14949 + Interview Questions in Maths in Class 11 Page 268 InterviewSolution

13351.	Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
Answer» ANSWER :98450

Discussion

13352.	Prove that the equation y^(2)+2ax+2by+c=0 represents a parabola whose axis is parallel to the axis of x. Find its vertex.
Answer» ANSWER :`((B^2-c)/(2A),-b)`

Discussion

13353.	Find the rank of 55 from the following data: 90, 85, 80, 80, 80, 80,78, 72, 69, 69, 55, 54
Answer» ANSWER :10

Discussion

13354.	Statement-I: If f(x) = coshx - sinhx for x in R then f(x-y)=f(x) divf(y) Statement -II: If f(x) = coshx + sinhx for x in Rthen f(x) is a bijective function Statement-III: coth^(-1)x="cosh"^(-1)(\|x\|)/(sqrt(x^(2)-1)) Which of the above statement is correct?
Answer» only I, II only II, III only I and III I, II, III ANSWER :C

Discussion

13355.	(ii) Find the 4th term from the end in the expansion of ((3)/(x^2) - (x^3)/(6) )^7.
Answer» ANSWER :`= (35)/( 48) x^6`.

Discussion

13356.	If bar(OA)=bar(i)+2bar(j)-3bar(k), bar(OB)=3bar(i)-2bar(j)+5bar(k) and 2bar(AC)=3bar(AB)" then "bar(AC)=
Answer» `4bar(i)-4bar(J)+9bar(K)` `4bar(i)+4bar(j)-9bar(k)` `4bar(i)+4bar(j)+9bar(k)` `4bar(i)-4bar(j)-9bar(k)` ANSWER :A

Discussion

13357.	Find Lt_(xto1)(1+5x^(3))/(2-x^(2)).
Answer» ANSWER :`-OO`

Discussion

13358.	Sum of infinite terms of the series cot^(-1)(1^(2)+3/4)+cot^(-1)(2^(2)+3/4)+cot^(-1)(3^(2)+3/4)+….. is
Answer» `pi//4` `tan^(-1)2` `tan^(-1)3` `tan^(-1)4` ANSWER :B::C::D

Discussion

13359.	The solution of the equation 9cos^(12)x+cos^(2)2x+1=6cos^(6)xcos3x+6cos^(6)x-2cos2x is /are
Answer» `X=npi+(PI)/2, N in I` `x -n pi +cos^(-1)(root(4)(2/3)), n in I` `x=n pi -cos^(-1)(root(4)(2/3)), n in I` `x=npi-(pi)/2, n in I` Answer :A::B::C

Discussion

13360.	If A+B+C =(3pi)/(2), then cos2A+cos2B+cos2C is equal to-
Answer» `1-4cosAcosBcosC` `4sinAsinBsinC` `1+2cosA+cosBcosC` `1-4sinAsinBsinC` Solution :`cos2A+cos2B+cos2C=2COS(A+B)COS(A-B)+cos2C` `=2cos((3pi)/2-C) cos(A-B)+cos2C THEREFORE A+B+C=(3pi)/(2)` `=-2sinCcos(A-B)+1-2sin^(2)C=1-2sinC[cos(A-B)+sinC]` `=1-2sinC[cos(A-B)+SIN((3pi)/(2)-(A+B))]` `=1-2sinC[cos(A-B)-cos(A+B)]=1-4sinBsinC` `=1-2sinC[cos(A-B)+sin((3pi)/2-(A+B))]` `=1-2sinC[cos(A-B)-cos(A+B)]=1-4sinAsinBsinC`

Discussion

13361.	Let f(x)=e^(cos^(-1)sin(x+pi//3)) then
Answer» `F((8pi)/9)=E^(5pi//18)` `f((8pi)/9)=e^(13pi//18)` `f(-(7pi)/4)=e^(pi//12)` `f(-(7pi)/4)=e^(11pi//12)` ANSWER :B::C

Discussion

13362.	Find the value(s) of k so that the line 2x+y+k=0 may touch the hyperbola 3x^(2)-y^(2)=3
Answer» ANSWER :`K = PM 1 `

