14949 + Interview Questions in Maths in Class 11 Page 18 InterviewSolution

851.	Therange of f(x)=cos^(-1)((1+x^(2))/(2x))+sqrt(2-x^(2)) is
Answer» `{0, 1 + PI/2}` `{0, 1 + pi}` `{1, 1 + pi/2}` `{1, 1+pi}` ANSWER :C

Discussion

852.	The range of f(x)=cos^(-1)((1+x^(2))/(2x))+sqrt(2-x^(2)) is
Answer» `{0, 1 + PI/2}` `{0, 1 + pi}` `{1, 1 + pi/2}` `{1, 1+pi}` ANSWER :C

Discussion

853.	Find the locus of the point (a-bsectheta,a-btantheta) where theta is the parameter.
Answer» ANSWER :`B^(2)`

Discussion

854.	Which of the following statements are true. Statement-I: (vec(r ).vec(i)) (vec(r )xx vec(i)) + (vec(r ).vec(j)) (vec(r ) xx vec(j)) + (vec(r ).vec(k)) (vec(r )xx vec(k)) = vec(r ) Statement-II: If vec(a) xx vec(b)= vec(0), vec(a).vec(b)=0, then one of vec(a),vec(b) is a null vector.
Answer» only I Only II neither I nor II both I and II Answer :B

Discussion

855.	If bara,barb are two vectors of length 2, 1 respectively and abs(bara-barb) = sqrt3, " then " (bara,barb)=
Answer» `pi//4` `pi//6` `pi//3` `pi//2` ANSWER :C

Discussion

856.	A point in the XZ plane is ………a) (1,1,1)b) (2,0,3)
Answer» `(1,1,1)` `(2,0,3)` `(2,3,0)` `(-1,2,3)` ANSWER :B

Discussion

857.	If bar(OP)=2bar(i)+3bar(j)-bar(k), bar(OQ)=3bar(i)-4bar(j)+2bar(k) then d.c's of bar(PQ) are
Answer» `1/sqrt(59)(-1, 7, 3)` `1/sqrt(59)(1, -7, 3)` `1/sqrt(59)(1, 7, -3)` `1/sqrt(59)(1, -7, -3)` Answer :B

Discussion

858.	AB is a line of fixed length, 6 units, joining the points A (t, 0) and B which lies on the positive y-axis. P is a point on AB distant 2 units from A.Express the co-ordinates of B and P in terms of t. Find the locus of P as t varies.
Answer» Answer :`B(0, sqrt(36-t^(2))), P((2T)/(3), sqrt(36-t^(2))/3), X^(2)+4y^(2)=16`

Discussion

859.	Write the converse, inverse and contrapositive of the following statements. If you do not drink your milk, you will not be strong.
Answer» Answer :CONVERSE : If you are not STRONG, then you do not drink your milk. Inverse : If you drink your milk, then you are strong. Contrapositive : If you are strong, then you drink your milk .

Discussion

860.	Position of the point (3,4) with respect to hyperbola x^(2) - 4y^(2) + 24y - 37 = 0 is ………..
Answer» INSIDE hyperbola Outside hyperbola On the hyperbola None of these Answer :B

Discussion

861.	For any event A,
Answer» <P>`P(A)+P(A')=0` `P(A)+P(A')=1` `P(A)gt1` `P(A)=P(A')` Answer :B

Discussion

862.	Simplify: -sqrt((-7)/(4))-sqrt((-1)/(7))
Answer» ANSWER :`(-9 sqrt7i)/(14)`

Discussion

863.	Solve the equation: log_(2x+3)x^(2) lt log_(2x)(2x+3)
Answer» SOLUTION :This inequation is EQUIVALENT to the collection of the systems HENCE, solution of the original inequation is `x in (-3/2,-1) cup (-1,0) cup (0,3)`

Discussion

864.	Sin^(-1)(xsqrt(1-y^(2))+ysqrt(1-x^(2)))=
Answer» `SIN^(-1)X+sin^(-1)SQRT(x)` `sin^(-1)x-sin^(-1)sqrt(x)` `sin^(-1)sqrt(x)-sin^(-1)x` 0 Answer :B

Discussion

865.	Examine Lim_(xto 2) [ x] , where [ x] denotes the greatest integarless than or equal to x.
Answer» ANSWER :SINCE L.H.L `!= ` R.H.L ., therefore `Lim_(X to 2)` [x] does not exist .

