14949 + Interview Questions in Maths in Class 11 Page 48 InterviewSolution

2351.	Which term of the expansion (sqrt((x)/(3))-(sqrt(3))/(2x))^(12)is independent of x.
Answer» ANSWER :`5^(TH` TERM

Discussion

2352.	If A is a 3xx4 matrix and B is a matrix such that both A^(T)B and BA^(T) are defined, what is the order of the matrix B?
Answer» ANSWER :`(3xx4)`

Discussion

2353.	If A=[(-1,2),(0,1)] then A A^(T). Do A and A^(T) commute with respect to multiplication of matrices ?
Answer» ANSWER :SINCE `A A^(T)!=A^(T)A, A` and `A^(T)` do not COMMUTE with respect to MULTIPLICATION of MATRICES.

Discussion

2354.	Find the mean deviation using median for the following observations: (a) 17,25,9,12,18,26,21 (b) 6,10,11,15,9,7,15,16,5 (c) 2,4,6,8,10,9,15,12,3,7 (d) 28,32,31,25,22,12,17,26 (e) 5,7,17,9,19,11,18
Answer» SOLUTION :NA

Discussion

2355.	(2+sqrt(3))^(4)+(2-sqrt(3))^(4) = x+ ysqrt(3) then y = ………..
Answer» 0 56 112 97 Answer :A

Discussion

2356.	If the sides a, b, c of a triangle ABC form successive terms of G.P. with common ratio r (gt 1) then which of the following is correct?
Answer» `A gt (pi)/(3)` `B GE (pi)/(3)` `C lt (pi)/(3)` `A lt B lt pi//3` Answer :D

Discussion

2357.	Choose the most appropriate answer from those given in bracket If lim_(xrarr2)(x^p-2^p)/(x-2)=192 then p=………
Answer» 2 4 6 10 Answer :C

Discussion

2358.	If y = log_("sin x") (tan x), then ((dy)/(dx))_(pi//4) is equal to
Answer» `4/("LOG 2")` `-4 log 2` `(-4)/(log 2)` `4 log 2` ANSWER :C

Discussion

2359.	Let U be universal set of all the students of Class XI of a coeducational school and A be the set of all girls in Class XI. Find A′.
Answer» Answer :SINCE A is the SET of all girls, A' is CLEARLY the set of all BOYS in the class.

Discussion

2360.	Let f(x)=(alpha x)/((x+1)), x != -1. Then for which value of alpha is f(f(x))=x ?
Answer» `SQRT(2)` `-sqrt(2)` 1 -1 Answer :D

Discussion

2361.	Find the coordinates of the point at whichyz plane intersects the line segment joining the points (-2, 3, 7) and (6, -1, 2).
Answer» <P> ANSWER :`P=(0,2,(23)/(4))`

Discussion

2362.	If h denote the arithmetic mean, k denote G.M. of the intercepts made on axes by the lines passing through (1, 1) then (h, k) lies on
Answer» a circle a parabola a STRAIGHT LINE a hyperbola Answer :B

Discussion

2363.	Evaluate :lim_(xto1)(x^18-1)/(18x-18)
Answer» ANSWER :1

Discussion

2364.	A triangle is formed by the lines whose equations are 3x+4y-6=0,12x-5y-3 = 0 and4x-3y + 12 = 0. Find the internal bisector of the angle opposite to the side 3x + 4y -6=0.
Answer» SOLUTION :N/A

Discussion

2365.	Given xgt0, the value of f(x) = -3cossqrt(3+x+x^(2)) lie in the interval ………….
Answer» ANSWER :`[-3,3]`

Discussion

2366.	Normal form of the line x-y+sqrt(2)=0 is
Answer» `X"cos"(PI)/4+y"SIN"(pi)/4=1` `x"cos"(3pi)/4+y"sin"(3pi)/4=1` `x"cos"(5pi)/4+y"sin"(5pi)/4=1` `x"cos"(7pi)/4+y"sin"(7pi)/4=1` ANSWER :B

Discussion

2367.	Solve the following equations and write general solutions sin^(2) theta - cos theta = (1)/(4)
Answer» ANSWER :`2NPI PM (PI)/(3)`

Discussion

2368.	Write down the contrapositive of the following statements.:If n is a natural number, then n is an integer.
Answer» ANSWER :NATURAL NUMBER.

