14949 + Interview Questions in Maths in Class 11 Page 110 InterviewSolution

5451.	The ratio in which the line 3x+4y+2=0 divides the distance between 3x+4y+5=0 and 3x+4y-5=0 is
Answer» `7:3` `3:7` `2:3` `3:2` ANSWER :B

Discussion

5452.	Obsereve the following the lists {:("List-I","List-II"),("A) "f(x)=x^2-2x+5" is increasing in","1) "xgt1/e),("B) "f(x)=x^x" decreases for","2) "(-oo,-1)uu(1,oo)),("C) "f(x)=x+1/x" is increasing in","3) "(1,oo)),("D) "f(x)=9-6x-2x^2-x^3" is decreasing for","4) "(-oo,oo)),("","5) "0ltxlt1/e):}
Answer» `{:(A,B,C,D),(3,4,2,5):}` `{:(A,B,C,D),(2,3,5,4):}` `{:(A,B,C,D),(3,1,4,2):}` `{:(A,B,C,D),(2,3,5,4):}` ANSWER :C

Discussion

5453.	If f(x)= (x-1)/(x+1), Then show that f((1)/(x))= -f(x)
Answer» ANSWER :`-F(X)`

Discussion

5454.	If x = sec theta - cos theta and y = sec^(n) theta - cos^(n) theta then ((dy)/(dx))^2 is equal to
Answer» `(n^2(y^2+4))/(X^2+4)` `(n^2(y^2-4))/(x^2)` `(n^2(y^2-4))/(x^2-4)` `((NY)/x)^2-4` ANSWER :A

Discussion

5455.	If (2)/(11) is the probability of an event, what is the probability of the event 'not' A'.
Answer» ANSWER :`=(9)/(11)`

Discussion

5456.	If sintheta+sqrt(3)costhetage1 then
Answer» `-(PI)/(3)lethetale(pi)/(3)` `-(pi)/(4)lethetale(pi)/(4)` `-(pi)/(6)lethetale(pi)/(2)` `-(pi)/(2)lethetale(pi)/(2)` Answer :C

Discussion

5457.	The orthocentre of the triangle formed by the line x^2-3y^2=0 and the line x=a is
Answer» `(a/3,0)` `((2A)/3,0)` (a,0) `((4A)/3,0)` ANSWER :B

Discussion

5458.	Let f(x) be a polynomial with positive degree satisfying the relation f(x)f(y) = f(x)+ f(y) + f(xy) -2 and f(4) = 65, then
Answer» `f(2)=9` `f(3 sqrt(3))=27` `f(5)=126` The roots of the equation `f(X)=2X^(2)` are all real Answer :A::C::D

Discussion

5459.	Find the centriod and hence find the area of the triangle formed by the following lines 12x^(2)-20xy+7y^(2)=0, 2x-3y+4=0
Answer» ANSWER :`((8)/(3),(8)/(3)), 4` sq. UNITS

Discussion

5460.	Evaluate the following limits : Lt_(xtooo)((x^(2)+2x+3)/(2x^(2)+x+5))^((3x-2)/(3x+2))
Answer» ANSWER :`1/2`

Discussion

5461.	matchthe following
Answer» ANSWER :d

Discussion

5462.	If (x + 1)(x + 2) …(x + n) = A_0 + A_1 x + ….+ A_n x^n then A_1 + 2A_2 + ….+ nA_n =
Answer» `(N+1)! [1/2 + 1/3+ ....+ 1/(n + 1)]` `n! [1/2 + 1/3+ ....+ 1/(n + 1)]` `(n+1)! [1 + 1/3+ ....+ 1/(n + 1)]` `n! [1 +1/2 + 1/3+ ....+ 1/(n + 1)]` ANSWER :A

Discussion

5463.	matchthe following
Answer» ANSWER :d

Discussion

5464.	If bar(a) = bar(i) + bar(j)+bar(k), bar(b) = 2bar(i) + 3bar(j) + bar(k) then find the projection vector of bar(b) on bar(a) and its magnitude.
Answer» ANSWER :`2bari+2barj+2bark and 2SQRT3`

Discussion

5465.	sec h^(-1)(cos theta) =
Answer» `log\|tan((pi)/(6) + (THETA)/(2))\|` `log\|tan((pi)/(3) + (theta)/(2))\|` `log\|tan((pi)/(4) + (theta)/(2))\|` `log\|tan((pi)/(4) - (theta)/(2))\|` ANSWER :C

Discussion

5466.	2tan^(-1)(1//2)+sin^(-1)(3//5)=
Answer» `TAN^(_1)(12/55)` `(PI)/4` `(pi)/2` `tan^(-1)(25/12)` ANSWER :C