Discussion

866.	Find the derivative of w.r.to x sec (tan sqrtx)
Answer» ANSWER :`(SEC (TAN SQRTX).tan (tan sqrtx) sec ^(2) sqrtx)/(2 sqrtx)`

Discussion

867.	Let L_1: 3X+4Y-1=0and L_2 : 5z-12y+2=0 be two given lines. Let image of every point on L_1 w.r.t a line L lies on L_2 then possible equation of 'L' can be
Answer» `14x+112y-23=0 `64x-8y-3=0` `11x-4y=0` `52y-45x=7` ANSWER :A::B

Discussion

868.	(cos h2 + sin h 2)^(n) =
Answer» `COS H(2N) + SIN (2n)` `cos h(2n) - sin h(2n)` `cos h (2n)` `sin h (2n)` ANSWER :A

Discussion

869.	The range of f(x)=(1-tan x)/(1+tan x) is
Answer» `(-OO, oo)` `(-oo, 0)` `(0, oo)` `(-oo, -1) UU (-1, oo)` ANSWER :A

Discussion

870.	If alpha, beta, gamma are the angles made by a line with the positive directions of the coordinate axes, then sin^(2)alpha+sin^(2)beta+sin^(2)gamma=
Answer» ANSWER :2

Discussion

871.	Find the value of the expression sqrt3 cosec 20^@-sec20^@=…….
Answer» 2 `2sin 20^(@)//SIN 40^(@)` 4 `4sin20^(@)//sin 40^(@)` Answer :C

Discussion

872.	Show that the function f(x) = 2x^(2) - 3(lambda + 2) x^(2) + 2 lambdax + 5 has one maximum and one minimum for all lambda in R
Answer» ANSWER :Which is TRUE `AA` REAL `LAMBDA`.

Discussion

873.	In which ratio XY plane divides line segment joining points (2, 4, -3) and (-3, 5, 4).
Answer» ANSWER :In RATIO 3 : 4 INTERNALLY

Discussion

874.	If the projections of a line segment on the axes are 3, -4, 12 then the length of the segment and d.c.'s of the line are
Answer» ANSWER :`((3)/(13)-(4)/(13)(12)/(13))`

Discussion

875.	Write each sentence in the " If ................Then " form. Any two parallel lines are coplanar.
Answer» ANSWER :If TWO LINES are PARALLEL, then they are COPLANAR.

Discussion

876.	A class consists of 100 students, 25 of them are girls and 75 boys, 20 of them are rich and remaining poor, and 40 of them are fair-complexioned. Probability of selecting a fair-complexioned rich girl from this class is
Answer» `0.02` `0.04` `0.05` `0.08` ANSWER :A

Discussion

877.	Theperiodof sin ((pi x )/( 2 )) + 2 cos((pi x)/(3 ) ) - tan((pi x)/(4))is
Answer» 4 6 12 24 Answer :3

Discussion

878.	Find the value of n if: (i) (n+2)! = 12. n! (ii) (n+2)! = 60-. (n-1)! =({2.4.6....(2n)}{1.3.5....(2.-1)})/(n!) = (2^(n){1.2.3...n}{1.3.5.......(2n-1)})/(n!) = 2^(n) {1.3.5....(2n-1)} = R.H.S. Hence Proved. (iii) (n+3)! = 2550 (n+1)! (iv) (n-2)! = 132. (n-4)!.
Answer» ANSWER :(i) `n = 2` (ii) `n = 3` (III) `n = 48` (IV) `n = 14`

Discussion

879.	A polygon of nine sides, each side of length 2, is inscribed in a circle. The radius of the circle is.....
Answer» `sec(pi/9)` `COS ec (pi/9)` `COT. (pi/9)` `TAN. (pi/9)` ANSWER :b