Discussion

2369.	Differentiate the following w.r.t. x : (x-2) (x+3) (2x +5)
Answer» ANSWER :`2 (x-2) (x+3) + (x-2) (2X +5) + (x+3) (2x +5)`

Discussion

2370.	How many 3 - digit numbers can be formed by using the digits 1 to 9 if no digit is repeated ?
Answer» ANSWER :504

Discussion

2371.	Find the angle between the lines 3x+5y=7,2x-y+4=0
Answer» ANSWER :`TAN^(-1)13`

Discussion

2372.	x - 2y le 4
Answer» SOLUTION :

Discussion

2373.	If B={phi} then,
Answer» B is an EMPTY set B is a FINITE set B is an INFINITE set B is not a set Answer :B

Discussion

2374.	Find equation of line at the distance 3 from origin and perpendicular to the line sqrt(3) x - y+5=0.
Answer» ANSWER :`X+ SQRT(3) y PM 6=0`

Discussion

2375.	If sec^(-1)(1/(sqrt(1-x^(2))))+cot^(-1)((sqrt(1-x^(2)))/x)=sin^(-1)(k) then k=
Answer» `xsqrt(1-x^(2))` `2xsqrt(1-x^(2))` `SQRT(1-x^(2))` `2X` ANSWER :B

Discussion

2376.	For each of the following statements, determine whether an inclusive 'or' or exclusive 'or' is used. Give reasons for your anser. (i) For identification you need a passport or an Adhar Card. (ii) The school is closed if it is a holiday or a Sunday. (iii) sqrt(3) is a rational number or an irrational number. (iv) Two lines intersect at a point or are parallel. (v) Students can take Sanskrit or French as their third language.
Answer» Solution :(i) Here 'or' is inclusive since a person can have both a PASSPORT and an Adhar Card of identification. (ii) Here 'or' is inclusive since the SCHOOL is closed on holiday as well as on Sunday. (III) LET p: `sqrt(3)` is a rational number And q: `sqrt(3)` is an irrational number Clearly, p is false and q is true. `therefore` (p or q) is true and 'or' is EXCLUSIVE. (iv) Here 'or' is exclusive because it is not possible for two lines to intersect and be parallel together. (v) Here 'or' is exclusive because a student cannot take both Sanskrit and French.

Discussion

2377.	Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= 8- n^(3)
Answer» ANSWER :`7, 0, -19, -56, -117`

Discussion

2378.	If RR is the set of all real number and if f : RR - {3} to RR is defined by f(x) = (3x + x)/(3-x) for x in RR - {3}, then the range of f is
Answer» `RR` `RR - {1}` `RR - {-1}` `RR - {-3}` ANSWER :A::C

Discussion

2379.	If sin alpha=A sin(alpha + beta), A ne 0,then: Which of the following is the value of tan (alpha+beta)= ?
Answer» `(SIN beta)/(sin beta - A )` `(sin alpha COS alpha)/(A cos beta - sin^(2)alpha)` `(sin alpha cos alpha)/(A cos alpha cos beta)` `(COSALPHA(1+A sin beta))/(A cos alpha cos beta)` Answer :A

Discussion

2380.	What is the number of terms in the expansion of the following? [ ( x-2)^(3) ]^3
Answer» ANSWER :10

Discussion

2381.	Determine all values of alpha for which the point (alpha, alpha^(2)) lies inside the triangle formed by the lines 2x+3y-1=0, x+2y-3=0 and 5x-6y-1=0
Answer» ANSWER :`ALPHA in ((-3)/2,-1)UU(1/2,1)`

Discussion

2382.	EvaluateC(8,5)
Answer» ANSWER :` 56`

Discussion

2383.	If cos x=3, cos y,then 2 tan ((y-x)/(2))=
Answer» `COT ((y-x)/(2))` ` cot ((x+y)/(4))` `cot ((y-x)/(4))` `cot ((x+y)/(2))` ANSWER :D

Discussion

2384.	Find the mean and variance for each of the data in 6, 7, 10, 12, 13, 4, 8, 12
Answer» ANSWER :9, 9.25

Discussion

2385.	Statement 1 : If f : R rarr R , y = f(x) is a periodic and continuous function, then y=f(x) cannot be onto Statement 2 : A continuous periodic function is bounded.
Answer» Statement 1 is TRUE, statement 2 is true, statement 2 iscorrect explanation for statement 1. Statement 1 is true, statement 2 is true, statement 2 is notcorrect explanation for statement 1. Statement1 is FALSE, but statement 2 is true Statement 1 is true, but statement 2 is false Answer :A