Discussion

13363.	Write down the fourth term in the binomial expansion of (px + (1)/(x) )^(n). If this term is independent of x, find the value of n. With this value of n, calculate the value of p given that the fourth term is equal to (5)/(2).
Answer» <P> ANSWER :`""^(n) C_(3) P^(n-3) x^(n-6), n=6, p= (1)/(2)`

Discussion

13364.	thenumber of values of a for which the pair of lines represented by 3ax^(2) +5xy +(a^(2) -2)y^(2) = 0are at right angles to each other , is
Answer» Two VALUES of a For all values of a For ONE VALUE of a For no value of a Answer :A

Discussion

13365.	If f(x) = sqrt(1-sin2x),then f'(x) is equal to
Answer» `-(cosx+SINX), ` for `x in(pi//4, pi//2)` `COS x + sinx,` for `x in (0,pi/4)` `-(cosx+sinx), ` for `x in( pi//4)` `cos x - sinx ` , for `x in (pi//4,pi//2)` Answer :C

Discussion

13366.	The perimeter of a sector is 24 cm. Its maximum area in sq.cm is
Answer» 20 25 30 36 Answer :D

Discussion

13367.	Determine real values of x and y(x-yi)= (2+i)/(1+i)
Answer» ANSWER :`X= (3)/(2) , y= (1)/(2)`

Discussion

13368.	A card is drawn from a pack of 100 cards numbered 1 to 100. Find the probability of drawing a number which is a square.
Answer» ANSWER :`=(1)/(10)`.

Discussion

13369.	If veca=bari-2barj-3bark,barb=2bari+barj-bark,barc=bari+3barj-2bark then compute bara.(barbxxbarc)
Answer» ANSWER :`-20`

Discussion

13370.	Find the angle between bar(DC) and bar(AB) where A = (3,4,5), B = (4,6,3), C = (-1,2,4) and D(1,0,5_
Answer» ANSWER :`COS^(-1)((4)/(9))`

Discussion

13371.	If the sum to 'n' terms of an A.P. is (4n^(2) -2n)/( 4) then the n^( th) term of the A.P. is
Answer» `(5n-1)/( 4)` `( 8n-6)/( 4)` `( 3n^2 - 2)/( 4)` `(7n-8)/( 4)` ANSWER :B

Discussion

13372.	If y= sin^(-1)x, show that (1-x^(2)) (d^(2)y)/(dx^(2))-x(dy)/(dx)0.
Answer» `n^2y` `-n^2y` `-y` `2x^2y` ANSWER :A

Discussion

13373.	If the functions f satisfies the relation f(x+ y ) +f( x-y)= 2f ( x)f(y) AA x, yin R and f (0) ne 0 , then
Answer» `F(x)` is an even FUNCTION `f(x)` is an odd function If `f(2)=a`, then `f(-2)=a` If `f(4)=b`, then `f(-4)= - b` Answer :A::C

Discussion

13374.	If asin^(-1)x-bcos^(-1)x=c, then the value of asin^(-1)x+bcos^(-1)x (whenever exists) is equal to
Answer» 0 `(piab+c(b-a))/(a+b)` `pi/2` `(piab+c(a-b))/(a+b)` ANSWER :D

Discussion

13375.	Convert 40^(@)20' into radian meassure.
Answer» ANSWER :`40 ^(@)20' =(121pi)/(540)` RADIAN.

Discussion

13376.	f(x) = {{:((36^(x) - 9^(x) - 4^(x) + 1)/(2sin^(2) ((x)/(4)) )" if "x ne 0),(k "if "x = 0):} is continuous at x = 0 then k =
Answer» `8 log (6)` 8 log 5 32 log 2 . Log 3 log 2 . Log 3 ANSWER :C

Discussion

13377.	Write the following sets in roster form: F = The set of all letters in the word BETTER
Answer» ANSWER :`F = {B, E, T, R}`

Discussion

13378.	Find k if line y = sqrt(3)x + k touches the circle x^(2) + y^(2) = 16.
Answer» ANSWER :`K = PM 8`

Discussion

13379.	If sinx + sin ((pi)/(8) sqrt((1 - cos 2 x)^(2) + sin ^(2) 2 x)) = 0, x e [(5 pi)/(2), (7 pi)/(2)], then x is
Answer» `pi` `3 pi` `5 pi` `7 pi` ANSWER :B

