14949 + Interview Questions in Maths in Class 11 Page 221 InterviewSolution

11001.	If f : R to R is defined by f(x) = {{:(x+4" for " x lt - 4),(3x+2" for " -4 le x
Answer» ANSWER :A-iii; B-vi; C-ii; D-v

Discussion

11002.	Find the most general value of theta that satisfying both the equations sin theta = (sqrt(3))/(2), cosec theta = (2)/(sqrt(3))
Answer» ANSWER :`2NPI + (2PI)/(3)`

Discussion

11003.	ABCD is a quadrilateral. E is the point of intersection of the line joining the middle points of the opposite sides. If O is any point then bar(OA)+bar(OB)+bar(OC)+bar(OD)=
Answer» `4bar(OE)` `3BAR(OE)` `2BAR(OE)` `BAR(OE)` ANSWER :A

Discussion

11004.	Find the product of the following pairs? 11a^(2)b,3a^(3)b^(2)
Answer» ANSWER :`107x - 3Y - 92 = 0 `

Discussion

11005.	The total number of solutions of sin[x]= cos [x] where [*] denotes the fractional part ) in [0, 2 pi] equal to
Answer» 5 6 8 7 Answer :B

Discussion

11006.	Let the lines L_(1), L_(2), L_(3) lie in a plane pi. If a line L is equally inclinded with these lines, show tat L is normal to the plane pi.
Answer» ANSWER :L is PERPENDICULAR to PLANE `PI`

Discussion

11007.	((1)/(2), (2)/(2) )/(1^3) + ((2)/(2) , (3)/(2) )/( 1^3 + 2^3) + ((3)/(2) , (4)/(2) ) / (1^(3) + 2^(3) + 3^(3) ) + ..... n terms
Answer» `(N^2)/( (n+1)^2)` `(n^3)/( (n+1)^3)` `(n)/(n+1)` `(1)/( n+1)` ANSWER :B::C

Discussion

11008.	If n(A) = 4, n (B) = 9 and AsubB" then " n(AcapB)= ….. .
Answer» ANSWER :4

Discussion

11009.	Find the sum to indicated number of terms in each of the geometric progressions in 0.15, 0.015, 0.0015 ,.........20 terms .
Answer» ANSWER :`1/6[1-(0.1)^(20)]`

Discussion

11010.	Find the centre and the radius of the circle x^(2)+y^(2)+8x+10y-8=0.
Answer» Answer :Centre (-4, -5), RADIUS 7

Discussion

11011.	If A.M. and G.M. of two positive numbers a and b are 10 and 8, respectively, find the numbers.
Answer» ANSWER :the number a and B are 4, 16or 16, 4 respectively.

Discussion

11012.	If bara, barb, barc are any three vectors then (baraxxbarb)xxbarc is a vector
Answer» PARALLEL to `barc` parallel to `BARA` parallel to `bara` and `barb` `bot` to `BARAXXBARB`, COPLANER with `bara` and `barb` Answer :D

Discussion

11013.	Let f(x)= (x^2 - x)/(x^2 + 2x) , then d/(dx) (f^(-1)(x))^(-) is equal to
Answer» `(1-)/((1-x)^(2))` `(3)/((1-x)^(2))` `(1)/((1-x)^(2))` `(-3)/((1-x)^(2))` ANSWER :D

Discussion

11014.	For two sets A and B, prove that A- (B cap C)= (A - B) cup (A - C).
Answer» `(A - B)n cup (A - C)` `(A - B) cap (A - C)` `(B - A) cup (C - A)` NONE of these Answer :A

Discussion

11015.	sqrt3"cosec"20^(@) - sec20^@ =
Answer» 2 3 1 4 Answer :D

Discussion

11016.	If [baraxx(barbxxbarc)]xxbarc=(bara·barc)barR then barR=
Answer» `barcxxbarb` `BARBXXBARC` `BARCXXBARA` `baraxxbarc` ANSWER :B

Discussion

11017.	A card is drawn at random from a well shuffled pack of cards . What is the probability that it is a heart or a queen ?
Answer» ANSWER :`(4)/(13)`

Discussion

11018.	If (2+5i) z = (3 - 7 i) then z = ......... .
Answer» ANSWER :`-1-i`

Discussion

11019.	Length of perpendicular from origin to the line l:x-sqrt(3)y+4=0 is 4 unit.
Answer» ANSWER :FALSE STATEMENT

Discussion

11020.	If f(x)=Cos^(2)x+Cos^(2)2x+Cos^(2)3x then the number of x epsilon[0,2pi] for which f(x)=1 is
Answer» 4 6 8 10 Answer :D