Discussion

2386.	If log_(2)x ge0 then log_(1/(pi))(sin^(-1)((2x)/(1+x^(2)))+2Tan^(-1)x)=lamda then \|lamda\|=
Answer» 1 2 3 4 Answer :A

Discussion

2387.	If vec(a) + vec(b) + vec(c )= vec(0) and \|vec(a) xx vec(b)\|=3, then \|vec(b) xx vec(c )\|=
Answer» 1 2 3 4 Answer :C

Discussion

2388.	Using the half angle formulas, find the exact value of (i) sin 15 ^(@) (ii) sin 22 (1)/(2) ""^(@).
Answer» ANSWER :`SQRT (2 + SQRT2)`

Discussion

2389.	If cot theta-tantheta=2 then the principal value of theta is
Answer» `(PI)/(4)` `(pi)/(2)` `(pi)/(8)` `(3pi)/(4)` ANSWER :C

Discussion

2390.	Find the co-ordinates of a point on the parabola y^(2) = 8x whose focal distance is 4.
Answer» ANSWER :` y = PM 4`

Discussion

2391.	Let P(n) denote the statement that n^(2) +n is odd. It is seen that P(n) rArr P(n+1), P(n) is true for all
Answer» `N GT 1` `n` `n gt 2` no VALUE of n Answer :D

Discussion

2392.	List all theproper subsets of {0,{1},3}.
Answer» ANSWER :`PHI{0},{{1}},{3},{0,{1}},{{1},3},{0,3}`

Discussion

2393.	Find the locus of the point such that the sum of the squares of its distances from the points (2, 4) and (-3, -1) is 30.
Answer» ANSWER : `X^(2)+y^(2)+x-3y=0`

Discussion

2394.	For ""^(n) C_(r)+ 2""^(n) C_(r-1)+ ""^(n) C_(r-2)=
Answer» (a)`""^(n+1) C_(R-1) ` (B)` ""^(n+2) C_(r+1)` (C)` ""^(n+2) C_(r)` (d)` ""^(n+2)C_r` ANSWER :D

Discussion

2395.	Consider a DeltaABCwhose sides AB,BC, and CA are perresent byt the straight lines x-y=3 ,2x+y=0, x+py=q, and x-y=3, respectively. The point P(2,3) is the orthocenter. The value of (p+q)//10 is ______
Answer» ANSWER :5

Discussion

2396.	Which of the following sets are finite or infinite : Set of concentric circle in a plane.
Answer» ANSWER :it is an INFINITE SET

Discussion

2397.	The volume of a sphere is calculated by the formula V=(4)/(3)pir^(3). If deltar is the error in measuring the radius r, then the approximate error in the volume is
Answer» `4pirdeltar^(2)` `2pirdeltar^(2)` `4pideltar^(2)` `4pir^(2)DELTAR` ANSWER :D

Discussion

2398.	Let the point P lies in the interior of an equilateral triangle with side lengths 2 units, each. Find the sum of the shortest distances from P to the sides of the triangle.
Answer» ANSWER :`SQRT3`

Discussion

2399.	If semi Inter quartile range is 19.38,Q_(3)=72.5 then , Q_(1) is
Answer» (a)`38.75` (B)`35.75` (C)`33.74` (d)`34.75` ANSWER :C

Discussion

2400.	Differentiate the following functions: Given f(x) = (7)/(4) x^(2), find f'((1)/(7))
Answer» ANSWER :`(1)/(2)`

Discussion

Explore topic-wise InterviewSolutions in .

Which term of the expansion (sqrt((x)/(3))-(sqrt(3))/(2x))^(12)is independent of x.

If A is a 3xx4 matrix and B is a matrix such that both A^(T)B and BA^(T) are defined, what is the order of the matrix B?

If A=[(-1,2),(0,1)] then A A^(T). Do A and A^(T) commute with respect to multiplication of matrices ?

Find the mean deviation using median for the following observations: (a) 17,25,9,12,18,26,21 (b) 6,10,11,15,9,7,15,16,5 (c) 2,4,6,8,10,9,15,12,3,7 (d) 28,32,31,25,22,12,17,26 (e) 5,7,17,9,19,11,18

(2+sqrt(3))^(4)+(2-sqrt(3))^(4) = x+ ysqrt(3) then y = ………..

If the sides a, b, c of a triangle ABC form successive terms of G.P. with common ratio r (gt 1) then which of the following is correct?

