14949 + Interview Questions in Maths in Class 11 Page 136 InterviewSolution

6751.	Calculate the mean , variance and standard deviation for the following distribution:
Answer» ANSWER :62,201,14.18

Discussion

6752.	If y= f((2x+3)/(3-2x)) and f(x) = sin (logx) then (dy)/(dx)=
Answer» `12/(9+4x^2)COS(LOG((2x-3)/(3+2x)))` `12/(9-4x^2)SIN(log((2x-3)/(3+2x)))` `12/(9-4x^2)cos(log((2x-3)/(3+2x)))` `cos(log((2x-3)/(3+2x)))` ANSWER :C

Discussion

6753.	Find dy/dx if x^(3) + y^(3) -3xy + 1 = 0.
Answer» ANSWER :`dy/dx = y-X^(2)/(y^(2)-x)`

Discussion

6754.	Evaluate : cos ^(2) ""(pi)/(12) - sin ^(2) ""(pi)/(12)
Answer» ANSWER :`(-SQRT3)/(4)`

Discussion

6755.	Express the following in the form a+bi (5-6i)^(2)
Answer» ANSWER :`-11-60i`

Discussion

6756.	One of the four persons John, Rita, Aslam or Gurpreet will be promoted next month. Consequently the sample space consists of four elementary outcomes S = {John promoted, Rita promoted, Aslam promoted, Gurpreet promoted} You are told that the chances of John's promotion is same as that of Gurpreet, Rita's chances of promotion are twice as likely as Johns. Aslam's chances are four times that of John. (a) P Determine (John promoted) P (Rita promoted) P (Aslam promoted) P (Gurpreet promoted) (b) If A= { John promoted or Gurpreet promoted}, find P(A).
Answer» ANSWER :`(1)/(4)`

Discussion

6757.	If bara = 3bari - 4barj +5bark, barb = 2bari+3barj-bark ," then the angle between " bara and barb is
Answer» `pi+COS^(-1)(11/(10sqrt7))` `pi-cos^(-1)(11/(10sqrt7))` `cos^(-1)(11/(10sqrt7))` `-cos^(-1)(11/(10sqrt7))` ANSWER :B

Discussion

6758.	Vector equation of the plane passing through bara, barb and parallel to the line barr = barc + alphabard is
Answer» `[barrbarb-barabard]=[BARABARBBARC]` `[barrbarb-barabard]=[barabarbbard]` `[barrbarb-barcbara]=[barabarbbard]` `[barrbarc-barabarb]=[barabarcbard]` ANSWER :B

Discussion

6759.	Evaluate the following limits : Lt_(ntooo)(1/3+1/3^(2)+1/3^(3)+...+1/3^(n)).
Answer» ANSWER :`1/2`

Discussion

6760.	If f(1) = 3 ,f'(1)=-1/3 , then the derivative of {x^(11) +f(x)}^(-2) at x = 1 is
Answer» `-1/2` `-1` 1 `F^(1)(1)` ANSWER :D

Discussion

6761.	If 0 le x le (pi)/3then range of f(x)= sec (pi/6 -x) + sec (pi/6+x)is
Answer» `(4/sqrt3,OO)` `[4/sqrt3,oo)` `(0,4/sqrt3]` `(0,4/sqrt3)` ANSWER :B

Discussion

6762.	If x^(2)-3xy+2y^(2)=0 represents two sides of triangle and orthocentre is (2,1) then equation of third side is
Answer» `x+2y=5` `2x+y=5` `2x+y+5=0` `2x+y=6` ANSWER :B

Discussion

6763.	If the ratio of major and minor axis of ellipse is 5:3 then eccentricity e = ........... .
Answer» ANSWER :`4/5`

Discussion

6764.	Assertion (A) :Every bodyin a roomshakeshandswith everybodyelse. The totalnumberof persons in the room is n . The numberof handshakesis( n (n-1))/2 Reason( R): Thenumberof handshakes is.^(n) C_(2)
Answer» Both A and RARE TRUEAND Ris the correct explanation of A Both A and Rare true but R is NOTTHE correct explanation of A A is true R is false A is FALSER is true Answer :A

