Answer» `SQRT(2)+2:sqrt(3)` `3:2` `sqrt(3)+2:sqrt(2)` `sqrt(3)+2:sqrt(3)` ANSWER :C

Discussion

9317.	If the hypotenuse of a right angled triangle is four times the lengthof the perpendicular drawn from the opposite vertex to it, then the difference of twoacute angles is
Answer» ` 30 ^(@) ` ` 45 ^(@ ) ` ` 60 ^(@) ` ` 75 ^(@) ` ANSWER :C

Discussion

9318.	Find the derivative of f(x) = x^(2) .
Answer» ANSWER :2X

Discussion

9319.	Domain of f(x)=(1)/(6)sqrt(log_(10)(5x-x^(2))) is
Answer» (0, 5) (1, 4) (1 , 3) `[(5-SQRT(21))/(2) . (5 + sqrt(21))/(2)]` ANSWER :D

Discussion

9320.	If y = ae ^(- bx) cos (cx -d )show thaty _(1) + 2 by _(1) + (b^(2)+ c ^(2)) y=0
Answer» ANSWER :`(B ^(2) + X ^(2)) y`

Discussion

9321.	The plane x-y-z =2 is rotated through an angle 90^(@) about its line of intersection with the plane x + 2y + z=2. Then equation of this pane in new position is
Answer» `5x + 4y + z - 10 =0` `4X + 5y - 3z =0` `2x + y + 2z =9` `3X + 4y - 5Z =9` ANSWER :A

Discussion

9322.	Find the mean of the given data 5,4,11,15,5,13,17,10.
Answer»

Discussion

9323.	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

9324.	Find the derivatives of the function log (sin ^(-1) e ^(x))
Answer» ANSWER :`(e ^(x))/( SIN ^(-1) (e ^(x)). SQRT (1 - e ^(2X )))`

Discussion

9325.	Express sumr_(1)cot.(A)/(2) interms of s .
Answer» ANSWER :` 3S`

Discussion

9326.	Through the centroid of an equilateral triangle, A line parallel to the base is drawn. On this line an arbitrary point P is taken inside the triangle. Let h denote the bot^("lar") distance of P from the base, h_1 h_2 are bot^("lar") distances from other two sides then
Answer» `h=(h_(1)+h_(2))/(2)` `h=SQRT(h_(1)h_(2))` `h=(2h_(1)h_(2))/(h_(1)+h_(2))` `h=((h+h_(2))sqrt(3))/(4)` Answer :a

Discussion

9327.	Let P(n) be statement and let P(k) rArr P(k+1) ,for some natural number k, then P(n) is true for all n in N
Answer» ANSWER :FALSE

Discussion

9328.	List all the elements of the following sets : B= {x : x is a letter of the word ''EQUATION''}
Answer» ANSWER :`B= {B, Q, U, A, T, I, O, N}`

Discussion

9329.	{ n (n+1) (2n+1) : n in Z} sub
Answer» `{ 6K : k in Z}` `{ 12k : k in Z}` `{ 18 k : k in Z}` `{ 24k: k in Z}` ANSWER :A

Discussion

9330.	The straight lines represented by the equation 135x^2+136xy+33y^2=0 are eqally inclined to the line
Answer» x-2y=7 x+2y=7 x-2y=4 3x+2y=4 Answer :B

Discussion

9331.	A) 49^(n) + 16n +1 is divisible by A ( n in N) B) 3^(2n) + 7 is divisible by B ( n in N) C) 4^(n ) - 3n -1 is divisible by C ( n in n) D) 3^( 3n ) - 26 n - 1 is divisible by D (n in N) then the increasing order of A, B, C, D is
Answer» A, B, C, D C, B, A, D B, C, A, D A, C, B, D Answer :C

Discussion

9332.	If x =cos^3 theta, y = sin^3 theta then sqrt(1+((dy)/(dx))^2)=
Answer» `tan^2 THETA` `Sec^2 theta` `SECTHETA` `\|Sectheta\|` ANSWER :D

Discussion

9333.	A line cuts x-axis at A and y-axis B such that AB=l Match the following
Answer» ANSWER :A-q;B-r;C-s;D-p

Discussion

9334.	If three points (h,0), (a,b) and (0,k) lie on a line, show that (a)/( h) + (b)/(k)=1.
Answer» ANSWER :`(a)/(H) + (B)/( K) =1`