Choose the most appropriate answer from those given in bracket If lim_(xrarr2)(x^p-2^p)/(x-2)=192 then p=………

If y = log_("sin x") (tan x), then ((dy)/(dx))_(pi//4) is equal to

Let U be universal set of all the students of Class XI of a coeducational school and A be the set of all girls in Class XI. Find A′.

Let f(x)=(alpha x)/((x+1)), x != -1. Then for which value of alpha is f(f(x))=x ?

Find the coordinates of the point at whichyz plane intersects the line segment joining the points (-2, 3, 7) and (6, -1, 2).

If h denote the arithmetic mean, k denote G.M. of the intercepts made on axes by the lines passing through (1, 1) then (h, k) lies on

Evaluate :lim_(xto1)(x^18-1)/(18x-18)

A triangle is formed by the lines whose equations are 3x+4y-6=0,12x-5y-3 = 0 and4x-3y + 12 = 0. Find the internal bisector of the angle opposite to the side 3x + 4y -6=0.

Given xgt0, the value of f(x) = -3cossqrt(3+x+x^(2)) lie in the interval ………….

Normal form of the line x-y+sqrt(2)=0 is

Solve the following equations and write general solutions sin^(2) theta - cos theta = (1)/(4)

Write down the contrapositive of the following statements.:If n is a natural number, then n is an integer.

Differentiate the following w.r.t. x : (x-2) (x+3) (2x +5)

How many 3 - digit numbers can be formed by using the digits 1 to 9 if no digit is repeated ?

Find the angle between the lines 3x+5y=7,2x-y+4=0

x - 2y le 4

If B={phi} then,

Find equation of line at the distance 3 from origin and perpendicular to the line sqrt(3) x - y+5=0.

If sec^(-1)(1/(sqrt(1-x^(2))))+cot^(-1)((sqrt(1-x^(2)))/x)=sin^(-1)(k) then k=

Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= 8- n^(3)

If RR is the set of all real number and if f : RR - {3} to RR is defined by f(x) = (3x + x)/(3-x) for x in RR - {3}, then the range of f is

If sin alpha=A sin(alpha + beta), A ne 0,then: Which of the following is the value of tan (alpha+beta)= ?

What is the number of terms in the expansion of the following? [ ( x-2)^(3) ]^3

Determine all values of alpha for which the point (alpha, alpha^(2)) lies inside the triangle formed by the lines 2x+3y-1=0, x+2y-3=0 and 5x-6y-1=0

EvaluateC(8,5)

If cos x=3, cos y,then 2 tan ((y-x)/(2))=

Find the mean and variance for each of the data in 6, 7, 10, 12, 13, 4, 8, 12

Statement 1 : If f : R rarr R , y = f(x) is a periodic and continuous function, then y=f(x) cannot be onto Statement 2 : A continuous periodic function is bounded.

If log_(2)x ge0 then log_(1/(pi))(sin^(-1)((2x)/(1+x^(2)))+2Tan^(-1)x)=lamda then |lamda|=

If vec(a) + vec(b) + vec(c )= vec(0) and |vec(a) xx vec(b)|=3, then |vec(b) xx vec(c )|=

Using the half angle formulas, find the exact value of (i) sin 15 ^(@) (ii) sin 22 (1)/(2) ""^(@).

If cot theta-tantheta=2 then the principal value of theta is

Find the co-ordinates of a point on the parabola y^(2) = 8x whose focal distance is 4.

Let P(n) denote the statement that n^(2) +n is odd. It is seen that P(n) rArr P(n+1), P(n) is true for all

List all theproper subsets of {0,{1},3}.

Find the locus of the point such that the sum of the squares of its distances from the points (2, 4) and (-3, -1) is 30.

For ""^(n) C_(r)+ 2""^(n) C_(r-1)+ ""^(n) C_(r-2)=

Consider a DeltaABCwhose sides AB,BC, and CA are perresent byt the straight lines x-y=3 ,2x+y=0, x+py=q, and x-y=3, respectively. The point P(2,3) is the orthocenter. The value of (p+q)//10 is ______

Which of the following sets are finite or infinite : Set of concentric circle in a plane.

The volume of a sphere is calculated by the formula V=(4)/(3)pir^(3). If deltar is the error in measuring the radius r, then the approximate error in the volume is

Let the point P lies in the interior of an equilateral triangle with side lengths 2 units, each. Find the sum of the shortest distances from P to the sides of the triangle.

If semi Inter quartile range is 19.38,Q_(3)=72.5 then , Q_(1) is

Differentiate the following functions: Given f(x) = (7)/(4) x^(2), find f'((1)/(7))