Discussion

6765.	If f is a function satisfying f (x +y) = f(x) f(y) for all x, yin Nsuch that f(1) = 3 and sum _(x=1)^nf(x)=120 , find the value of n.
Answer» ANSWER :4

Discussion

6766.	If a_(k) = (1)/( k(k+1) ) for k= 1,2,3,….n then (sum_(k=1)^(n) a_(k) )=
Answer» `(N)/( n+1)` `(n^2)/( (n+1)^2)``(n^6)/( (n+1)^6)` ANSWER :B

Discussion

6767.	If Cov(x,y) = -2, Sigma y = 30 , Sigma x = 25 and Sigma xy = 140, find the number of observations .
Answer» ANSWER :5

Discussion

6768.	Find coefficient of quartile deviation for the following data.
Answer» ANSWER :COEFFICIENT of QUARTILE DEVIATION ` = 7.69% `

Discussion

6769.	Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= n^(th) prime number
Answer» ANSWER :`2,3,5,7,11`

Discussion

6770.	If 1/2lexle1 then Cos^(-1)x+Cos^(-1)(x/2+1/2sqrt(3-3x^(2)))=
Answer» `PI//6` `pi//3` `pi` `0` ANSWER :B

Discussion

6771.	A(1,2,3),B(0,4,1),C(-1,-1,-3) are verticesof triangle ABC, find the point at which the bisector of angleBAC meets BC.
Answer» ANSWER :`(-(3)/(10),(5)/(2),-(1)/(5))`

Discussion

6772.	Statement 1: f(x)=(cos^(-1)x)^(2)+(pi)/2sin^(-1)x then Range of f(x) is [(3pi^(2))/16,3/4pi^(2)] Statement 2: If f(x)=ax^(2)+bx+c and if x_(1)lt(-b)/(2a)ltx_(2) then Range of f(x) in the interval [x_(1),x_(2)] is ["min"{f(x_(1)),f(x_(2)),f(-b/(2a))},"max"{f(x_(1)),f(x_(2)),f(-b/(2a))}]
Answer» Both I and II are INDIVIDUALLY TRUE and II is the CORRECT EXPLANATION of I Both I and II are individually true but II is not the correct explanation of I I is true but II is false I is false but II is true Answer :A

Discussion

6773.	Find the distance between the points (3,4,-2)and(1,0,7)
Answer» ANSWER :`SQRT(101)`

Discussion

6774.	If tantheta - tan^(2) theta = 1 , then tan^(4) theta-2tan^3theta-tan^2theta+2tantheta+1 has value 4.
Answer» ANSWER :TRUE STATEMENT

Discussion

6775.	U= {h, i, j, k, l, m, n, o, p} then find the complement of the following sets :A= {h, k, o, p}
Answer» ANSWER :`= {i, J, L, m, N}`

Discussion

6776.	Solve the following equations : (i) 2x^(2)-(3+7i)x-3+9i=0 (ii) (2+i)x^(2)-(5-i)x+2(1-i)=0 (iii) x^(2)-(4+i)x+(5-i)=0 (iv) x^(2)-(5+5i)x+13i=0 (v) x^(2)-(5+2i)x+(9+7i)=0 (vi) x^(2)-(5-i)x+(18+i)=0
Answer» Solution :(i) ` 3i, (3+i)/(2)` (ii) `1-i, (4-2i)/(5)` (iii) `3+2i, 1-i` (IV) `2+3i, 3+2i` (V) `3-i, 2+3i` (vi) ` 3-4i, 2+ 3i`

Discussion

6777.	Find the derivativ of the function from first principles : (1)/(x ^(2) +1 )
Answer» ANSWER :`(-2X )/( (X ^(2) + 1 ) ^(2))`

Discussion

6778.	Evaluate : lim_(x to 0) (e^(x) -e^(x))/x
Answer» ANSWER :a

Discussion

6779.	Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Passes from point (-4,3) and parallel to Y-axis.
Answer» ANSWER :`x+4=0`