Discussion

13380.	Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3).
Answer» ANSWER :`X + y = 5`

Discussion

13381.	If5 cos 2 theta + 2 cos ^(2) ""(theta)/(2) + 1 = 0 , - pi lt theta lt pi then number of solutions are
Answer» 3 4 5 6 Answer :B

Discussion

13382.	The percentage error in measuring the radius of a sphere is 1%. If S_(1) = percentage error in volume of the sphere, S_(2) = percentage error in surface area of the sphere, S_(3) = relative error in the diameter of the sphere then arrange S_(1) S_(2) S_(3)according to the values in ascending order
Answer» `S_(3) S_(2) S_(1)` `S_(1) S_(2) S_(3)` `S_(2) S_(1) S_(3)` `S_(3) S_(1) S_(2)` ANSWER :A

Discussion

13383.	A coin is tossed. If it shows head, we draw a ball from a bagconsisting of 3 blue and 4 white balls, if it shows tail we throw a die. Describe the sample space of this experiment.
Answer» Answer :`S={HB_(1),HB_(2),HB_(3),HW_(1),HW_(2),HW_(3),HW_(4),T1,T2,T3,T4,T5,T6}`

Discussion

13384.	Find the derivative of the function e ^(logsqrt(1+ tan ^(2) x))
Answer» ANSWER :`SEC X TAN `

Discussion

13385.	The perimeter of a triangle right angled at C is 70, and the in-radius is 6, then \|a-b\|=
Answer» 1 2 8 9 Answer :A

Discussion

13386.	Find the value of the expression 3[sin^(4)((3pi)/(2)-alpha)+sin^(4)(3pi+alpha)]-2[sin^(6)((pi)/(2)+alpha)+sin^(6)(5pi-alpha)].
Answer» ANSWER :1

Discussion

13387.	Are the following pari of sets equal? Give reasons A= {x : x in Z, x^(2) le 8} B= {y : y in R, y " is a solution of "y^(2)-4y+3=0}
Answer» ANSWER :it is not an EQUAL SET

Discussion

13388.	1-i
Answer» Solution :LET `1-i=r(costheta+isintheta)` then `rcostheta=1 andr sintheta=-1` SQUARING and adding both equations, `r^(2)COS^(2)theta+ r^(2)sin^(2)theta=(1)^(2)+(-1)^(2)=1+1=2` `rArr""r^(2)(cos^(2)+sin^(2)theta)=2" "rArr" "r^(2) =2 orr=sqrt(2)` and `""TANTHETA=(rsintheta)/(rcos theta )=(-1)/(1)=-1` `""=TAN(-45^(@))=tan(-(pi)/(4))` `rArr""theta=(-pi)/(4)` Therefore, `1-i=r(costheta+isintheta)` `""=sqrt(2)[ cos(-(pi)/(4))+sin((-pi)/(4))]`

Discussion

13389.	Let A be 3xx3 matrix such A^(2)-5A+7I=0 statement 1 : A^(-1)=(1)/(7)(5I-A) Statement 2 : The polynomial A^(3)-2A^(2)-3A+I can be reduce to 5 (A-4I) then
Answer» both STETEMENTS are TRUE both statement are false statemennt 1 is true, but statement 2 is false statement 1 if false, but statement 2 true Answer :C

Discussion

13390.	Three non-zero non-collinear vectors bar(a), bar(b), bar(c) are such that bar(a)+3bar(b) is collinear with bar(c), while bar(c) is 3bar(b)+2bar(c) collinear with bar(a).Then bar(a)+3bar(b)+2bar(c)=
Answer» `bar(0)` `2BAR(a)` `3bar(b)` `4bar(C)` ANSWER :A

Discussion

13391.	If the perimeter of a sector of a circle is constant then find the angle of the sector, when its area is maximum.
Answer» 1 radian 2 radians 3 radian 4 ridians Answer :B

Discussion

13392.	Let x_1, x_2 ,…………,x_n be n observations and barx be their arithmetic mean. The formula for the standard deviation is given by ……….. .
Answer» `SUM (x_i = BARX)^2` `(sum(x_i - barx)^2)/(n)` `sqrt((sum(x_i - barx)^2)/(n)) ` `sqrt((sumx_i^2)/(n)) - (barx)^(-2)` ANSWER :C

