14949 + Interview Questions in Maths in Class 11 Page 50 InterviewSolution

2451.	If the points with position vectors 60bar(i)+3bar(j), 40bar(i)-8bar(j), abar(i)-52bar(j) are collinear then a =
Answer» -40 40 -80 80 Answer :A

Discussion

2452.	Briefly explain the types of physical quantities.
Answer» Solution :(i) Physical quantities are classified into two TYPES. There are FUNDAMENTAL and derived quantities. (ii) Fundamental or BASE quantities are quantities which cannot be EXPRESSED in terms of any other physical quantities. These are length, mass, time, electric current, temperature, luminous intensity and amount of substance. (iii) Quantities that can be expressed in terms of fundamental quantities are called derived quantities. For example, area, volume, velocity, acceleration, FORCE.

Discussion

2453.	"Sech"^(-1) (sin theta)=
Answer» `log("cos"(THETA)/(2))` `log("SIN"(theta)/(2))` `log("cos"(theta)/(2))` `log("cot"(theta)/(2))` Answer :D

Discussion

2454.	Find the domain and the range of the real function f defined by f(x)= \|x-1\|
Answer» ANSWER :`[0, OO)`

Discussion

2455.	In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy (a) one ticket (b) two tickets (c ) 10 tickets.
Answer» ANSWER :`=(""^(9990)C_(10))/(""^(10000)C_(10))`

Discussion

2456.	Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C.
Answer» ANSWER :`B= C`.

Discussion

2457.	If a,b,c are unit vectors satisfying the relation a + b+sqrt(3) c = 0, then the angle between a and b is
Answer» `(PI)/(6)` `(pi)/(4)` `(pi)/(3)` `(pi)/(2)` Answer :C

Discussion

2458.	Write the following sets in the set builder form : C= {(1)/(2), (2)/(5), (3)/(10), (4)/(17), (5)/(26), (6)/(37), (7)/(50)}
Answer» Answer :`C= {x : x =(n)/(n^(2)+1), n in N, n le 7}`

Discussion

2459.	Domain of f(x)= sqrt(2-2x-x^(2)) is………
Answer» `[-SQRT3, sqrt3]` `[-1-sqrt3, -1 + sqrt3]` `[-2, 2]` `[-2- sqrt3, -2 + sqrt3]` ANSWER :B

Discussion

2460.	If the roots of the equation x^(3)-10x+11=0 are u, v, and w, then the value of 3cosec^(2)(tan^(-1)u+tan^(-1)v+tan^(-1)w) is
Answer» ANSWER :6

Discussion

2461.	f(X) = (7\|x\| + 5x)/(7\|x\| - 5x) , x ne , f(0) = 6at x = 0 f(x) is
Answer» continuous discontinuous not DETERMINED NONE ANSWER :B

Discussion

2462.	The radius of the circle : 2x^(2) + 2y^(2) = x is
Answer» `(1)/(2)` `(1)/(4)` `(1)/(8)` 4 Answer :B

Discussion

2463.	Write down the equation of the straight line cuttting off intercepts a and b from the axes where a = -2, b= 3
Answer» ANSWER : `3x-2y+6=0`

Discussion

2464.	Let a function y = y(x) be defined parametrically by x = 2t -\|t\| , y = t^2 + t\|t\| then
Answer» `y'(x) = 4X` when `x gt -` `y'(x) = 0` when `x lt 0` `y'(x)` does not exist at x= 0 `y'(x) = 2` for all x ANSWER :A::B

Discussion

2465.	Find the domains of the following functions f(x) = ( x^(2) + 1)/( x^(2) - 3x + 2)
Answer» ANSWER :R-{1,2]

Discussion

2466.	Find equation of parallel line to line 2x+3y+11=0 and whose sum of intercept is 15.
Answer» ANSWER :`2x+3y-18=0`

Discussion

2467.	Consider the function f(x) = (x^2 - 4)/(x - 2) Evaluate lim_(x rarr 2) (x^2 - 4)/(x -2). choose the correct answer from the bracket given below
Answer» 6 7 4 5 Solution :4

