14949 + Interview Questions in Maths in Class 11 Page 53 InterviewSolution

2601.	Vector component of barb perpendicular to bara is
Answer» `(barb.barc)bara` `(BARAXX(barbxxbara))/(abs(bara)^(2))` `((barb.barc).bara))/(abs(bara)^(2))` `baraxx(barbxxbara)` Answer :B

Discussion

2602.	If the equation (a_(1)-a_(2))x+(b_(1)-b_(2))y=c represents the perpendicular bisector of the segment joining (a_(1),b_(1)),(a_(2),b_(2)) then 2c=
Answer» `a_(1)^(2)+b_(1)^(2)-a_(2)^(2)-b_(2)^(2)` `a_(1)^(2)+b_(1)^(2)+a_(2)^(2)+b_(2)^(2)` `a_(1)^(2)-b_(1)^(2)+a_(2)^(2)-b_(2)^(2)` `a_(1)a^(2)+b_(1)B^(2)` ANSWER :A

Discussion

2603.	A flag staff of length 10 mt stands on a tower if from a point on the ground , the angle of elevation of the foot and the top of the flagstaff are 45 ^(@) and 75 ^(@)then height of the tower is
Answer» ` 5( SQRT3+ 1) ` ` (80 )/(sqrt3) (sqrt3+ 1) ` ` ( 80 (sqrt3+ 1)) /( 3sqrt3) ` ` 5(sqrt3-1) ` Answer :D

Discussion

2604.	Find the component statements of the following and check whether they are true or not: A person who has taken Mathematics or computer Science can go for MCA.
Answer» ANSWER :TRUE.

Discussion

2605.	For ninz, cos(2theta)=(sqrt(5)+1)/(4) implies theta =
Answer» `2npipm(PI)/(5)` `npipm(pi)/(5)` `(npi)/(5)+(-1)^(N).(pi)/(10)` `npipm(pi)/(10)` Answer :D

Discussion

2606.	Let bare_(1) and bare_(2) be unit vectors which include anangel theta."If " 1/2abs(bare_(1) - bare_(2)) = sin (k theta), then k=
Answer» `1/3` `1/4` `1/2` `1/5` ANSWER :C

Discussion

2607.	For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If x in (1/2,1) then the value of lim_(ytoa)b cos (y) is
Answer» `-1/3` `-3` `1/3` `3` ANSWER :D

Discussion

2608.	A man starts repaying a loan as first installment of Rs. 100 If he increases the installment by Rs. 5 every month , what amount he will pay in the 30 th installment ?
Answer» ANSWER :RS 245

Discussion

2609.	There are 2n guests at a dinner party. Supposing that the master annd mistress of the house have fixed seats opposite one another and that there are two specified guests who must not be placed next to one another. Find the number of ways in which the company can be placed.
Answer» Answer :`(11!)/(6!5!) xx 9! xx 9!.`

Discussion

2610.	Find the value of the product:\|(log_(3)64,log_(4)3),(log_(3)8,log_(4)9)\|xx\|(log_(2)3,log_(8)3),(log_(3)4,log_(3)4)\|
Answer» ANSWER :6

Discussion

2611.	Expand (1+ 2 x + 3x^(2) )^(n) in a series of ascending powers of x up to and including the term in x^2.
Answer» ANSWER :`1+ 2nx + x^(2) ( 2n^(2) + N)`

Discussion

2612.	From mean value theorem, f(b)-f(a) = (b-a)f^(1)(x_(1)), a lt x_(1) lt b if f(x) = ( 1)/( x) then x_(1) =
Answer» `SQRT(AB)` `(a+b)/(2)` `(ab)/(a+b)` `(b-a)/(b-a)` ANSWER :A

Discussion

2613.	Which of the following pairs of sets are disjoint { a, e, i, o, u } and { c, d, e, f }
Answer» ANSWER :A and B are not DISJOINT SET

Discussion

2614.	Consider the following population and year graph (Fig 10.10), find the slope of the line AB and using it, find what will be the population in the year 2010?
Answer» ANSWER :`1/2 , 104.5` CRORES