Discussion

11021.	The value k such that 3x^2+11xy+10y^2+7x+13+k=0 represents a pair ofstraight lines is
Answer» 1 2 3 4 Answer :D

Discussion

11022.	Matching thefollowing
Answer» 1-c,2-a,3-d,4-b 1-d,2-a,3-b,4-c 1-a,2-c,3-b,4-d 1-b,2-d,3-a,4-c Answer :1

Discussion

11023.	If vec(a)= 2vec(i)-3 vec(j) + vec(k). vec(b)= vec(i) + 4vec(j)- 2vec(k), then find (vec(a) + vec(b)) xx (vec(a) - vec(b)).
Answer» ANSWER :`-2(2vec(i) + 5vec(J) + 11vec(K))`

Discussion

11024.	The value of cos y cos ((pi)/(2) - x) - cos ((pi)/(2) - y) cos x + sin y cos ((pi)/(2) - x) + cos x sin ((pi)/(2) - y) iszero if
Answer» `X = 0` y = 0 x = y `n PI + y - (pi)/(4) (n in Z)` Answer :D

Discussion

11025.	InDelta ABC tan "" ( A)/(2) = ( 5)/( 6), tan "" ( C )/(2) = (2)/(5)then a,b,c are such that
Answer» `B^(2)=AC` `2b=a+c` `2ac=b(a+c)` `a+b=c` ANSWER :B

Discussion

11026.	If the arc of the same lengths in two circles subtend angles 65^(@) and 110^(@) at the centre, find the ratio of their radii.
Answer» ANSWER :`22:13`

Discussion

11027.	Consider the expansion of ((4x)/5-5/(4x))^8 Find the (r+1)^(th) term in the expansion
Answer» SOLUTION :`(-1)^rc_r((4X)/5)^(8-R)(5/(4x))^r`

Discussion

11028.	Write out the expansion of the following:(2x + (y)/(2) )^(5)
Answer» Answer :`32x^(5) + 40x^(4) y + 20x^(3) y^(2) + 5x^(2) y^(3) + (5)/(8) xy^(4) + (1)/(32) y^(5)`

Discussion

11029.	The number of solutions of the equation tan x +sec x = 2 cos xlying in the interval [0, 2 pi] is
Answer» 0 1 2 3 Answer :C

Discussion

11030.	How many words can be formed by the letters of the word 'SCHOLAR', if each word starts with 'O' and ends with 'S'?
Answer» ANSWER :120

Discussion

11031.	Find r : ""^(5) P_(r) =42 ""^(6)P_(r-1)
Answer» ANSWER :(i) R = 13, (II) r = 6

Discussion

11032.	Every set has two subsets .
Answer» ANSWER :FALSE STATEMENT

Discussion

11033.	State whether the or used in the following statements is exclusive or inclusive. Give reasons for your answer: To apply for a driving licence you should have a ration card or a passport.
Answer» ANSWER :INCLUSIVE SENSE.

Discussion

11034.	State whether the or used in the following statements is exclusive or inclusive. Give reasons for your answer: All integers are positive or negative.
Answer» ANSWER :not NEGATIVE.

Discussion

11035.	Find the odd one out : f(x)=[x-\|x\|]/x x ne 0
Answer» CONTINUOUS no where continuous everywhere continuous EXCEPT X=5 continuous for all x except x=0 Answer :D

Discussion

11036.	State whether the or used in the following statements is exclusive or inclusive. Give reasons for your answer: Sun rises or Moon sets.
Answer» ANSWER :Any once can EXISTS of ONE TIME.

Discussion

11037.	Let alpha, beta and gamma be some angles in the first quadrant satisfying tan(alpha+beta)=15//8 and cosec gamma = 17//8, then which of the following hold(s) good ?
Answer» `alpha+beta+GAMMA=pi` `cot alpha cot beta cot gamma = cot alpha + cot beta + cot gamma` `TAN alpha + tan beta + tan gamma = tan alpha tan beta tan gamma` `tan alpha tan beta + tan beta tan gamma + tan gamma tan alpha =1` Answer :B::D

Discussion

11038.	A and B are two events such that P(A)=0.54, P(B)=0.69 and P(A,C, B) =0.35. Find (i) P(AcupB) (ii) P(A'capB') (iii) P(AcapB') (iv) P(BcapA')
Answer» <P> ANSWER :`(ACUPB)=0.88""P(A'capB')=0.12` `P(A'cupB')=0.65,""P(ACAPB')=0.19`