Discussion

2468.	If the two pairs of lines ax^(2)+2pxy-ay^(2)=0 and bx^(2)+2qxy-by^(2)=0 are such that each pair bisects the angle between other pair then
Answer» <P>pq-ab=0 pq+ab=0 `(p)/(Q)+(a)/(B)=0` `(p)/(q)-(a)/(b)=0` ANSWER :B

Discussion

2469.	If f(x) = \|(x,x^2,x^3),(1,2x,3x^2),(0,2,6x)\|, then f^(1)(x)=
Answer» 0 6x `12x^3` `6x^2` ANSWER :D

Discussion

2470.	Evaluate the following limits : lim_(x to 0) (3^(2x)-2^(3x))/x
Answer» ANSWER :` LOG (9/8)`

Discussion

2471.	If a,b,c are the three consecutive odd numbers then the line ax-by+c=0 passes through the fixed point
Answer» (2,3) (-1,2) (0,1) (1,2) ANSWER :D

Discussion

2472.	Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls such that the selection consists of 3 balls of each colour.
Answer» ANSWER :2000

Discussion

2473.	Solve 2 sin ^(2) phi = sin phi, ( 0^(@) le phi lt 360^(@)).
Answer» ANSWER :`150^(@)`

Discussion

2474.	Evaluate the following limits : Lim_(x to 0) (3^(2x)-2^(3x))/x
Answer» ANSWER :`LOG (9/8)`

Discussion

2475.	The value of tan3A-tan2A-tanA is
Answer» `tan3Atan2AtanA` `-tan3Atan2AtanA` `tanAtan2A-tan2Atan3A-tan3AtanA` NONE of the above Answer :A

Discussion

2476.	Evaluate the following limits : Lim_(xto pi) (sin 2x)/(sinx)
Answer» ANSWER :`-2`

Discussion

2477.	A dieis rolled . Ifthe outcome is an even number , what is the probability it is a prime number .
Answer» ANSWER :`(1)/(3)`

Discussion

2478.	Solve the general vlaue. sin theta + cos theta = sqrt2
Answer» ANSWER :`(2N + (1)/(4)) PI`

Discussion

2479.	If (cos (alpha - 3 theta))/( cos^(3) theta)=(sin (alpha - 3 theta))/(sin^(3) theta) = m then
Answer» `cos 2 ALPHA = (2 m^(2) - 9 m^(2) + 8)/( m^(2))` `cos alpha = ( 2 - m^(2))/( m)` `cos 2 alpha = (2 m^(2) + 9 m ^(2) + 8)/( m^(2))` `cos alpha = ( 2 + m^(2))/(m)` ANSWER :A::B

Discussion

2480.	If the roots of x^(2)-bx+c=0 be two consecutive integers, then find the value of b^(2)-4c.
Answer» ANSWER :1

Discussion

2481.	Find the eccentricity of the ellipse ""(x-3)^(2)/8+(y-4)^(2)/6=1.
Answer» ANSWER :`1/2`

Discussion

2482.	If cos^(3) theta + cos^(3)((2pi)/(3) + theta) + cos^(3)((4pi)/(3) + theta) = a cos 3 theta, then a =
Answer» `1/4` `3/4` `5/4` `7/4` ANSWER :B

Discussion

2483.	The minimum value of expression sin alha + sin beta + sin gammawhere alpha, beta , gamma are positive real numbers satisfying alpha + beta + gamma = pi
Answer» 0 `-3` NEGATIVE possitive ANSWER :D

Discussion

2484.	Let f(x) = x^2 - 2x + 3. Then find f (f (x) )
Answer» SOLUTION :`x^4 - 4x^3 + 8X^2 - 8x +6]`

Discussion

2485.	Given that a,b,c are the sides of a triangleABCwhich is right angled at vertex C, then the minimum value of: (c/a + c/b)^(2) is:
Answer» 0 8 1 2 Answer :B