Discussion

2615.	For the function f(x) satisfying 2. f(sin x)+f(cos x) = x, AA x in R
Answer» DOMAIN is [0, 1] range is `[(-2pi)/(3), PI/3]` Domain is [-1, 1] range is`[(-pi)/(2), pi/2]` Answer :B::C

Discussion

2616.	Let x,y,z be elements from interval [0,2pi] satisfying the inequality (4+sin 4x)(2+cot^(2)y)(1+sin^(4)z)le12sin^(2)z then
Answer» The NUMBER of ordered PAIRS (z,X) is 8 The number of ordered pairs (y,z) such that `z=y` is 2 The number of ordered pairs (x,y) is 4 The number of ordered pairs (y,z) is 6 Answer :A::B

Discussion

2617.	Origin shifted to the point (1, 2) without changing the direction of the axes then (4, 3) is transformed to
Answer» (3, 1) (5, 5) (-3, -1) (2, -1) ANSWER :A

Discussion

2618.	If in a Delta ABC, a, b, care in A.P . Thencos ((A- C)/( 2))is equal to
Answer» ` ( 1)/ (2)SIN ""( B)/(2) ` `2 sin "" (B)/2` ` (1)/(3)sin ""( B)/(2) - 4 ` ` 3 sin ""( B)/(2) ` ANSWER :B

Discussion

2619.	A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that is rusted or is a nail is ......
Answer» `(3)/(16)` `(5)/(16)` `(11)/(16)` `(14)/(16)` ANSWER :C

Discussion

2620.	Find the equation of a line perpendicular to the line x-2y+ 3=0 and passing through the point (1,-2).
Answer» ANSWER :`y=-2x`

Discussion

2621.	Evaluate the following limits : Lim_( x to 0 )(ax +b)/(cx +d)
Answer» ANSWER :`b/d`

Discussion

2622.	If (sin(alpha+beta))/(sin(alpha-beta)) = (a+b)/(a-b), then prove that a tan beta = b tan alpha.
Answer» ANSWER :`a TAN BETA = B Tan ALPHA`

Discussion

2623.	An equilateral triangle ABC has its centroid at the origin and one side 'AC' isx+y=1 IfA(X_1,Y_1), B(x_2,y_2),C(x_3,y_3) " be the vertices of the equilateral triangle. Then " x_1x_2+x_2x_3+x_3x_1=
Answer» -1 `-3//2` 1 none of these Answer :B

Discussion

2624.	Two cards are drawn at randomfrom 8 cards numbered from 1 to 8 . Whatis the probability that the sum of the numbers is odd , if the two cards are drawn together ?
Answer» ANSWER :`(4)/(7)`

Discussion

2625.	Let f: [ 0,4] rarr R be a differentiable function . There exist alpha and beta in the open interval (0,2) such that int_(0)^(4) f(t) dt=
Answer» `2[alphaf(ALPHA) +BETA F(beta)]` `2 [ alpha^(2) f( alpha) + beta^(2) f (beta) ]` `2[beta ^(2) f( alpha^(2)) + alpha^(2) f ( beta^(2)) ]` `2[ 2 alpha f ( alpha^(2)) + beta f ( beta^(2))]` ANSWER :D

Discussion

2626.	A container is in the shape of an inverted cone has height 8m and radius 6m at the top. If it is filled with water at the rate of 2m^(3)/minute, how fast is the height of water changing when the level is 4m?
Answer» ANSWER :`(2)/(9pi)`

Discussion

2627.	Statement -1 : If f(x) = x ( x+ 3) e^(-x//2), then Rolle's theorem applies for f(x) in [-3,0]. Statement-2 : LMVT is applied in f(x) = x ( x+3) e^(-x//2) in any interval.
Answer» STATEMENT-1 is TRUE, Statement-2 is FALSE Statement-1 is false , Statement-2 is true Statement-1 is true, Statement-2 true, Statement-2 is a CORRECT EXPLANATION for Statement -1 Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1 Answer :D

Discussion

2628.	When (0,0) shifted to (3,-3) the co-ordinates of P, Q, R are (5, 5), (-2, 4) and (7, -7) in the new system are A, B, C then area of triangle ABC in sq units is
Answer» 43 23 45 50 Answer :A