Discussion

11039.	Write the negative of the compound proposition p vv(~pvvq)
Answer» <P> ANSWER :`~p^^[~(~PVVQ)]`

Discussion

11040.	The sum of the solutions in (0, 2pi) of the equation cos x cos ((pi)/(3)-x)cos((pi)/(3)+x)=(1)/(4) is
Answer» `PI` `2pi` `3pi` `4PI` ANSWER :B

Discussion

11041.	Find the range of cosec^(-1)[1+sin^(2)x], where [.] denotes the greatest integer function
Answer» `{pi/2}` `{COSEC^(-1)2}` `{pi/2, cosec^(-1)2}` `PHI` Answer :C

Discussion

11042.	ABCD is a trapezium such that AB and CD are parallel and BC bot CD. If angle ADB= theta , BC= p and CD=q then AB is equal to ......
Answer» <P>`((p^(2)+q^(2)) sin THETA)/(p COS theta+ q sin theta)` `(p^(2)+q^(2) cos theta)/(p cos theta+ q sin theta)` `(p^(2)+q^(2))/(p^(2) cos theta+ q^(2) sin theta)` `((p^(2)+q^(2)) sin theta)/((p cos theta+q sin theta)^(2))` ANSWER :A

Discussion

11043.	Differentiate 2^(x) with respect to x.
Answer» ANSWER :`(LOG2)2^(X)`

Discussion

11044.	Differentiate the w.r.t.x: e ^(sin ^(-1) x)
Answer» Answer :`(E ^(sin ^(-1) x ))/( SQRT (1- x ^(2))) ,x in (-1,1)`

Discussion

11045.	An advertising executive is stydying television viewing habits of married men and women during prime time hours. Based on the past viewing records he has determined that during prime time wives are watching television 60% of the time. It has also been determined that when the wife is watching television, 40% of the time the husband is also watching. When the wife is not watching the television,30% of the time the husband is watching the televison. Find the probability that (i)the husband is watching the television during the prime time of television(ii)if the husband is watching the television, the wife is also watching the television.
Answer» ANSWER :`(2)/(3)`

Discussion

11046.	Write the contrapositive of the following statement: If a number is divisible by 9, then it is divisible by 3.
Answer» ANSWER :not DIVISIBLE by 9.

Discussion

11047.	cot 15^(@) + cot 75^(@) + cot 315^(@) =
Answer» 0 1 2 3 Answer :D

Discussion

11048.	The value of f(0), so that the function f(x)=(sqrt(a^(2)-ax+x^(2))-sqrt(a^(2)+ax+x^(2)))/(sqrt(a+x)-sqrt(a-x)) becomes continuous for all x in given by
Answer» `a SQRT(a)` `sqrt(a)` `-sqrt(a)` `-asqrt(a)` ANSWER :A

Discussion

11049.	Prove that sin^(2)alpha + cos^(2) (alpha + beta) + 2 sin alpha sin beta cos (alpha + beta) is independent of alpha.
Answer» `SIN^(2) alpha` `sin^(2) BETA` `COS^(2)alpha` `cos^(2) beta` Answer :D

Discussion

11050.	Let a sample space be S={omega_(1),omega_(2),.........,omega_(6)}. Which of the following assignments of probabilities to each outcome are valid ?
Answer» ANSWER :` 1/2`

Discussion

Explore topic-wise InterviewSolutions in .

If f : R to R is defined by f(x) = {{:(x+4" for " x lt - 4),(3x+2" for " -4 le x

Find the most general value of theta that satisfying both the equations sin theta = (sqrt(3))/(2), cosec theta = (2)/(sqrt(3))

ABCD is a quadrilateral. E is the point of intersection of the line joining the middle points of the opposite sides. If O is any point then bar(OA)+bar(OB)+bar(OC)+bar(OD)=

Find the product of the following pairs? 11a^(2)b,3a^(3)b^(2)

The total number of solutions of sin[x]= cos [x] where [*] denotes the fractional part ) in [0, 2 pi] equal to

Let the lines L_(1), L_(2), L_(3) lie in a plane pi. If a line L is equally inclinded with these lines, show tat L is normal to the plane pi.

((1)/(2), (2)/(2) )/(1^3) + ((2)/(2) , (3)/(2) )/( 1^3 + 2^3) + ((3)/(2) , (4)/(2) ) / (1^(3) + 2^(3) + 3^(3) ) + ..... n terms

If n(A) = 4, n (B) = 9 and AsubB" then " n(AcapB)= ….. .