Discussion

13393.	Find the coordinates of the point which divides the line segment joining the points (1, -2, 3) and (3, 4, -5) in the ratio 2 : 3 (i) internally, and (ii) externally.
Answer» ANSWER :`2:3`

Discussion

13394.	In two factories A and B engaged in the same industrial area, the average weekly wages (in rupees) and the standard deviations are as follows: (i) Which factory, A or B, pays out a larger amount as weekly wages? (ii) Which factory, A or B, has greater variability in individual wages?
Answer» ANSWER :(i) FACTORY A pays out larger amounts as weekly wages (II) Factory B has greater VARIABILITY in individual wages.

Discussion

13395.	Form the bicoditional statement phArrq. Where p: The unit digit of an integer is zero. q: It is divisible by 5.
Answer» ANSWER :DIVISIBLE by 5.

Discussion

13396.	The range of f(x)=sqrt((1-cos x)sqrt((1-cos)sqrt(1-cos xsqrt(...oo)))) is
Answer» [0, 1] `[0, 1//2]` `[0, 2]` `[1/2, 1]` ANSWER :C

Discussion

13397.	Evaluate : 5!
Answer» ANSWER :120

Discussion

13398.	Write each of the following statements in the form if then: The banana trees will bloom if it stays warm for a month.
Answer» ANSWER :If it stays warm for a MONTH then BANANA TREES will bloon.

Discussion

13399.	If n(A) = p and n (B) = q then numbers of non void relations from A to B are (2^(p+q)-1).
Answer» ANSWER :FALSE STATEMENT

Discussion

13400.	Expres sqrt3 sin 0 + cos 0as a sine of an angle .
Answer» Answer :`2 sin (THETA + (PI)/(6))`

Discussion

Explore topic-wise InterviewSolutions in .

Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

Prove that the equation y^(2)+2ax+2by+c=0 represents a parabola whose axis is parallel to the axis of x. Find its vertex.

Find the rank of 55 from the following data: 90, 85, 80, 80, 80, 80,78, 72, 69, 69, 55, 54

Statement-I: If f(x) = coshx - sinhx for x in R then f(x-y)=f(x) divf(y) Statement -II: If f(x) = coshx + sinhx for x in Rthen f(x) is a bijective function Statement-III: coth^(-1)x="cosh"^(-1)(|x|)/(sqrt(x^(2)-1)) Which of the above statement is correct?

(ii) Find the 4th term from the end in the expansion of ((3)/(x^2) - (x^3)/(6) )^7.

If bar(OA)=bar(i)+2bar(j)-3bar(k), bar(OB)=3bar(i)-2bar(j)+5bar(k) and 2bar(AC)=3bar(AB)" then "bar(AC)=

Find Lt_(xto1)(1+5x^(3))/(2-x^(2)).

Sum of infinite terms of the series cot^(-1)(1^(2)+3/4)+cot^(-1)(2^(2)+3/4)+cot^(-1)(3^(2)+3/4)+….. is

The solution of the equation 9cos^(12)x+cos^(2)2x+1=6cos^(6)xcos3x+6cos^(6)x-2cos2x is /are

If A+B+C =(3pi)/(2), then cos2A+cos2B+cos2C is equal to-

Let f(x)=e^(cos^(-1)sin(x+pi//3)) then

Find the value(s) of k so that the line 2x+y+k=0 may touch the hyperbola 3x^(2)-y^(2)=3

Write down the fourth term in the binomial expansion of (px + (1)/(x) )^(n). If this term is independent of x, find the value of n. With this value of n, calculate the value of p given that the fourth term is equal to (5)/(2).

thenumber of values of a for which the pair of lines represented by 3ax^(2) +5xy +(a^(2) -2)y^(2) = 0are at right angles to each other , is

If f(x) = sqrt(1-sin2x),then f'(x) is equal to

The perimeter of a sector is 24 cm. Its maximum area in sq.cm is

Determine real values of x and y(x-yi)= (2+i)/(1+i)

A card is drawn from a pack of 100 cards numbered 1 to 100. Find the probability of drawing a number which is a square.

