14949 + Interview Questions in Maths in Class 11 Page 124 InterviewSolution

6151.	If perpendicular distance between lines 3x + 4y + 10 = 0and 6x + 8y + k = 0is 7/2 unit then k = ........
Answer» ANSWER :55

Discussion

6152.	Simplify: i+ 2i^(2) + 3i^(3) + i^(4)
Answer» ANSWER :`-1-2i`

Discussion

6153.	Iff'(x) = 4x - 5 and f(2) = 1, find f(x).
Answer» ANSWER :` 2X^(2) -5X + 3`

Discussion

6154.	sqrt((y)/( x))+ sqrt((x)/(y))= 2 implies (dy)/(dx) =
Answer» `(x^2+y^2)/(x+y)` `(x^2-y^2)/(x+y)` 1 2 Answer :C

Discussion

6155.	If the domain of f(x) is [0, 5], then the number of integers in the domain of f(log_(2)(x^(2)+2x-3)) is ________
Answer» ANSWER :8

Discussion

6156.	Find the derivative of the w.r.to x. (tan x)^( sin x)
Answer» ANSWER :`(tan x ) ^( SIN x ) [cos x. LOG ( tan x ) + sec x]`

Discussion

6157.	Equation of line equidistance from the lines 2x+y+4=0 and 3x+6y-5=0 is
Answer» 3x-3y+17=0 5x+7y-5=0 3x-3y+19=0 9x-9y+17=0 Answer :A

Discussion

6158.	Obtain equation of circle in Centre (3,4) Touches X - axis.
Answer» Answer :`X^(2) + y^(2) - 6x - 8y + 9 = 0`

Discussion

6159.	If the distance from the origin to the line ax+by+5=0 is5/(sqrt(10)), then the distance from the origin to the line ax+by+10=0 is
Answer» `sqrt(5)` `sqrt(2)` `sqrt(10)` `sqrt(20)` Answer :C

Discussion

6160.	What is the general form of the equation of a parabola with vertex at the origin and axis as the x-axis?
Answer» SOLUTION :`y^2=+-4ax`

Discussion

6161.	If 0 lt alpha, beta lt pi//4, cos ( alpha + beta )=4//5 , sin (alpha - beta) =5//13 " then " tan 2alpha =
Answer» `33//56` `56//33` `16//63` `14//63` ANSWER :B

Discussion

6162.	sin x + sin^(2) x + sin^(3) x = 1 rArr cos^(6) x - 4cos^(4) x + cos^(2) x=
Answer» 4 2 1 0 Answer :A

Discussion

6163.	The value of cos ^(2) 10^(@) cos 50^(@) + cos ^(2) 50^(@) is equal to
Answer» `4/3` `1/3` `3/4` 3 Answer :C

Discussion

6164.	Write the negation of the following statements: r: For every real number x such that xgt1 or xlt1.
Answer» ANSWER :There EXISTS AREAL number x such that `xgt1` and `XLT1`.

Discussion

6165.	If Agt0,Bgt0,andA+B=(pi)/(3), then the maximum value of tan A tan B is
Answer» `(1)/(SQRT(3))` `(1)/(3)` 3 `sqrt(3)` ANSWER :B

Discussion

6166.	Find the area of the triangle formed by the lines y - x = 0, x + y = 0 " and " x - k = 0 .
Answer» ANSWER :`K^(2)` SQUARE UNITS

Discussion

6167.	State the converse and contrapositive of each of the following statements: q: I go to a beach whenever it is a sunny day.
Answer» Answer :The given statement can be written as ''If it is a SUNNY DAY, then I go to a BEACH. The CONVERSE of the statement is If I go to beach, then it is a sunny day. The CONTRAPOSITIVE is If I do not go to a beach, then it is not a sunny day.

Discussion

6168.	Obtain equation of circle in Centre (-3,4) Touches X - axis.
Answer» ANSWER :`x^(2) + y^(2) + 6X - 4y - 36 = 0`

Discussion

6169.	For what value of k will be the equations x^(2)-kx-21=0 and x^(2)-3kx+35=0 have one common root.
Answer» ANSWER :`k=+-4`

Discussion

6170.	Write the equation of the lines for which tan theta = 1/2 , " where " thetais the inclination of the line and (i) y- intercept is - 3/2 (ii) x - interecept is 4.
Answer» ANSWER :`2Y - X + 4= 0 `