Discussion

9335.	Find all the values oftheta satisfying the equationcos 2 theta - cos 8 theta + cos 6 theta =1, such that 0 le theta le pi.
Answer» ANSWER :`PI`

Discussion

9336.	If 1+sin theta=9 costheta and 0^(0) le theta le 90^(@) then 5(1-cos theta)=
Answer» `sin THETA` `2 sin theta` `4 sin theta ` `tan theta` Answer :C

Discussion

9337.	Find the ratio in which the following straight lines divide the line segments joining the given points. State whether the points lie on the same side or on either side of the straight line 3x-4y=7,(2,-7) and (-1,3)
Answer» ANSWER :27:22 OPPOSITE SIDE

Discussion

9338.	Find the ratio in which the following straight lines divide the line segments joining the given points. State whether the points lie on the same side or on either side of the straight line 2x+3y-20=,(2,3)(2,10)
Answer» ANSWER :`1:2` same SIDE

Discussion

9339.	Find the ratio in which the following straight lines divide the line segments joining the given points. State whether the points lie on the same side or on either side of the straight line 2x+3y=5,(0,0) and (-2,1)
Answer» ANSWER :`-5:6` same SIDE

Discussion

9340.	A function f satisfies the condition f(x) - f'(x) +f'(x) + f''(x) + ......, where f(x) is a differentiable function indefinitely and dash denotes the order of derivative . If f(0) =1 , then f(x) is
Answer» `E^(X//2)` `e^(x)` `e^(2X)` `e^(4X)` ANSWER :A

Discussion

9341.	A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. A cup B
Answer» Answer :`={1, 2, 3, 4, 5, 6, 7, 8}`

Discussion

9342.	Find the equation of the ellipse with focus at (1, -1), directrix x = 0, and e=sqrt(2)/2,
Answer» ANSWER :`X^(2)+2Y^(2)-4x+4y+4=0`

Discussion

9343.	The sum of three numbers in G.P. is 56. If we subtact 1,7,21 from these numbers in that order, we obtai an A.P. Find the numbers.
Answer» ANSWER :8,16,32

Discussion

9344.	Express the following in the form a+ bi (i-1)/(i+1)
Answer» ANSWER :`0+1i`

Discussion

9345.	Let f(theta) =(cot theta)/(1+ cot theta) and alpha+ beta=(5pi)/4, then the value of f(alpha)f(beta) is:
Answer» `1/2` `-1/2` 2 3 Answer :A

Discussion

9346.	Which of the following are sets ? Justify your answer. A team of eleven best-cricket batsmen of the world.
Answer» ANSWER :V

Discussion

9347.	If the foot of the perpendicular from the origin to plane is P (a,b,c), the equation of the plane is
Answer» `x/a + y/b + z/c =3` `AX + by + CZ = 3` `ax + by + cz =a ^(2) + b ^(2) + c ^(2)` `ax + by + cz =a + b + c` ANSWER :C

Discussion

9348.	In triangle ABC, b^(2), sin2C+c^(2) sin 2B-2bc where b=20 c=21 then inradius =
Answer» 4 6 5 7 Answer :B

Discussion

9349.	If x = (1 + t)/(t^3) and (3 + 4t)/(2t^2) then =
Answer» `1 - y'` `1 + y'` `y' -1` `y'` ANSWER :B

Discussion

9350.	List all the elements of the following sets : C = {x : x is an integer, x^(2) ≤ 4}
Answer» ANSWER :`C= { –2, –1, 0, 1, 2 }`

Discussion

Explore topic-wise InterviewSolutions in .

Without solving, find the nature of the roots of the following equations: (i) 3x^(2)-7x+5=0. (ii) 4x^(2)+4x+1=0. (iii) 3x^(2)+7x+2=0. (iv) x^(2)+px-q^(2)=0.

A box contains 1 red and 3 identical white balls. Two balls are draw at random in succession without replacement. Write the sample space for this experiment.

The range of alpha for which the equation sin^(4)x+cos^(4)x+sin2x+alpha=0 has solution

The function f:(-oo, -1) to (0, e^(5)] defined by f(x)=e^(x^(3)-3x+2) is

Evaluate the following limits in lim_(xrarr0)(sinax)/(bx)

If |(alpha,x,x,x),(x,beta,x,x),(x,x,gamma,x),(x,x,x,delta)| = f(x) - x f' (x) then f(x) is equal to

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. The sand heats up quickly in the Sun and does not cool down fast at night.

The contrapositive of p implies q is …….