Discussion

2629.	If the distance between the plane 'Ax -2y + z =d and the plane containing the lies (x +1)/(3) = (y-1)/(2) = (z-2)/(4) and (x-2)/(3) = (y-3)/(4) = (z-4)/(5) is sqrt6, the find the value of \|d\|.
Answer» ANSWER :6

Discussion

2630.	(a) In a right angled triangle , thedifference between two acute angles is (pi)/(5) in radians Express the angles in degrees. (b)Evaluate : 6"cos"(pi)/(9)-8"cos"^(3)pi/(9)
Answer» ANSWER :(a) `27^(@),63^(@),90^(@)` `-1`

Discussion

2631.	If X and Y are two sets and X' denotes the complement of X, then X cap (X cup Y)' is equal to
Answer» `X` `Y` `PHI` `X CAP Y` ANSWER :C

Discussion

2632.	Write down the converse of following statements: If two triangles are similar then the ratio of their corresponding sides are equal.
Answer» ANSWER :TRIANGLES are SIMILAR.

Discussion

2633.	sin^(2) x + 4 sin x+5 in [k, 5k ] rArr k =
Answer» `1` `2` `3` `4` Answer :B

Discussion

2634.	Find the value of f(0) so thatf(x) = (1 + x)^(1//5x)is continuous at x = 0 .
Answer» ANSWER :`E^(1//5)`

Discussion

2635.	If f(x) = \|("sec" theta, "tan"^2 theta,1),(theta"sec"x,"tan"x,x),(1,"tan"x-"tan"theta,0)\| then f^(1)(theta) is
Answer» `0` `-1` independent of `THETA` `2` Answer :B

Discussion

2636.	cot^(-1)((sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1+sinx)))=
Answer» 1)`pi-x/2` 2)`pi+x/2` 3)`x/2` `4)2pi-x/2` ANSWER :A

Discussion

2637.	Given the following result " The dual of any result in set theory will be another result, where the dual is obtained by changing' cup to cap', 'cap to cup','phi to U' and ' Uto phi'" Write the dual results of the following resultsA cup A = A
Answer» SOLUTION :`A CAP A = A`

Discussion

2638.	If e^(f(x))=(10+x)/(10-x), x in (-10, 10) and f(x)=kf ((200x)/(100+x^(2))), then k =
Answer» 0.5 0.6 0.7 0.8 Answer :A

Discussion

2639.	Given the following result " The dual of any result in set theory will be another result, where the dual is obtained by changing' cup to cap', 'cap to cup', 'phi to U' and ' Uto phi'" Write the dual results of the following results (A cup B)' = A' cap B'
Answer» SOLUTION :`(A CAP B). = A. CUP B.`

Discussion

2640.	Given the following result " The dual of any result in set theory will be another result, where the dual is obtained by changing' cup to cap', 'cap to cup', 'phi to U' and ' Uto phi'" Write the dual results of the following results A cap U = A
Answer» SOLUTION :`A CUP PHI = A`

Discussion

2641.	Given the following result" The dual of any result in set theory will be another result, where the dual is obtained by changing' cup to cap', 'cap to cup', 'phi to U' and ' Uto phi'" Write the dual results of the following results A cup A' = U
Answer» SOLUTION :`A CAP A. = PHI`

Discussion

2642.	Given the following result " The dual of any result in set theory will be another result, where the dual is obtained by changing' cup to cap', 'cap to cup', 'phi to U' and ' Uto phi'" Write the dual results of the following resultsA cup (B cap C) = ( A cup B) cap (A cup C)
Answer» SOLUTION :`A CAP(B CUP C) = (A cap B) cup (A cap C)`

Discussion

2643.	If R_(3) = {(x, \|x\|),x " is a real number"} is a relation, then find domain and range of R_(3).
Answer» ANSWER :`(0, PROP)`

Discussion

2644.	The set of points of discontinuity off(x) = (1)/(log \|x\|) is
Answer» `{-1,1}` `{-1,0,1}` `{-2,-1,0,1,2}` `{0}` ANSWER :B

Discussion

2645.	One Of the general solutions of 4 sin^(4) x + cos^(4) x = 1 is
Answer» `n pi pm ALPHA //2, alpha = COS^(-1) (1//5), AA n in Z` `n pi pm alpha // 2, alpha = cos ^(-1) (3//5), AA n in Z` `2 n pi pm alpha//2, alpha = cos ^(-1) (1 //3), AA n in Z` `n pi pm (alpha)/(2), alpha = cos^(-1) ((1)/(3)), AA n in Z` Answer :A