Discussion

5467.	Evaluate lim_(x rarr 0) [(10^x - 2^x - 5^x + 1)/( x tanx)]
Answer» SOLUTION :`(log_e 2)(log_e 5)`

Discussion

5468.	Evaluate the following limits : Lim_(x to 1)(1-x^(-1//3))/(1-x^(-2//3))
Answer» ANSWER :`1/2`

Discussion

5469.	The two planes 2x+6y +10z-14=0,x+3y+5z+8=0 are
Answer» perpendicular parallel inclined at `30^(@)` inclined at `60^(@)` ANSWER :B

Discussion

5470.	If a is a 3xx3 matrix and \|"Adj A"\|=16 then \|A\|=
Answer» 4 `-4` `PM4` 8 Answer :C

Discussion

5471.	x_1,x_2, x_3,………., x_n are n observations . sum_(i=1)^(n) (x_i- 2) = 100 " and " sum_(i=1)^(n) (x_i- 5) = 20 then mean barx = …….
Answer» `23/4` `14/3` `3/11` `10` ANSWER :A

Discussion

5472.	Convert the following complex number in the polar form : (2+6 sqrt(3)i)/(5+ sqrt(3)i)
Answer» ANSWER :`2("cos"(PI)/(3)+I"SIN"(pi)/(3))`

Discussion

5473.	Find (dy)/(dx)if x =a ((1- t ^(2))/( 1 + t ^(2))), y = (2 bt)/(1 + t ^(2)).
Answer» ANSWER : `(B)/(2A) (t - (1)/(t))`

Discussion

5474.	Let f(x=sin""pi/x and D= { x : f (x) gt 0} , then D contains
Answer» `(1/3, 1/2)` `(1/5, 1/4)` `(-1, - 1/2)` `( - PI, - 1/2)` ANSWER :A::B::C

Discussion

5475.	If the controid of the tetrahedron OABC where A,B,C are the points (a,2,3), (1,b,2) and (2,1,c) be (1,2,3) and the point (a,b,c) is at distance 5sqrt(lambda) from origin, then lambda^(2) must be equal to.
Answer» ANSWER :9

Discussion

5476.	A die is rolled. If the outcome is an odd number, what is theprobability that it is prime?
Answer» ANSWER :`=(2)/(3)`.

Discussion

5477.	Consider the following sets: A = {x:x is a natural number and 1lt xle 4}B ={x:x is a natural number and 4lt x le8} Find A cup B
Answer» SOLUTION :`A CUP B` = {2,3,4,5,6,7,8}

Discussion

5478.	Consider the following sets: A = {x:x is a natural number and 1lt xle 4}B ={x:x is a natural number and 4lt x le8} Find P(A)
Answer» <P> Solution :P(A) = {`PHI`,A,{2},{3},{4},{2,3},{2,4},{3,4}}

Discussion

5479.	Consider the following sets: A = {x:x is a natural number and 1lt xle 4}B ={x:x is a natural number and 4lt x le8} Represent these sets on Roster form
Answer» SOLUTION :A = {2,3,4}, B ={5,6,7,8}

Discussion

5480.	If (cos x)/(a)=(cos(x+ theta))/(b)=(cos (x+2 theta))/(c)=(cos(x+3 theta))/(d) then (b+d)/(a+c)=
Answer» d/a a/d C/b b/c Answer :C

Discussion

5481.	Construct truth tables for each of the following : qimplies [(~p)vv q]
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E06_018_A01##)` [Recall that p => q is false only when p is TRUE and q is false ]

Discussion

5482.	Let f(x)=log_(e)(x+ sqrt(x^(2)+1)), domain of f is where f(x) is defined for real values of x, If f is bijective then f^(-1)(x) exists The inverse of f is positive on
Answer» `(0, OO)` `(-oo, oo)` `[0, E]` `(-oo, 0)` ANSWER :A

Discussion

5483.	Let f(x)=log_(e)(x+ sqrt(x^(2)+1)), domain of f is where f(x) is defined for real values of x, If f is bijective then f^(-1)(x) exists f^(-1)(x)isdefined on
Answer» `(0,OO)` `(-oo,oo)` `[0, E]` `(-oo, 0)` ANSWER :B

Discussion

5484.	The perpendicular from the origin to the line y=mx+c meets it at the point (-1,2). Find the values of m and c.
Answer» ANSWER :`C= (5)/(2)`

Discussion

5485.	Let R=(8+3sqrt(7))^20 and [.] denotes greatest integer function, then prove that : (a) [R] is odd(b) R-[R] =1-(1)/((8+3sqrt(7))^20
Answer»

Discussion

5486.	If A is a square matrix such that A^(2)=A,then the value of A+(A-I)^(4)is:
Answer» A 0 identity matrix of ORDER 1 NONE of these Answer :C