Discussion

880.	Find the coordinates of the points which trisect the line segment joining the points P(4,2,-6) and Q(10,-16,6).
Answer» ANSWER :`(6,-4,-2)and(8,-10,2)`

Discussion

881.	If the range of the functionf(x) = ((1+x+x^(2))(1+x^(4)))/( x^(3)) " when "x gt0is[K, infty )then K is
Answer» ANSWER :6

Discussion

882.	An open recangular tank with a square base and 32 c.c of capacity has least surface aren in sq. cms is
Answer» 48 16 32 12 Answer :A

Discussion

883.	If sin^(2) x tan x + cos ^(2) x cot x - sin 2 x = 1 + tan x + cot x x in (0, pi) then x =
Answer» `(3 pi)/( 12), (5 pi)/(12)` `(5 pi)/( 12), (7 pi)/(12)` `(7 pi)/( 12), (11 pi)/( 12)` `(9 pi)/(12), (9 pi)/( 12)` ANSWER :C

Discussion

884.	(i)Suppose8 peopleenteran eventin a swimmingmeet. In how manywayscouldthe gold, silverand bronzeprizes be awarded ? (ii)Three menhave4 coats , 5waist coats and 6 caps. In howmany wayscan they wearthem ?
Answer» ANSWER :(i)336 (II)172800

Discussion

885.	A lette is chosen at random from the 'ASSASSINATION'. Find the probability that letter is (i) a vowel (ii) a consonant.
Answer» ANSWER :(i) `6/13` (II) `7/13`

Discussion

886.	Evaluate the following limits : Lim_(xto3^(-)) ([x]-x)
Answer» ANSWER :`1`

Discussion

887.	Let A= {1, 2, 3}, B= {3, 4} and C= {4, 5, 6}. Find (A xx B) nn (A xx C)
Answer» ANSWER :{(1,4),(2,4),(3,4)}

Discussion

888.	If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are the direction cosines of two vectors and theta is the angle between them, then the value of cos theta is
Answer» `SIN theta=l_(1)-l_(2)` `cos theta=(l_(1)-l_(2))/(2)` `sin theta =sqrt(2)(l_(1)-l_(2))` `cos theta=((l_(1)+l_(2)))/(sqrt(2))` Answer :D

Discussion

889.	If Deltarepresents the area of acute angled triangle ABC, then sqrt(a^(2)b^(2)-4Delta^(2))+ sqrt(b^(2)c^(2)-4Delta^(2))+sqrt(c^(2)a^(2)-4Delta^(2))=
Answer» `a^(2)+B^(2)+c^(2)` `(a^(2)+b^(2))+c^(2))/(2)` `ab COS C+ bc cos A+ca cosB` `ab sinC+bc SINA+ ca SINB` Answer :B::C

Discussion

890.	if ""^nc_(r-1)=36, ""^nc_r=84 and ""^nc_(r+1)=126,than find the value of ""^rc_(2.
Answer» ANSWER :3

Discussion

891.	cos^(4)alpha+sin^(4)alpha-6sin^(2)alpha cos^(2)alpha=
Answer» `COS 2ALPHA` `SIN 2alpha` `cos4alpha` `sin4alpha` ANSWER :C

Discussion

892.	Consider the compound statements ''35 is divisible by 5 or 6''Write the truth values of the compound statement and the component statements given above
Answer» SOLUTION :T,T,F RESPECTIVELY]

Discussion

893.	If AD, BE and CF are the medians of a triangle ABC, then AD^(2) + BE^(2) + CF^(2) :BC^(2)+CA^(2)+AB^(2)is equal to
Answer» `4 : 3 ` `3 : 2` `3 : 4` `2 : 3` ANSWER :C

Discussion

894.	The remainder when 2^(2020) is divided by 15 is
Answer» 4 8 1 2 Answer :A::C

Discussion

895.	The scores of two golfers for 10 rounds each are: Which may be regarded as the more consistent player?
Answer» ANSWER :a