Discussion

6171.	Let vec(a)= vec(i) + vec(j), vec(b)= 2vec(j)-vec(k). If vec(r ) xx vec(a) = vec(b) xx vec(a), vec(r ) xx vec(b) = vec(a) xx vec(b), then (vec(r ))/(\|vec(r )\|)=
Answer» `(1)/(sqrt11) (vec(i) + 3vec(j)-vec(k))` `(1)/(sqrt11) (vec(i) -3vec(j) + vec(k))` `(1)/(SQRT3) (vec(i) -vec(j) + vec(k))` `(1)/(sqrt3) (vec(i) + vec(j) -vec(k))` ANSWER :A

Discussion

6172.	If the function f: [2, oo) rarr [-1, oo) is defined by f(x)=x^(2)-4x+3 then f^(-1)(x)=
Answer» `2-SQRT(x+1)` `2+ sqrt(x+1)` `(2-sqrt(x+1))/(5)` `(2+sqrt(x+1))/(5)` ANSWER :B

Discussion

6173.	The point on the line 4x-y-2=0 which is equidistant from the points (-5,6) and (3,2) is
Answer» (2,6) (4,14) (1,2) (3,10) ANSWER :B

Discussion

6174.	Refer to question 6 above, state tru or false: (give reaon for your answer) (i) A and B are mutully exclusive (ii) A and B are mutually exclusive and exhaustive (iii) A = B' (iv) A and Care mutually exclusive. (v) A and B' are mutually exclusive. (vi0 A', B', C are mutually exclusive and exhaustive.
Answer» Answer :(i) True, (III) True, (iii) True, (iv) False, (V) False, (VI) False.

Discussion

6175.	Find the sum of n terms of each of the following 3^(2) + 7^(2) + 11^(2) +……
Answer» ANSWER :`(N)/(3) (16N^(2)+ 12n-1)`

Discussion

6176.	If [a b c] = 3, then the volume (in cube units) of the parallelopiped with 2a + b, 2b + c and 2c + a as coteminous edges is
Answer» 15 22 25 27 Answer :D

Discussion

6177.	If Sigma_(0)^(n=1)(r+2)/(r+1)= prod-(r=10)^(99)log_(r)(31), lies two successive integers whose sum is equal to
Answer» 5 7 9 100 Solution :N//A

Discussion

6178.	Two dice are thrown write the sample space for this experiment. Describe the following events. Event A : The sum of the number on the dice is divisible by 4. Event B : The sum of the numbers on the dice is divisible by 3. Event C: The sum of the numbers is less than 7. Event D: Both the numbers on the dice are even.
Answer» ANSWER :`S={{:(x,y):{:(x=1,2,3,4,5,6),(y=1,2,3,4,5,6):}}` `A = {(1, 3) (2, 2) (2, 6) (3, 1) (3,5) (4, 4) (5, 3) (6, 2) (6, 6)}` `B = {(1, 2) (1,5) (2, 1) (2, 4) (3, 3) (3, 6) (4, 2)(4, 5) (5, 1) (5, 4) (6, 3) (6, 6)}` `C = {(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (2, 1) (2, 2)(2, 3) (2, 4) (3, 1) (3, 2) (3, 3) (4, 1) (4, 2)(5, 1)}` `D = {(2, 2) (2, 4) (2, 6) (4, 2) (4, 4) (4, 6) (6, 2)(6, 4) (6, 6)}`

Discussion

6179.	For a gt 0, t in (0, (pi)/(2)). Let x= sqrt(a^(sin^(-1)t)) and y= sqrt(a^(cos^(-1)t)), then 1+((dy)/(dx))^(2) equals.
Answer» `(X^(2))/(y^(2))` `(y^(2))/(x^(2))` `(x^(2)+y^(2))/(y^(2))` `(x^(2)+y^(2))/(x^(2))` ANSWER :D

Discussion

6180.	Three numbers, whose sum is 21, are in A.P. If 2, 2, 14 are added to them respectively, the resulting numbers are in G.P. Find the numbers.
Answer» ANSWER :1,7,13, or 25 ,7,-11

Discussion

6181.	The sides of a rectangle are (6-x) cm and (x-3) cm . If its area is maximum then x=
Answer» 4 4.5 4.8 4.6 Answer :B

Discussion

6182.	Let P(1,1) and Q(3,2) be given points. Find the point R on the x-axis such that PR+RQ is minimum
Answer» `(-2//3,0)` `(-5//3,0)` `(5//2,0)` `(5//3,0)` ANSWER :D

Discussion

6183.	Write the 4th term from the end in the expansion of ((x^3)/( 2) - (2)/(x^2) )^9.
Answer» ANSWER :`(672)/(x^3)`

Discussion

6184.	Find the derivative of the function 5 sin x + log gx
Answer» ANSWER :`5 COS + E ^(X) ((1)/(x) + LOG x )`

Discussion

6185.	If A=cos^(2)10^(@)+cos^(2)50^(@)+cos^(2)70^(@), B="sin"^(4)(3pi)/8-"cos"^(4)(3pi)/8 C="cos"^(2)pi/10+"cos"^(2)(2pi)/5+"cos"^(2)(3pi)/5+"cos"^(2)(9pi)/10 then the descending order A,B,C is
Answer» C,A,B A,B,C b,a,c,d C,B,A Answer :A