Discussion

5487.	Find the coefficient of (ii) x^7 in the expansion of (x^(2) + (1)/(x) )^(11)
Answer» ANSWER :`462`

Discussion

5488.	Fill in the blanks to make each of the following a true statement : A ∪ A′ = . . .
Answer» ANSWER :U

Discussion

5489.	Sum of first 'n' terms of the series = (3)/(2) + (5)/(4) + (9)/(8) + (17)/( 16) + …..... =
Answer» `N -1 + 2^(-n)` `n+1+2^(-n)` `n+1-2^(-n)` `n-1-2^(-n)` ANSWER :C

Discussion

5490.	Let a, b, c be positive number. If ax^(2) + (b)/(x) = c for all x gt 0, then that the minimum value of (ab^(2))/(c^(3)) is (4)/(27)
Answer» Answer :`((27 ab^(2))/(4))^(1//3) GE C rArr (ab^(2))/(c^(3)) ge (4)/(27)`

Discussion

5491.	An experiment yields 3 mutually exclusive and exclusive events A, B and C . If P(A) = 2P(B) = 3 P( C ) , then P(A) is equal to
Answer» ANSWER :`(6)/(11)`

Discussion

5492.	Evaluate the following limits : Lim_( x to 0) ((1+5x^(2))/(1+3x^(2)))^(x^(1/2))
Answer» ANSWER :`E^(2)`

Discussion

5493.	What is the probability that in a leap year chosen at random will contain 53 Sunday?
Answer» ANSWER :`(3)/(7)`

Discussion

5494.	i) Let bara, barb and barc be non - coplanar vectors and baralpha=bara+2barb+3barc,barbeta=2bara+barb-2barc and bargamma=3bara-7barc, then find [baralphabarbetabargamma] (ii) If bara,barbbarc are non coplanar vectors, then find ((bara+2barb-barc).[(bara-barb)xx(bara-barb-barc)])/([barabarbbarc])
Answer» ANSWER :0,3

Discussion

5495.	Write the first five terms of each of the sequenceswhose n^(th)terms are: a_n = 2^n
Answer» ANSWER :2,4,8,16 and 32

Discussion

5496.	Graph of inequality x - 3 lt 5 and 3x + 5 lt 2 x in Ris as follows
Answer» ANSWER :TRUE STATEMENT

Discussion

5497.	If 'x' is a negative real number then the value of Cos^(-1)x+Sec^(-1)x is
Answer» RATIONAL number irrational number integer imaginary Answer :B

Discussion

5498.	Identify the quantifier in the following statement, For every real number x, x is less thanx + 1
Answer» ANSWER :For EVERY

Discussion

5499.	If cosh(x)=sec alpha then "cosech"(x)=
Answer» `sin alpha` `COS alpha` `TAN alpha` `COT alpha` Answer :D

Discussion

5500.	Find the approximate value of sqrt(82)
Answer» ANSWER :9.056

Discussion

Explore topic-wise InterviewSolutions in .

The ratio in which the line 3x+4y+2=0 divides the distance between 3x+4y+5=0 and 3x+4y-5=0 is

Obsereve the following the lists {:("List-I","List-II"),("A) "f(x)=x^2-2x+5" is increasing in","1) "xgt1/e),("B) "f(x)=x^x" decreases for","2) "(-oo,-1)uu(1,oo)),("C) "f(x)=x+1/x" is increasing in","3) "(1,oo)),("D) "f(x)=9-6x-2x^2-x^3" is decreasing for","4) "(-oo,oo)),("","5) "0ltxlt1/e):}

If f(x)= (x-1)/(x+1), Then show that f((1)/(x))= -f(x)

If x = sec theta - cos theta and y = sec^(n) theta - cos^(n) theta then ((dy)/(dx))^2 is equal to

If (2)/(11) is the probability of an event, what is the probability of the event 'not' A'.

If sintheta+sqrt(3)costhetage1 then

The orthocentre of the triangle formed by the line x^2-3y^2=0 and the line x=a is

Let f(x) be a polynomial with positive degree satisfying the relation f(x)f(y) = f(x)+ f(y) + f(xy) -2 and f(4) = 65, then

Find the centriod and hence find the area of the triangle formed by the following lines 12x^(2)-20xy+7y^(2)=0, 2x-3y+4=0

Evaluate the following limits : Lt_(xtooo)((x^(2)+2x+3)/(2x^(2)+x+5))^((3x-2)/(3x+2))

matchthe following

If (x + 1)(x + 2) …(x + n) = A_0 + A_1 x + ….+ A_n x^n then A_1 + 2A_2 + ….+ nA_n =

matchthe following

If bar(a) = bar(i) + bar(j)+bar(k), bar(b) = 2bar(i) + 3bar(j) + bar(k) then find the projection vector of bar(b) on bar(a) and its magnitude.