If veca=bari-2barj-3bark,barb=2bari+barj-bark,barc=bari+3barj-2bark then compute bara.(barbxxbarc)

Find the angle between bar(DC) and bar(AB) where A = (3,4,5), B = (4,6,3), C = (-1,2,4) and D(1,0,5_

If the sum to 'n' terms of an A.P. is (4n^(2) -2n)/( 4) then the n^( th) term of the A.P. is

If y= sin^(-1)x, show that (1-x^(2)) (d^(2)y)/(dx^(2))-x(dy)/(dx)0.

If the functions f satisfies the relation f(x+ y ) +f( x-y)= 2f ( x)f(y) AA x, yin R and f (0) ne 0 , then

If asin^(-1)x-bcos^(-1)x=c, then the value of asin^(-1)x+bcos^(-1)x (whenever exists) is equal to

Convert 40^(@)20' into radian meassure.

f(x) = {{:((36^(x) - 9^(x) - 4^(x) + 1)/(2sin^(2) ((x)/(4)) )" if "x ne 0),(k "if "x = 0):} is continuous at x = 0 then k =

Write the following sets in roster form: F = The set of all letters in the word BETTER

Find k if line y = sqrt(3)x + k touches the circle x^(2) + y^(2) = 16.

If sinx + sin ((pi)/(8) sqrt((1 - cos 2 x)^(2) + sin ^(2) 2 x)) = 0, x e [(5 pi)/(2), (7 pi)/(2)], then x is

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3).

If5 cos 2 theta + 2 cos ^(2) ""(theta)/(2) + 1 = 0 , - pi lt theta lt pi then number of solutions are

The percentage error in measuring the radius of a sphere is 1%. If S_(1) = percentage error in volume of the sphere, S_(2) = percentage error in surface area of the sphere, S_(3) = relative error in the diameter of the sphere then arrange S_(1) S_(2) S_(3)according to the values in ascending order

A coin is tossed. If it shows head, we draw a ball from a bagconsisting of 3 blue and 4 white balls, if it shows tail we throw a die. Describe the sample space of this experiment.

Find the derivative of the function e ^(logsqrt(1+ tan ^(2) x))

The perimeter of a triangle right angled at C is 70, and the in-radius is 6, then |a-b|=

Find the value of the expression 3[sin^(4)((3pi)/(2)-alpha)+sin^(4)(3pi+alpha)]-2[sin^(6)((pi)/(2)+alpha)+sin^(6)(5pi-alpha)].

Are the following pari of sets equal? Give reasons A= {x : x in Z, x^(2) le 8} B= {y : y in R, y " is a solution of "y^(2)-4y+3=0}

1-i

Let A be 3xx3 matrix such A^(2)-5A+7I=0 statement 1 : A^(-1)=(1)/(7)(5I-A) Statement 2 : The polynomial A^(3)-2A^(2)-3A+I can be reduce to 5 (A-4I) then

Three non-zero non-collinear vectors bar(a), bar(b), bar(c) are such that bar(a)+3bar(b) is collinear with bar(c), while bar(c) is 3bar(b)+2bar(c) collinear with bar(a).Then bar(a)+3bar(b)+2bar(c)=

If the perimeter of a sector of a circle is constant then find the angle of the sector, when its area is maximum.

Let x_1, x_2 ,…………,x_n be n observations and barx be their arithmetic mean. The formula for the standard deviation is given by ……….. .

Find the coordinates of the point which divides the line segment joining the points (1, -2, 3) and (3, 4, -5) in the ratio 2 : 3 (i) internally, and (ii) externally.

In two factories A and B engaged in the same industrial area, the average weekly wages (in rupees) and the standard deviations are as follows: (i) Which factory, A or B, pays out a larger amount as weekly wages? (ii) Which factory, A or B, has greater variability in individual wages?

Form the bicoditional statement phArrq. Where p: The unit digit of an integer is zero. q: It is divisible by 5.

The range of f(x)=sqrt((1-cos x)sqrt((1-cos)sqrt(1-cos xsqrt(...oo)))) is

Evaluate : 5!

Write each of the following statements in the form if then: The banana trees will bloom if it stays warm for a month.

If n(A) = p and n (B) = q then numbers of non void relations from A to B are (2^(p+q)-1).

Expres sqrt3 sin 0 + cos 0as a sine of an angle .