Discussion

6186.	Solve the general vlaue. sqrt2 sec theta + tan theta =1
Answer» ANSWER :`2 NPI - (PI)/(4)`

Discussion

6187.	If sin+cosecx = 2, then sin^(n)x +cosec^(n) x is equal to
Answer» 2 1 2 `2^(n-2)` ANSWER :A

Discussion

6188.	Calculate the mean and standard deviation using step deviation method for the following data : {:("Class marks"(x_(i)),15,30,45,60,75,90,105,120),("Frequency" (f_(i)),12,14,65,107,157,202,222,230):}
Answer» ANSWER :MEAN = 60.65, S.D. = 25.88

Discussion

6189.	If the equation sin x(sin x + cos x)=k has real solutions then k may lie in the interval
Answer» `[0,(SQRT(2)+1)/(2)]` `[2-sqrt(3),2+sqrt(3)]` `[0,2-sqrt(3)]` `[(1-sqrt(2))/(2),(1+sqrt(2))/(2)]` ANSWER :A::C::D

Discussion

6190.	If the equation x^(3)+bx^(2)+cx+1=0, (bltc) has only one real root alpha then the value of 2tan^(-1)(cosec alpha)+tan^(-1)(2sin alpha sec^(2)alpha) is
Answer» `-PI` `-(pi)/2` `(pi)/2` `pi` ANSWER :A

Discussion

6191.	A man from the top of 100 metres high tower sees a car moving towords the tower at an angle of depression of 30^(@).After some time the angle of depression becomes 60^(@). The distance travelled by the car during this time is _____ metres
Answer» `(100)/(sqrt(3))` `(200)/(sqrt(3))` `(10)/(sqrt(3))` `(20)/(sqrt(3))` ANSWER :B

Discussion

6192.	Write the conjugate of sqrt(-16)-3
Answer» ANSWER :`sqrt-16 -3 " is " -4i-3`

Discussion

6193.	Write the following in the standard notation100xx2+10xx3+4
Answer» ANSWER :`X + 2y - 6 = 0 , 2X + y - 6 = 0 `

Discussion

6194.	Evaluate:sqrt(7-30sqrt(-2))
Answer» ANSWER :`(5-3 SQRT(2)i)or(-5+3sqrt(2)i)`

Discussion

6195.	Determine the mean and standard deviation for the following distribution:
Answer» ANSWER :2.85

Discussion

6196.	The period of the function f(x) = {{:(1",", " when x is a rational"),(0","," when x is irrational"):} is
Answer» 1 2 non-periodic periodic but having no period Answer :D

Discussion

6197.	Find the equation of a circle with centre (2,2)and passes through the point (4,5) .
Answer» ANSWER :`X^(2)+y^(2)-4x-4y=5`

Discussion

6198.	p v q is false if….
Answer» <P>p and Q are TRUE p and q are FALSE p is true and q is false p is false and q is ture Answer :C

Discussion

6199.	Let A = { 1, 2, 3, 4, 5, 6}, B = { 2, 4, 6, 8 }. Find A – B and B – A.
Answer» ANSWER :`{1, 3, 5,}, {8}`

Discussion

6200.	If 3sin A + 4 cos A = 5, then find the value of 4 sin theta - 3 cos theta.
Answer» ANSWER :

Discussion

Explore topic-wise InterviewSolutions in .

If perpendicular distance between lines 3x + 4y + 10 = 0and 6x + 8y + k = 0is 7/2 unit then k = ........

Simplify: i+ 2i^(2) + 3i^(3) + i^(4)

Iff'(x) = 4x - 5 and f(2) = 1, find f(x).

sqrt((y)/( x))+ sqrt((x)/(y))= 2 implies (dy)/(dx) =

If the domain of f(x) is [0, 5], then the number of integers in the domain of f(log_(2)(x^(2)+2x-3)) is ________

Find the derivative of the w.r.to x. (tan x)^( sin x)

Equation of line equidistance from the lines 2x+y+4=0 and 3x+6y-5=0 is

Obtain equation of circle in Centre (3,4) Touches X - axis.

If the distance from the origin to the line ax+by+5=0 is5/(sqrt(10)), then the distance from the origin to the line ax+by+10=0 is

What is the general form of the equation of a parabola with vertex at the origin and axis as the x-axis?