Discussion

896.	Evaluate the following limits : Lim_(x to 0) (x(2^(x)-1))/(1-cos x)
Answer» ANSWER :`2 LOG 2 `

Discussion

897.	A committee of 5 is to be formed from a group of 10 people consisting 4 single men 4 single women and a married couple. The committee is to consist of a chairman , who must be a single man 2, other men and 2 women, Find the total number of committes possible.
Answer» ANSWER :` 240`

Discussion

898.	A committee of 5 is to be formed from a group of 10 people consisting 4 single men 4 single women and a married couple. The committee is to consist of a chairman , who must be a single man 2, other men and 2 women, How many of these would include the married couples?
Answer» ANSWER :` 48`

Discussion

899.	If (4k _(1), k _(2) ^(2) , 1) and ( 4k _(2) , k _(2) ^(2), 1) are two points lying on the plane in which (2,3,2) and (1,2,1) are mirror image to each other, then k _(1) k _(2) is equal to
Answer» `-3/2` `-/5/2` `-7/2` `-9/2` ANSWER :D

Discussion

900.	If 1+4 tan theta = 4 sec thetathen cos theta=
Answer» `17//8` `8//17` `-8//17` `-17//8` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Therange of f(x)=cos^(-1)((1+x^(2))/(2x))+sqrt(2-x^(2)) is

The range of f(x)=cos^(-1)((1+x^(2))/(2x))+sqrt(2-x^(2)) is

Find the locus of the point (a-bsectheta,a-btantheta) where theta is the parameter.

Which of the following statements are true. Statement-I: (vec(r ).vec(i)) (vec(r )xx vec(i)) + (vec(r ).vec(j)) (vec(r ) xx vec(j)) + (vec(r ).vec(k)) (vec(r )xx vec(k)) = vec(r ) Statement-II: If vec(a) xx vec(b)= vec(0), vec(a).vec(b)=0, then one of vec(a),vec(b) is a null vector.

If bara,barb are two vectors of length 2, 1 respectively and abs(bara-barb) = sqrt3, " then " (bara,barb)=

A point in the XZ plane is ………a) (1,1,1)b) (2,0,3)

If bar(OP)=2bar(i)+3bar(j)-bar(k), bar(OQ)=3bar(i)-4bar(j)+2bar(k) then d.c's of bar(PQ) are

AB is a line of fixed length, 6 units, joining the points A (t, 0) and B which lies on the positive y-axis. P is a point on AB distant 2 units from A.Express the co-ordinates of B and P in terms of t. Find the locus of P as t varies.

Write the converse, inverse and contrapositive of the following statements. If you do not drink your milk, you will not be strong.

Position of the point (3,4) with respect to hyperbola x^(2) - 4y^(2) + 24y - 37 = 0 is ………..

For any event A,

Simplify: -sqrt((-7)/(4))-sqrt((-1)/(7))

Solve the equation: log_(2x+3)x^(2) lt log_(2x)(2x+3)

Sin^(-1)(xsqrt(1-y^(2))+ysqrt(1-x^(2)))=

Examine Lim_(xto 2) [ x] , where [ x] denotes the greatest integarless than or equal to x.

Find the derivative of w.r.to x sec (tan sqrtx)

Let L_1: 3X+4Y-1=0and L_2 : 5z-12y+2=0 be two given lines. Let image of every point on L_1 w.r.t a line L lies on L_2 then possible equation of 'L' can be

(cos h2 + sin h 2)^(n) =

The range of f(x)=(1-tan x)/(1+tan x) is

If alpha, beta, gamma are the angles made by a line with the positive directions of the coordinate axes, then sin^(2)alpha+sin^(2)beta+sin^(2)gamma=

Find the value of the expression sqrt3 cosec 20^@-sec20^@=…….

Show that the function f(x) = 2x^(2) - 3(lambda + 2) x^(2) + 2 lambdax + 5 has one maximum and one minimum for all lambda in R

In which ratio XY plane divides line segment joining points (2, 4, -3) and (-3, 5, 4).