Solve the equations: Q. sqrt(x^(2)-3x)=4x^(2)-12x-3.

If the sum of reciprocals of x-and y-inercepts of a line is a constant k then theline passes through the fixed point whose co-ordinates are

An the following statement, identify the connecting word and break it in to components ''All rational numbers are real and all real numbers are not complex''.

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.

Find distance between following pair of points : (2, 3, 5) and (4, 3, 1)

If a,b,c are in A.P. thentan ""( A)/(2) tan "" ( C) /(2) =

IF the angles of triangle are in the ratio 1:1:4 then the ratio of the perimeter of the triangle to its largest side is

If the hypotenuse of a right angled triangle is four times the lengthof the perpendicular drawn from the opposite vertex to it, then the difference of twoacute angles is

Find the derivative of f(x) = x^(2) .

Domain of f(x)=(1)/(6)sqrt(log_(10)(5x-x^(2))) is

If y = ae ^(- bx) cos (cx -d )show thaty _(1) + 2 by _(1) + (b^(2)+ c ^(2)) y=0

The plane x-y-z =2 is rotated through an angle 90^(@) about its line of intersection with the plane x + 2y + z=2. Then equation of this pane in new position is

Find the mean of the given data 5,4,11,15,5,13,17,10.

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).

Find the derivatives of the function log (sin ^(-1) e ^(x))

Express sumr_(1)cot.(A)/(2) interms of s .

Through the centroid of an equilateral triangle, A line parallel to the base is drawn. On this line an arbitrary point P is taken inside the triangle. Let h denote the bot^("lar") distance of P from the base, h_1 h_2 are bot^("lar") distances from other two sides then

Let P(n) be statement and let P(k) rArr P(k+1) ,for some natural number k, then P(n) is true for all n in N

List all the elements of the following sets : B= {x : x is a letter of the word ''EQUATION''}

{ n (n+1) (2n+1) : n in Z} sub

The straight lines represented by the equation 135x^2+136xy+33y^2=0 are eqally inclined to the line

A) 49^(n) + 16n +1 is divisible by A ( n in N) B) 3^(2n) + 7 is divisible by B ( n in N) C) 4^(n ) - 3n -1 is divisible by C ( n in n) D) 3^( 3n ) - 26 n - 1 is divisible by D (n in N) then the increasing order of A, B, C, D is

If x =cos^3 theta, y = sin^3 theta then sqrt(1+((dy)/(dx))^2)=

A line cuts x-axis at A and y-axis B such that AB=l Match the following

If three points (h,0), (a,b) and (0,k) lie on a line, show that (a)/( h) + (b)/(k)=1.

Find all the values oftheta satisfying the equationcos 2 theta - cos 8 theta + cos 6 theta =1, such that 0 le theta le pi.

If 1+sin theta=9 costheta and 0^(0) le theta le 90^(@) then 5(1-cos theta)=

Find the ratio in which the following straight lines divide the line segments joining the given points. State whether the points lie on the same side or on either side of the straight line 3x-4y=7,(2,-7) and (-1,3)

Find the ratio in which the following straight lines divide the line segments joining the given points. State whether the points lie on the same side or on either side of the straight line 2x+3y-20=,(2,3)(2,10)

Find the ratio in which the following straight lines divide the line segments joining the given points. State whether the points lie on the same side or on either side of the straight line 2x+3y=5,(0,0) and (-2,1)

A function f satisfies the condition f(x) - f'(x) +f'(x) + f''(x) + ......, where f(x) is a differentiable function indefinitely and dash denotes the order of derivative . If f(0) =1 , then f(x) is

A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. A cup B

Find the equation of the ellipse with focus at (1, -1), directrix x = 0, and e=sqrt(2)/2,

The sum of three numbers in G.P. is 56. If we subtact 1,7,21 from these numbers in that order, we obtai an A.P. Find the numbers.

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

Let f(theta) =(cot theta)/(1+ cot theta) and alpha+ beta=(5pi)/4, then the value of f(alpha)f(beta) is:

Which of the following are sets ? Justify your answer. A team of eleven best-cricket batsmen of the world.

If the foot of the perpendicular from the origin to plane is P (a,b,c), the equation of the plane is

In triangle ABC, b^(2), sin2C+c^(2) sin 2B-2bc where b=20 c=21 then inradius =

If x = (1 + t)/(t^3) and (3 + 4t)/(2t^2) then =

List all the elements of the following sets : C = {x : x is an integer, x^(2) ≤ 4}