Discussion

2646.	How many words with or without meaning, each of two vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
Answer» ANSWER :3600

Discussion

2647.	If the pair of lines ax^(2)+2hyx+by^(2)+2gx+2fy+c=0 intersect on the x-axis, then 2fgh
Answer» `af^(2)+ch^(2)` `BG^(2)+ch^(2)` `af^(2)+bg^(2)` `af^(2)+G^(2)` ANSWER :A

Discussion

2648.	Find the cooordinates of the point (1, 2) in the new system when the origin is shifted to (-2,3).
Answer» ANSWER :-1

Discussion

2649.	A straight line passes through the points (a, 0) and (0, b). The length of the line segment contained between the axes is 13 and the product of their intercepts on the axes is 60. Calculate the values of a and b and find the equation of the straight line.
Answer» ANSWER :`a=12,b=5;X/(12)+y/(5)=1;a=-12,b=-5;x/(12)+y/(5)=-1`

Discussion

2650.	Find sun_(n+1)^(infty) 1/(4n^(2) -1)
Answer» ANSWER : `1/2`

Discussion

Explore topic-wise InterviewSolutions in .

Vector component of barb perpendicular to bara is

If the equation (a_(1)-a_(2))x+(b_(1)-b_(2))y=c represents the perpendicular bisector of the segment joining (a_(1),b_(1)),(a_(2),b_(2)) then 2c=

A flag staff of length 10 mt stands on a tower if from a point on the ground , the angle of elevation of the foot and the top of the flagstaff are 45 ^(@) and 75 ^(@)then height of the tower is

Find the component statements of the following and check whether they are true or not: A person who has taken Mathematics or computer Science can go for MCA.

For ninz, cos(2theta)=(sqrt(5)+1)/(4) implies theta =

Let bare_(1) and bare_(2) be unit vectors which include anangel theta."If " 1/2abs(bare_(1) - bare_(2)) = sin (k theta), then k=

For problems Let cos^(-1)(4x^(3)-3x)=a+bcos^(-1)x If x in (1/2,1) then the value of lim_(ytoa)b cos (y) is

A man starts repaying a loan as first installment of Rs. 100 If he increases the installment by Rs. 5 every month , what amount he will pay in the 30 th installment ?

There are 2n guests at a dinner party. Supposing that the master annd mistress of the house have fixed seats opposite one another and that there are two specified guests who must not be placed next to one another. Find the number of ways in which the company can be placed.

Find the value of the product:|(log_(3)64,log_(4)3),(log_(3)8,log_(4)9)|xx|(log_(2)3,log_(8)3),(log_(3)4,log_(3)4)|

Expand (1+ 2 x + 3x^(2) )^(n) in a series of ascending powers of x up to and including the term in x^2.

From mean value theorem, f(b)-f(a) = (b-a)f^(1)(x_(1)), a lt x_(1) lt b if f(x) = ( 1)/( x) then x_(1) =

Which of the following pairs of sets are disjoint { a, e, i, o, u } and { c, d, e, f }

Consider the following population and year graph (Fig 10.10), find the slope of the line AB and using it, find what will be the population in the year 2010?

For the function f(x) satisfying 2. f(sin x)+f(cos x) = x, AA x in R

Let x,y,z be elements from interval [0,2pi] satisfying the inequality (4+sin 4x)(2+cot^(2)y)(1+sin^(4)z)le12sin^(2)z then

Origin shifted to the point (1, 2) without changing the direction of the axes then (4, 3) is transformed to

If in a Delta ABC, a, b, care in A.P . Thencos ((A- C)/( 2))is equal to

A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that is rusted or is a nail is ......

Find the equation of a line perpendicular to the line x-2y+ 3=0 and passing through the point (1,-2).

Evaluate the following limits : Lim_( x to 0 )(ax +b)/(cx +d)

If (sin(alpha+beta))/(sin(alpha-beta)) = (a+b)/(a-b), then prove that a tan beta = b tan alpha.