If the projections of a line segment on the axes are 3, -4, 12 then the length of the segment and d.c.'s of the line are

Write each sentence in the " If ................Then " form. Any two parallel lines are coplanar.

A class consists of 100 students, 25 of them are girls and 75 boys, 20 of them are rich and remaining poor, and 40 of them are fair-complexioned. Probability of selecting a fair-complexioned rich girl from this class is

Theperiodof sin ((pi x )/( 2 )) + 2 cos((pi x)/(3 ) ) - tan((pi x)/(4))is

Find the value of n if: (i) (n+2)! = 12. n! (ii) (n+2)! = 60-. (n-1)! =({2.4.6....(2n)}{1.3.5....(2.-1)})/(n!) = (2^(n){1.2.3...n}{1.3.5.......(2n-1)})/(n!) = 2^(n) {1.3.5....(2n-1)} = R.H.S. Hence Proved. (iii) (n+3)! = 2550 (n+1)! (iv) (n-2)! = 132. (n-4)!.

A polygon of nine sides, each side of length 2, is inscribed in a circle. The radius of the circle is.....

Find the coordinates of the points which trisect the line segment joining the points P(4,2,-6) and Q(10,-16,6).

If the range of the functionf(x) = ((1+x+x^(2))(1+x^(4)))/( x^(3)) " when "x gt0is[K, infty )then K is

An open recangular tank with a square base and 32 c.c of capacity has least surface aren in sq. cms is

If sin^(2) x tan x + cos ^(2) x cot x - sin 2 x = 1 + tan x + cot x x in (0, pi) then x =

(i)Suppose8 peopleenteran eventin a swimmingmeet. In how manywayscouldthe gold, silverand bronzeprizes be awarded ? (ii)Three menhave4 coats , 5waist coats and 6 caps. In howmany wayscan they wearthem ?

A lette is chosen at random from the 'ASSASSINATION'. Find the probability that letter is (i) a vowel (ii) a consonant.

Evaluate the following limits : Lim_(xto3^(-)) ([x]-x)

Let A= {1, 2, 3}, B= {3, 4} and C= {4, 5, 6}. Find (A xx B) nn (A xx C)

If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are the direction cosines of two vectors and theta is the angle between them, then the value of cos theta is

If Deltarepresents the area of acute angled triangle ABC, then sqrt(a^(2)b^(2)-4Delta^(2))+ sqrt(b^(2)c^(2)-4Delta^(2))+sqrt(c^(2)a^(2)-4Delta^(2))=

if ""^nc_(r-1)=36, ""^nc_r=84 and ""^nc_(r+1)=126,than find the value of ""^rc_(2.

cos^(4)alpha+sin^(4)alpha-6sin^(2)alpha cos^(2)alpha=

Consider the compound statements ''35 is divisible by 5 or 6''Write the truth values of the compound statement and the component statements given above

If AD, BE and CF are the medians of a triangle ABC, then AD^(2) + BE^(2) + CF^(2) :BC^(2)+CA^(2)+AB^(2)is equal to

The remainder when 2^(2020) is divided by 15 is

The scores of two golfers for 10 rounds each are: Which may be regarded as the more consistent player?

Evaluate the following limits : Lim_(x to 0) (x(2^(x)-1))/(1-cos x)

A committee of 5 is to be formed from a group of 10 people consisting 4 single men 4 single women and a married couple. The committee is to consist of a chairman , who must be a single man 2, other men and 2 women, Find the total number of committes possible.

A committee of 5 is to be formed from a group of 10 people consisting 4 single men 4 single women and a married couple. The committee is to consist of a chairman , who must be a single man 2, other men and 2 women, How many of these would include the married couples?

If (4k _(1), k _(2) ^(2) , 1) and ( 4k _(2) , k _(2) ^(2), 1) are two points lying on the plane in which (2,3,2) and (1,2,1) are mirror image to each other, then k _(1) k _(2) is equal to

If 1+4 tan theta = 4 sec thetathen cos theta=