Find the sum to indicated number of terms in each of the geometric progressions in 0.15, 0.015, 0.0015 ,.........20 terms .

Find the centre and the radius of the circle x^(2)+y^(2)+8x+10y-8=0.

If A.M. and G.M. of two positive numbers a and b are 10 and 8, respectively, find the numbers.

If bara, barb, barc are any three vectors then (baraxxbarb)xxbarc is a vector

Let f(x)= (x^2 - x)/(x^2 + 2x) , then d/(dx) (f^(-1)(x))^(-) is equal to

For two sets A and B, prove that A- (B cap C)= (A - B) cup (A - C).

sqrt3"cosec"20^(@) - sec20^@ =

If [baraxx(barbxxbarc)]xxbarc=(bara·barc)barR then barR=

A card is drawn at random from a well shuffled pack of cards . What is the probability that it is a heart or a queen ?

If (2+5i) z = (3 - 7 i) then z = ......... .

Length of perpendicular from origin to the line l:x-sqrt(3)y+4=0 is 4 unit.

If f(x)=Cos^(2)x+Cos^(2)2x+Cos^(2)3x then the number of x epsilon[0,2pi] for which f(x)=1 is

The value k such that 3x^2+11xy+10y^2+7x+13+k=0 represents a pair ofstraight lines is

Matching thefollowing

If vec(a)= 2vec(i)-3 vec(j) + vec(k). vec(b)= vec(i) + 4vec(j)- 2vec(k), then find (vec(a) + vec(b)) xx (vec(a) - vec(b)).

The value of cos y cos ((pi)/(2) - x) - cos ((pi)/(2) - y) cos x + sin y cos ((pi)/(2) - x) + cos x sin ((pi)/(2) - y) iszero if

InDelta ABC tan "" ( A)/(2) = ( 5)/( 6), tan "" ( C )/(2) = (2)/(5)then a,b,c are such that

If the arc of the same lengths in two circles subtend angles 65^(@) and 110^(@) at the centre, find the ratio of their radii.

Consider the expansion of ((4x)/5-5/(4x))^8 Find the (r+1)^(th) term in the expansion

Write out the expansion of the following:(2x + (y)/(2) )^(5)

The number of solutions of the equation tan x +sec x = 2 cos xlying in the interval [0, 2 pi] is

How many words can be formed by the letters of the word 'SCHOLAR', if each word starts with 'O' and ends with 'S'?

Find r : ""^(5) P_(r) =42 ""^(6)P_(r-1)

Every set has two subsets .

State whether the or used in the following statements is exclusive or inclusive. Give reasons for your answer: To apply for a driving licence you should have a ration card or a passport.

State whether the or used in the following statements is exclusive or inclusive. Give reasons for your answer: All integers are positive or negative.

Find the odd one out : f(x)=[x-|x|]/x x ne 0

State whether the or used in the following statements is exclusive or inclusive. Give reasons for your answer: Sun rises or Moon sets.

Let alpha, beta and gamma be some angles in the first quadrant satisfying tan(alpha+beta)=15//8 and cosec gamma = 17//8, then which of the following hold(s) good ?

A and B are two events such that P(A)=0.54, P(B)=0.69 and P(A,C, B) =0.35. Find (i) P(AcupB) (ii) P(A'capB') (iii) P(AcapB') (iv) P(BcapA')

Write the negative of the compound proposition p vv(~pvvq)

The sum of the solutions in (0, 2pi) of the equation cos x cos ((pi)/(3)-x)cos((pi)/(3)+x)=(1)/(4) is

Find the range of cosec^(-1)[1+sin^(2)x], where [.] denotes the greatest integer function

ABCD is a trapezium such that AB and CD are parallel and BC bot CD. If angle ADB= theta , BC= p and CD=q then AB is equal to ......

Differentiate 2^(x) with respect to x.

Differentiate the w.r.t.x: e ^(sin ^(-1) x)

Write the contrapositive of the following statement: If a number is divisible by 9, then it is divisible by 3.

cot 15^(@) + cot 75^(@) + cot 315^(@) =

The value of f(0), so that the function f(x)=(sqrt(a^(2)-ax+x^(2))-sqrt(a^(2)+ax+x^(2)))/(sqrt(a+x)-sqrt(a-x)) becomes continuous for all x in given by

Prove that sin^(2)alpha + cos^(2) (alpha + beta) + 2 sin alpha sin beta cos (alpha + beta) is independent of alpha.

Let a sample space be S={omega_(1),omega_(2),.........,omega_(6)}. Which of the following assignments of probabilities to each outcome are valid ?