Discussion

6780.	Find the slope of the line which is perpendicular to the line 7x+11y-2=0.
Answer» ANSWER : `11/(7)`

Discussion

6781.	If \|vec(a)\|=1, \|vec(b)\|=2 and (vec(a), vec(b))= 120^(@), then {(vec(a) + 3 vec(b)) xx (3vec(a) - vec(b))}^(2)=
Answer» 225 275 325 300 Answer :D

Discussion

6782.	How many chords can be drawn through 21 points on a circle?
Answer» ANSWER :210

Discussion

6783.	A line OA of length r starts from its initial position OX and traces an angle AOB = alpha in the anticlockwise direction. It then traces back in the clockwise direction an angle BOC = 3 theta (where alpha gt 3 theta). L is the foot of the perpendicular from C on OA. (sin^(3)theta)/(CL) = (cos^(3) theta)/(OL) = 1 (2r^(2) - 1)/(r) is equal to
Answer» `sin alpha` `COS alpha` `sin THETA` `cos theta` Answer :B

Discussion

6784.	A line OA of length r starts from its initial position OX and traces an angle AOB = alpha in the anticlockwise direction. It then traces back in the clockwise direction an angle BOC = 3 theta (where alpha gt 3 theta). L is the foot of the perpendicular from C on OA. (sin^(3)theta)/(CL) = (cos^(3) theta)/(OL) = 1 (2r sin alpha)/(1 + 2 r cos alpha) is equal to
Answer» `TAN^(2) THETA` `COT^(2) theta` `cot 2 theta` `tan 2 theta` ANSWER :D

Discussion

6785.	A line OA length r starts from its initial position OX and traces an angle AOB = alpha in the anticlockwise direction. It then traces back in the clockwise direction an angle BOC = 3 theta ( where alpha gt 3 theta ) . L is the foot of the the perpendicular from C on OA. (sin^3 theta)/(CL) = (cos^3 theta)/(OL ) = 1 (1- r cos alpha)/(r sin alpha)is equal to
Answer» `tan 2 theta` `COT 2 theta` `SIN 2 theta` `COS 2 theta` Answer :A

Discussion

6786.	( sin 3 theta + sin 5 theta + sin 7 theta+ sin 9 theta)/( cos 3 theta + cos 5 theta + cos 7 theta + cos 9 theta)is equal to
Answer» `tan 3 THETA ` `cot 3 theta ` `tan 6 theta ` `cot 6 theta ` ANSWER :C

Discussion

6787.	Let f(x)=sin xand g(x)= log_(e)\|x\|. If the ranges of the composition functions fog and gof are R_(1) and R_(2), respectively, then
Answer» `R_(1)={U: -1 LE u lt 1}, { v: -oo v lt 0}` `R_(1)={u : - oo lt u lt 0}, R_(2)={v: -oo lt v lt0}` `R_(1)={u: -1 lt u lt 1},R_(2)= { v: oo lt v lt 0}` `R_(1)={u : -1 le u le 1}, R_(2)={v: -oo lt v lt 0}` ANSWER :D

Discussion

6788.	Prove that (1+sin theta)/(1-sin theta)=(sec theta+tantheta)^(2)
Answer» ANSWER :LEFT SIDE.

Discussion

6789.	If y^(n) -1 is divisible by y+ a for all values of n in N, then a must by
Answer» `-1` `0` `1` `2` ANSWER :A

Discussion

6790.	The set of solutions of the equation (sqrt(3)-1)sin theta + (sqrt(3) +1)cos theta = 2 is :
Answer» `{2npipm(PI)/(4)+(pi)/(12): ninZZ}` `{2npipm(pi)/(4)-(pi)/(12): ninZZ}` `{NPI+(-1)^(N)(pi)/(4)+(pi)/(12):ninZZ}` `{npi+(-1)^(n)(pi)/(4)-(pi)/(12):ninZZ}` ANSWER :A