If 0 lt alpha, beta lt pi//4, cos ( alpha + beta )=4//5 , sin (alpha - beta) =5//13 " then " tan 2alpha =

sin x + sin^(2) x + sin^(3) x = 1 rArr cos^(6) x - 4cos^(4) x + cos^(2) x=

The value of cos ^(2) 10^(@) cos 50^(@) + cos ^(2) 50^(@) is equal to

Write the negation of the following statements: r: For every real number x such that xgt1 or xlt1.

If Agt0,Bgt0,andA+B=(pi)/(3), then the maximum value of tan A tan B is

Find the area of the triangle formed by the lines y - x = 0, x + y = 0 " and " x - k = 0 .

State the converse and contrapositive of each of the following statements: q: I go to a beach whenever it is a sunny day.

Obtain equation of circle in Centre (-3,4) Touches X - axis.

For what value of k will be the equations x^(2)-kx-21=0 and x^(2)-3kx+35=0 have one common root.

Write the equation of the lines for which tan theta = 1/2 , " where " thetais the inclination of the line and (i) y- intercept is - 3/2 (ii) x - interecept is 4.

Let vec(a)= vec(i) + vec(j), vec(b)= 2vec(j)-vec(k). If vec(r ) xx vec(a) = vec(b) xx vec(a), vec(r ) xx vec(b) = vec(a) xx vec(b), then (vec(r ))/(|vec(r )|)=

If the function f: [2, oo) rarr [-1, oo) is defined by f(x)=x^(2)-4x+3 then f^(-1)(x)=

The point on the line 4x-y-2=0 which is equidistant from the points (-5,6) and (3,2) is

Find the sum of n terms of each of the following 3^(2) + 7^(2) + 11^(2) +……

If [a b c] = 3, then the volume (in cube units) of the parallelopiped with 2a + b, 2b + c and 2c + a as coteminous edges is

If Sigma_(0)^(n=1)(r+2)/(r+1)= prod-(r=10)^(99)log_(r)(31), lies two successive integers whose sum is equal to

For a gt 0, t in (0, (pi)/(2)). Let x= sqrt(a^(sin^(-1)t)) and y= sqrt(a^(cos^(-1)t)), then 1+((dy)/(dx))^(2) equals.

Three numbers, whose sum is 21, are in A.P. If 2, 2, 14 are added to them respectively, the resulting numbers are in G.P. Find the numbers.

The sides of a rectangle are (6-x) cm and (x-3) cm . If its area is maximum then x=

Let P(1,1) and Q(3,2) be given points. Find the point R on the x-axis such that PR+RQ is minimum

Write the 4th term from the end in the expansion of ((x^3)/( 2) - (2)/(x^2) )^9.

Find the derivative of the function 5 sin x + log gx

If A=cos^(2)10^(@)+cos^(2)50^(@)+cos^(2)70^(@), B="sin"^(4)(3pi)/8-"cos"^(4)(3pi)/8 C="cos"^(2)pi/10+"cos"^(2)(2pi)/5+"cos"^(2)(3pi)/5+"cos"^(2)(9pi)/10 then the descending order A,B,C is

Solve the general vlaue. sqrt2 sec theta + tan theta =1

If sin+cosecx = 2, then sin^(n)x +cosec^(n) x is equal to

Calculate the mean and standard deviation using step deviation method for the following data : {:("Class marks"(x_(i)),15,30,45,60,75,90,105,120),("Frequency" (f_(i)),12,14,65,107,157,202,222,230):}

If the equation sin x(sin x + cos x)=k has real solutions then k may lie in the interval

If the equation x^(3)+bx^(2)+cx+1=0, (bltc) has only one real root alpha then the value of 2tan^(-1)(cosec alpha)+tan^(-1)(2sin alpha sec^(2)alpha) is

A man from the top of 100 metres high tower sees a car moving towords the tower at an angle of depression of 30^(@).After some time the angle of depression becomes 60^(@). The distance travelled by the car during this time is _____ metres

Write the conjugate of sqrt(-16)-3

Write the following in the standard notation100xx2+10xx3+4

Evaluate:sqrt(7-30sqrt(-2))

Determine the mean and standard deviation for the following distribution:

The period of the function f(x) = {{:(1",", " when x is a rational"),(0","," when x is irrational"):} is

Find the equation of a circle with centre (2,2)and passes through the point (4,5) .

p v q is false if….

Let A = { 1, 2, 3, 4, 5, 6}, B = { 2, 4, 6, 8 }. Find A – B and B – A.

If 3sin A + 4 cos A = 5, then find the value of 4 sin theta - 3 cos theta.