Discussion

2486.	Find (dy)/(dx) in the following : y= cos^(-1) ((1-x^(2))/(1+x^(2))), 0 lt x lt 1.
Answer» ANSWER :`(2)/(1+x ^(2))`

Discussion

2487.	With usual notation , if in triangle ABC, (b+ c)/11 = (c + a)/12 = (a + b)/13 , then cos A : cos B : cos C=
Answer» `7 : 19 : 25` `19 : 25 : 7` `19 : 7 : 25` `7 : 25 : 19` ANSWER :A

Discussion

2488.	If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following \|z-z_(1)\|= \|z-z_(2)\|
Answer» ANSWER :P lies on the PERPENDICULAR bisector of the LINE segment AB

Discussion

2489.	If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following \|z-z_(1)\| + \|z-z_(2)\| = \|z_(1)-z_(2)\|
Answer» ANSWER :`A(z_(1)) and B (z_(2))`

Discussion

2490.	Points D,E are taken on the side BC of a triangle ABC, such that BD=DE=EC. IF angle BAD=x, angle DAE=y, angle EAC=z, then the value of (sin(x+y)sin (y+z))/(sinx sin z)=
Answer» 4 3 7 8 Answer :A

Discussion

2491.	Express each of the following in the form b or bi, where b is a real number (20i)/(4)
Answer» ANSWER :5I

Discussion

2492.	Find (dy)/(dx)if x =a cos ^(2) theta , y =b sin ^(2) theta .
Answer» ANSWER :`b/a`

Discussion

2493.	If 4 cos 36^@ + cot(7(1^@)/2)= sqrt(n_1)+sqrt(n_2)+sqrt(n_3)+sqrt(n_4)+sqrt(n_5)+sqrt(n_6) then the product of the digits in sum_(i=1)^(6) n_(i)^2 =
Answer» ANSWER :9

Discussion

2494.	Find the value of z satisfying the euqation \|z\|-z=1+2i.
Answer» ANSWER :`3//2-2i`

Discussion

2495.	If a^(2)+4b^(2)-9c^(2)=4ab, then the line on which is meet the point of concurrency of family of straight line ax+by+3c=0 lies is
Answer» x+y=-1 x+y=1 x+y=3 2x-y=0 Answer :C

Discussion

2496.	Evaluate the following limits : Lim_(x to 0 ) (x^(n)-1)/(x-1)
Answer» ANSWER :N

Discussion

2497.	if ""^18C_15 + 2(""^18C_16) + ""^17C_16 + 1 = ""^nC_3 then n = .....
Answer» 19 20 18 24 Answer :B

Discussion

2498.	If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find A ∩ B
Answer» ANSWER :B

Discussion

2499.	Write Negation of the following statements: In leap year there are 366 days.
Answer» ANSWER :LEAP YEAR has not 366 DAYS.

Discussion

2500.	Obtain the equation of the parabola with given conditions:Focus (-1,2) equation of the directrix x - y + 1 = 0.
Answer» ANSWER :`X^(2) + y^(2) + 2XY + 2x - 6y + 9 = 0`

Discussion

Explore topic-wise InterviewSolutions in .

If the points with position vectors 60bar(i)+3bar(j), 40bar(i)-8bar(j), abar(i)-52bar(j) are collinear then a =

Briefly explain the types of physical quantities.

"Sech"^(-1) (sin theta)=

Find the domain and the range of the real function f defined by f(x)= |x-1|

In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy (a) one ticket (b) two tickets (c ) 10 tickets.

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C.

If a,b,c are unit vectors satisfying the relation a + b+sqrt(3) c = 0, then the angle between a and b is

Write the following sets in the set builder form : C= {(1)/(2), (2)/(5), (3)/(10), (4)/(17), (5)/(26), (6)/(37), (7)/(50)}

Domain of f(x)= sqrt(2-2x-x^(2)) is………

If the roots of the equation x^(3)-10x+11=0 are u, v, and w, then the value of 3cosec^(2)(tan^(-1)u+tan^(-1)v+tan^(-1)w) is

f(X) = (7|x| + 5x)/(7|x| - 5x) , x ne , f(0) = 6at x = 0 f(x) is

The radius of the circle : 2x^(2) + 2y^(2) = x is

Write down the equation of the straight line cuttting off intercepts a and b from the axes where a = -2, b= 3

Let a function y = y(x) be defined parametrically by x = 2t -|t| , y = t^2 + t|t| then

Find the domains of the following functions f(x) = ( x^(2) + 1)/( x^(2) - 3x + 2)

Find equation of parallel line to line 2x+3y+11=0 and whose sum of intercept is 15.