An equilateral triangle ABC has its centroid at the origin and one side 'AC' isx+y=1 IfA(X_1,Y_1), B(x_2,y_2),C(x_3,y_3) " be the vertices of the equilateral triangle. Then " x_1x_2+x_2x_3+x_3x_1=

Two cards are drawn at randomfrom 8 cards numbered from 1 to 8 . Whatis the probability that the sum of the numbers is odd , if the two cards are drawn together ?

Let f: [ 0,4] rarr R be a differentiable function . There exist alpha and beta in the open interval (0,2) such that int_(0)^(4) f(t) dt=

A container is in the shape of an inverted cone has height 8m and radius 6m at the top. If it is filled with water at the rate of 2m^(3)/minute, how fast is the height of water changing when the level is 4m?

Statement -1 : If f(x) = x ( x+ 3) e^(-x//2), then Rolle's theorem applies for f(x) in [-3,0]. Statement-2 : LMVT is applied in f(x) = x ( x+3) e^(-x//2) in any interval.

When (0,0) shifted to (3,-3) the co-ordinates of P, Q, R are (5, 5), (-2, 4) and (7, -7) in the new system are A, B, C then area of triangle ABC in sq units is

If the distance between the plane 'Ax -2y + z =d and the plane containing the lies (x +1)/(3) = (y-1)/(2) = (z-2)/(4) and (x-2)/(3) = (y-3)/(4) = (z-4)/(5) is sqrt6, the find the value of |d|.

(a) In a right angled triangle , thedifference between two acute angles is (pi)/(5) in radians Express the angles in degrees. (b)Evaluate : 6"cos"(pi)/(9)-8"cos"^(3)pi/(9)

If X and Y are two sets and X' denotes the complement of X, then X cap (X cup Y)' is equal to

Write down the converse of following statements: If two triangles are similar then the ratio of their corresponding sides are equal.

sin^(2) x + 4 sin x+5 in [k, 5k ] rArr k =

Find the value of f(0) so thatf(x) = (1 + x)^(1//5x)is continuous at x = 0 .

If f(x) = |("sec" theta, "tan"^2 theta,1),(theta"sec"x,"tan"x,x),(1,"tan"x-"tan"theta,0)| then f^(1)(theta) is

cot^(-1)((sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1+sinx)))=

Given the following result " The dual of any result in set theory will be another result, where the dual is obtained by changing' cup to cap', 'cap to cup','phi to U' and ' Uto phi'" Write the dual results of the following resultsA cup A = A

If e^(f(x))=(10+x)/(10-x), x in (-10, 10) and f(x)=kf ((200x)/(100+x^(2))), then k =

Given the following result " The dual of any result in set theory will be another result, where the dual is obtained by changing' cup to cap', 'cap to cup', 'phi to U' and ' Uto phi'" Write the dual results of the following results (A cup B)' = A' cap B'

Given the following result " The dual of any result in set theory will be another result, where the dual is obtained by changing' cup to cap', 'cap to cup', 'phi to U' and ' Uto phi'" Write the dual results of the following results A cap U = A

Given the following result" The dual of any result in set theory will be another result, where the dual is obtained by changing' cup to cap', 'cap to cup', 'phi to U' and ' Uto phi'" Write the dual results of the following results A cup A' = U

Given the following result " The dual of any result in set theory will be another result, where the dual is obtained by changing' cup to cap', 'cap to cup', 'phi to U' and ' Uto phi'" Write the dual results of the following resultsA cup (B cap C) = ( A cup B) cap (A cup C)

If R_(3) = {(x, |x|),x " is a real number"} is a relation, then find domain and range of R_(3).

The set of points of discontinuity off(x) = (1)/(log |x|) is

One Of the general solutions of 4 sin^(4) x + cos^(4) x = 1 is

How many words with or without meaning, each of two vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

If the pair of lines ax^(2)+2hyx+by^(2)+2gx+2fy+c=0 intersect on the x-axis, then 2fgh

Find the cooordinates of the point (1, 2) in the new system when the origin is shifted to (-2,3).

A straight line passes through the points (a, 0) and (0, b). The length of the line segment contained between the axes is 13 and the product of their intercepts on the axes is 60. Calculate the values of a and b and find the equation of the straight line.

Find sun_(n+1)^(infty) 1/(4n^(2) -1)