Discussion

6791.	Solve: (x+1)(x+2)(x+3)(x+4)+1=0.
Answer» ANSWER :`X=(-5pmsqrt(25-20))/(2)=(-5pmsqrt(5))/(2)`.

Discussion

6792.	Equation of the circle with centre on the Y - axis and passing through the origin and the point (2,3) is ……
Answer» `x^(2) + y^(2) + 13Y = 0` `3x^(2) + 3y^(2) + 13x + 3 = 0` `6x^(2) + 6y^(2) - 13y = 0` `x^(2) + y^(2) + 13x + 3 = 0` ANSWER :C

Discussion

6793.	If A=[(1^(2),2^(2),3^(2)),(2^(2),3^(2),4^(2)),(3^(2),4^(2),5^(2))] then \|"Adj A"\|=
Answer» 64 256 8 6 Answer :A

Discussion

6794.	The extremevalues of 4cos(x^(2)).cos((pi)/(3)+x^(2)).cos((pi)/(3)-x^(2)) are
Answer» `-1, 1` `-2,2` `-3,3` `-4,4` ANSWER :A

Discussion

6795.	If the lines (x-1)/(k ) = (y-4)/(2) = (z-5)/(1) and (x -1)/(k) = (y -4)/(2) = (z -5)/(1) are coplanar then k can have
Answer» any VALUE EXACTLY one value exactly TWO values exactly THREE values Answer :C

Discussion

6796.	The maximum value of y= (1)/( sin^(6) x + cos^(6) x) is __________
Answer» ANSWER :4

Discussion

6797.	Let f(x)= sqrt(1+x^(2)) then,
Answer» `F(xy)= f(X). F(y)` `f(xy) ge f(x).f (y)` `f(xy) le f(x).f(y)` NONE of these Answer :C

Discussion

6798.	A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
Answer» ANSWER :8

Discussion

6799.	A line is parallel to XY-plane if all the points on the line have equal ______ .
Answer» ANSWER :Z COORDINATES

Discussion

6800.	Find the ratio in which the linejointof A (2,1,5) and B(3,4,3) is divided by the plane 2x+ 2y - 2z = 1. Also , find the coordinates of the point of division .
Answer» ANSWER :`(29/12,9/4,25/6)`

Discussion

Explore topic-wise InterviewSolutions in .

Calculate the mean , variance and standard deviation for the following distribution:

If y= f((2x+3)/(3-2x)) and f(x) = sin (logx) then (dy)/(dx)=

Find dy/dx if x^(3) + y^(3) -3xy + 1 = 0.

Evaluate : cos ^(2) ""(pi)/(12) - sin ^(2) ""(pi)/(12)

Express the following in the form a+bi (5-6i)^(2)

If bara = 3bari - 4barj +5bark, barb = 2bari+3barj-bark ," then the angle between " bara and barb is

Vector equation of the plane passing through bara, barb and parallel to the line barr = barc + alphabard is

Evaluate the following limits : Lt_(ntooo)(1/3+1/3^(2)+1/3^(3)+...+1/3^(n)).

If f(1) = 3 ,f'(1)=-1/3 , then the derivative of {x^(11) +f(x)}^(-2) at x = 1 is

If 0 le x le (pi)/3then range of f(x)= sec (pi/6 -x) + sec (pi/6+x)is

If x^(2)-3xy+2y^(2)=0 represents two sides of triangle and orthocentre is (2,1) then equation of third side is

If the ratio of major and minor axis of ellipse is 5:3 then eccentricity e = ........... .

Assertion (A) :Every bodyin a roomshakeshandswith everybodyelse. The totalnumberof persons in the room is n . The numberof handshakesis( n (n-1))/2 Reason( R): Thenumberof handshakes is.^(n) C_(2)

If f is a function satisfying f (x +y) = f(x) f(y) for all x, yin Nsuch that f(1) = 3 and sum _(x=1)^nf(x)=120 , find the value of n.

If a_(k) = (1)/( k(k+1) ) for k= 1,2,3,….n then (sum_(k=1)^(n) a_(k) )=

If Cov(x,y) = -2, Sigma y = 30 , Sigma x = 25 and Sigma xy = 140, find the number of observations .