sec h^(-1)(cos theta) =

2tan^(-1)(1//2)+sin^(-1)(3//5)=

Evaluate lim_(x rarr 0) [(10^x - 2^x - 5^x + 1)/( x tanx)]

Evaluate the following limits : Lim_(x to 1)(1-x^(-1//3))/(1-x^(-2//3))

The two planes 2x+6y +10z-14=0,x+3y+5z+8=0 are

If a is a 3xx3 matrix and |"Adj A"|=16 then |A|=

x_1,x_2, x_3,………., x_n are n observations . sum_(i=1)^(n) (x_i- 2) = 100 " and " sum_(i=1)^(n) (x_i- 5) = 20 then mean barx = …….

Convert the following complex number in the polar form : (2+6 sqrt(3)i)/(5+ sqrt(3)i)

Find (dy)/(dx)if x =a ((1- t ^(2))/( 1 + t ^(2))), y = (2 bt)/(1 + t ^(2)).

Let f(x=sin""pi/x and D= { x : f (x) gt 0} , then D contains

If the controid of the tetrahedron OABC where A,B,C are the points (a,2,3), (1,b,2) and (2,1,c) be (1,2,3) and the point (a,b,c) is at distance 5sqrt(lambda) from origin, then lambda^(2) must be equal to.

A die is rolled. If the outcome is an odd number, what is theprobability that it is prime?

Consider the following sets: A = {x:x is a natural number and 1lt xle 4}B ={x:x is a natural number and 4lt x le8} Find A cup B

Consider the following sets: A = {x:x is a natural number and 1lt xle 4}B ={x:x is a natural number and 4lt x le8} Find P(A)

Consider the following sets: A = {x:x is a natural number and 1lt xle 4}B ={x:x is a natural number and 4lt x le8} Represent these sets on Roster form

If (cos x)/(a)=(cos(x+ theta))/(b)=(cos (x+2 theta))/(c)=(cos(x+3 theta))/(d) then (b+d)/(a+c)=

Construct truth tables for each of the following : qimplies [(~p)vv q]

Let f(x)=log_(e)(x+ sqrt(x^(2)+1)), domain of f is where f(x) is defined for real values of x, If f is bijective then f^(-1)(x) exists The inverse of f is positive on

Let f(x)=log_(e)(x+ sqrt(x^(2)+1)), domain of f is where f(x) is defined for real values of x, If f is bijective then f^(-1)(x) exists f^(-1)(x)isdefined on

The perpendicular from the origin to the line y=mx+c meets it at the point (-1,2). Find the values of m and c.

Let R=(8+3sqrt(7))^20 and [.] denotes greatest integer function, then prove that : (a) [R] is odd(b) R-[R] =1-(1)/((8+3sqrt(7))^20

If A is a square matrix such that A^(2)=A,then the value of A+(A-I)^(4)is:

Find the coefficient of (ii) x^7 in the expansion of (x^(2) + (1)/(x) )^(11)

Fill in the blanks to make each of the following a true statement : A ∪ A′ = . . .

Sum of first 'n' terms of the series = (3)/(2) + (5)/(4) + (9)/(8) + (17)/( 16) + …..... =

Let a, b, c be positive number. If ax^(2) + (b)/(x) = c for all x gt 0, then that the minimum value of (ab^(2))/(c^(3)) is (4)/(27)

An experiment yields 3 mutually exclusive and exclusive events A, B and C . If P(A) = 2P(B) = 3 P( C ) , then P(A) is equal to

Evaluate the following limits : Lim_( x to 0) ((1+5x^(2))/(1+3x^(2)))^(x^(1/2))

What is the probability that in a leap year chosen at random will contain 53 Sunday?

i) Let bara, barb and barc be non - coplanar vectors and baralpha=bara+2barb+3barc,barbeta=2bara+barb-2barc and bargamma=3bara-7barc, then find [baralphabarbetabargamma] (ii) If bara,barbbarc are non coplanar vectors, then find ((bara+2barb-barc).[(bara-barb)xx(bara-barb-barc)])/([barabarbbarc])

Write the first five terms of each of the sequenceswhose n^(th)terms are: a_n = 2^n

Graph of inequality x - 3 lt 5 and 3x + 5 lt 2 x in Ris as follows

If 'x' is a negative real number then the value of Cos^(-1)x+Sec^(-1)x is

Identify the quantifier in the following statement, For every real number x, x is less thanx + 1

If cosh(x)=sec alpha then "cosech"(x)=

Find the approximate value of sqrt(82)