Consider the function f(x) = (x^2 - 4)/(x - 2) Evaluate lim_(x rarr 2) (x^2 - 4)/(x -2). choose the correct answer from the bracket given below

If the two pairs of lines ax^(2)+2pxy-ay^(2)=0 and bx^(2)+2qxy-by^(2)=0 are such that each pair bisects the angle between other pair then

If f(x) = |(x,x^2,x^3),(1,2x,3x^2),(0,2,6x)|, then f^(1)(x)=

Evaluate the following limits : lim_(x to 0) (3^(2x)-2^(3x))/x

If a,b,c are the three consecutive odd numbers then the line ax-by+c=0 passes through the fixed point

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls such that the selection consists of 3 balls of each colour.

Solve 2 sin ^(2) phi = sin phi, ( 0^(@) le phi lt 360^(@)).

Evaluate the following limits : Lim_(x to 0) (3^(2x)-2^(3x))/x

The value of tan3A-tan2A-tanA is

Evaluate the following limits : Lim_(xto pi) (sin 2x)/(sinx)

A dieis rolled . Ifthe outcome is an even number , what is the probability it is a prime number .

Solve the general vlaue. sin theta + cos theta = sqrt2

If (cos (alpha - 3 theta))/( cos^(3) theta)=(sin (alpha - 3 theta))/(sin^(3) theta) = m then

If the roots of x^(2)-bx+c=0 be two consecutive integers, then find the value of b^(2)-4c.

Find the eccentricity of the ellipse ""(x-3)^(2)/8+(y-4)^(2)/6=1.

If cos^(3) theta + cos^(3)((2pi)/(3) + theta) + cos^(3)((4pi)/(3) + theta) = a cos 3 theta, then a =

The minimum value of expression sin alha + sin beta + sin gammawhere alpha, beta , gamma are positive real numbers satisfying alpha + beta + gamma = pi

Let f(x) = x^2 - 2x + 3. Then find f (f (x) )

Given that a,b,c are the sides of a triangleABCwhich is right angled at vertex C, then the minimum value of: (c/a + c/b)^(2) is:

Find (dy)/(dx) in the following : y= cos^(-1) ((1-x^(2))/(1+x^(2))), 0 lt x lt 1.

With usual notation , if in triangle ABC, (b+ c)/11 = (c + a)/12 = (a + b)/13 , then cos A : cos B : cos C=

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)|= |z-z_(2)|

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| + |z-z_(2)| = |z_(1)-z_(2)|

Points D,E are taken on the side BC of a triangle ABC, such that BD=DE=EC. IF angle BAD=x, angle DAE=y, angle EAC=z, then the value of (sin(x+y)sin (y+z))/(sinx sin z)=

Express each of the following in the form b or bi, where b is a real number (20i)/(4)

Find (dy)/(dx)if x =a cos ^(2) theta , y =b sin ^(2) theta .

If 4 cos 36^@ + cot(7(1^@)/2)= sqrt(n_1)+sqrt(n_2)+sqrt(n_3)+sqrt(n_4)+sqrt(n_5)+sqrt(n_6) then the product of the digits in sum_(i=1)^(6) n_(i)^2 =

Find the value of z satisfying the euqation |z|-z=1+2i.

If a^(2)+4b^(2)-9c^(2)=4ab, then the line on which is meet the point of concurrency of family of straight line ax+by+3c=0 lies is

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

if ""^18C_15 + 2(""^18C_16) + ""^17C_16 + 1 = ""^nC_3 then n = .....

If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find A ∩ B

Write Negation of the following statements: In leap year there are 366 days.

Obtain the equation of the parabola with given conditions:Focus (-1,2) equation of the directrix x - y + 1 = 0.