Find coefficient of quartile deviation for the following data.

Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= n^(th) prime number

If 1/2lexle1 then Cos^(-1)x+Cos^(-1)(x/2+1/2sqrt(3-3x^(2)))=

A(1,2,3),B(0,4,1),C(-1,-1,-3) are verticesof triangle ABC, find the point at which the bisector of angleBAC meets BC.

Statement 1: f(x)=(cos^(-1)x)^(2)+(pi)/2sin^(-1)x then Range of f(x) is [(3pi^(2))/16,3/4pi^(2)] Statement 2: If f(x)=ax^(2)+bx+c and if x_(1)lt(-b)/(2a)ltx_(2) then Range of f(x) in the interval [x_(1),x_(2)] is ["min"{f(x_(1)),f(x_(2)),f(-b/(2a))},"max"{f(x_(1)),f(x_(2)),f(-b/(2a))}]

Find the distance between the points (3,4,-2)and(1,0,7)

If tantheta - tan^(2) theta = 1 , then tan^(4) theta-2tan^3theta-tan^2theta+2tantheta+1 has value 4.

U= {h, i, j, k, l, m, n, o, p} then find the complement of the following sets :A= {h, k, o, p}

Solve the following equations : (i) 2x^(2)-(3+7i)x-3+9i=0 (ii) (2+i)x^(2)-(5-i)x+2(1-i)=0 (iii) x^(2)-(4+i)x+(5-i)=0 (iv) x^(2)-(5+5i)x+13i=0 (v) x^(2)-(5+2i)x+(9+7i)=0 (vi) x^(2)-(5-i)x+(18+i)=0

Find the derivativ of the function from first principles : (1)/(x ^(2) +1 )

Evaluate : lim_(x to 0) (e^(x) -e^(x))/x

Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Passes from point (-4,3) and parallel to Y-axis.

Find the slope of the line which is perpendicular to the line 7x+11y-2=0.

If |vec(a)|=1, |vec(b)|=2 and (vec(a), vec(b))= 120^(@), then {(vec(a) + 3 vec(b)) xx (3vec(a) - vec(b))}^(2)=

How many chords can be drawn through 21 points on a circle?﻿

( sin 3 theta + sin 5 theta + sin 7 theta+ sin 9 theta)/( cos 3 theta + cos 5 theta + cos 7 theta + cos 9 theta)is equal to

Let f(x)=sin xand g(x)= log_(e)|x|. If the ranges of the composition functions fog and gof are R_(1) and R_(2), respectively, then

Prove that (1+sin theta)/(1-sin theta)=(sec theta+tantheta)^(2)

If y^(n) -1 is divisible by y+ a for all values of n in N, then a must by

The set of solutions of the equation (sqrt(3)-1)sin theta + (sqrt(3) +1)cos theta = 2 is :

Solve: (x+1)(x+2)(x+3)(x+4)+1=0.

Equation of the circle with centre on the Y - axis and passing through the origin and the point (2,3) is ……

If A=[(1^(2),2^(2),3^(2)),(2^(2),3^(2),4^(2)),(3^(2),4^(2),5^(2))] then |"Adj A"|=

The extremevalues of 4cos(x^(2)).cos((pi)/(3)+x^(2)).cos((pi)/(3)-x^(2)) are

If the lines (x-1)/(k ) = (y-4)/(2) = (z-5)/(1) and (x -1)/(k) = (y -4)/(2) = (z -5)/(1) are coplanar then k can have

The maximum value of y= (1)/( sin^(6) x + cos^(6) x) is __________

Let f(x)= sqrt(1+x^(2)) then,

A coin is tossed 3 times and the outcomes are recorded. How many possible﻿ outcomes are there?﻿

A line is parallel to XY-plane if all the points on the line have equal ______ .

Find the ratio in which the linejointof A (2,1,5) and B(3,4,3) is divided by the plane 2x+ 2y - 2z = 1. Also , find the coordinates of the point of division .

How many chords can be drawn through 21 points on a circle?

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?