14949 + Interview Questions in Maths in Class 11 Page 59 InterviewSolution

2901.	The value of expression (lambda tan + beta cot lambda + beta lambda)-4alpha beta cot^(2)-2lambda depends on
Answer» `ALPHA` `beta` `lambda` NONE of these Answer :A::B

Discussion

2902.	Find the solution set of (tan 2x - tan x)/(1+tan 2x tan x) = 1.
Answer» ANSWER :`PHI`

Discussion

2903.	Arun draws a circle with centre at (-1,-2) and radius sqrt5. What may be its algebric equation?
Answer» SOLUTION :`(x+1)^2+(y+2)^2=5`

Discussion

2904.	If an error of 0.05 is made while measruing the side 10 cm of a cube, then find the error, the relative error and the percentage error in the surface area and volume.
Answer» ANSWER :6sq. CM, 0.01, 1; 15 CUBIC cm, 0.015, 1.5

Discussion

2905.	A particle is moving along a line according to s=f(t) =4t^(3)-3t^(2)+5t-1 where s is measured in meter and t is measured in seconds. Find the velocity and acceleration at time t. At what time the acceleration is zero.
Answer» ANSWER :`t=1/4` SEC

Discussion

2906.	Let tanx-tan^(2)xgt0 and \|2sinx\|lt1. Then the intersection of which of the following two sets satisfies both the inequalities?
Answer» `X GTN pi, n in Z` `x gtnpi-pi//6, n INZ` `n LTN pi -pi//4, n inZ` `x LT n pi +pi//6, n in Z` Answer :A::D

Discussion

2907.	Translate the following statements into symbolic form: Students can take Hindi or English as an optional paper.
Answer» ANSWER :OPTIONAL PAPER.

Discussion

2908.	A man saved Rs 66,000 in 20yr. In each succeeding year after the first year, he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?
Answer» ANSWER :1400

Discussion

2909.	If in the expansion of (a+b)^(n) , (T_(2))/(T_(3)) is equalto (T_(3))/(T_(4))in the expansion of (a+b)^(n+3) then n = ……….
Answer» 3 4 5 6 Answer :C

Discussion

2910.	Given that lim_(x rarr 0) (a^x - 1)/x = log a and lim_(x rarr 0) (tan x)/x = 1 Evaluate lim_(x rarr 0) (2^x - 1)/x
Answer» SOLUTION :`log_e 2`

Discussion

2911.	The periodof3 cos 3x+ 3 tan 3xis
Answer» ANSWER :B::C::D

Discussion

2912.	If y=(1+tanA)(1-tanB)andA-B=(pi)/(4) then (y+1)^(y+1) = …………
Answer» 9 4 27 81 Answer :C

Discussion

2913.	Find the number of permutations of n distinct things taken r together, in which 3 parritcular things must occur together.
Answer» ANSWER :`= ((n-3),(r-3))XX (r-2)!xx3!`

Discussion

2914.	Let f(x) be a function defined as follows : f(x)=sin(x^(2)-3x),xle0,and at 6x+5x^(2),xgt0 then at x=0,f(x)
Answer» has a LOCAL maximum has a local MINIMUM is discontinuous is continuous Answer :B

Discussion

2915.	Find the real numbers x and y if (x-iy)(3+5i) is the conjugate of -6-24i.
Answer» ANSWER :x=3, y`=-3`

Discussion

2916.	A, B and C are mutually exclusive and exhaustive events. P(A) = 0.40, P(B) = P(C), then P(B) = ……..
Answer» `0.40` `0.60` `0.20` `0.30` ANSWER :D

Discussion

2917.	Sin^(2)50^(@)+Sin^(2)70^(@)+Sin^(2)170^(@)=
Answer» `1/2` 1 `3/2` 2 Answer :C

Discussion

2918.	The tw geometric means between the numbers 1 and 64 are
Answer» 1 and 64 4 and 16 2 and 16 8 and 16 Answer :B

Discussion

2919.	If the difference between the roots of the equation x^(2)+ax+1=0 is less than sqrt(5), then the set of possible values of a is(i) (3,oo)(ii) (-oo,-3)(iii) (-3,3)(iv) (-3,oo)
Answer» `(3,OO)` `(-oo,-3)` `(-3,3)` `(-3,oo)` ANSWER :C

Discussion

2920.	Evaluate the following limits : Lim_( x to 0) e^(x)
Answer» ANSWER :1

Discussion

2921.	For the above n, if (n,r) =136, find r
Answer» SOLUTION :R = 2 or 15

Discussion

2922.	sin^(2) ( 60^(@) + x) sin^(2) ( 60^(@) - x) in [ - (k)/(2) , (k)/(2) ] rArr k =
Answer» `3` `2` `SQRT3` `sqrt2` ANSWER :C

Discussion

2923.	A die is thrown twice. What is the probability that at least one of the two throws comes up with the number 4 ?
Answer» ANSWER :`(11)/(36)`

Discussion

2924.	How many 5-digit numbers can be formed by using the digits 5, 4, 3, 3, 0 ?
Answer» ANSWER :48

Discussion

2925.	If alpha, beta , gamma do not differ by a multiple of a pi and if ( cos (alpha + theta))/( sin (beta + gamma)) = (cos (bega + theta))/( sin (gamma + alpha )) = (cos (gamma + theta))/( sin (alpha + beta)) = k. Then k equals
Answer» `PM2` `PM 1/2` `0` `pm1` ANSWER :A

Discussion

2926.	If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(""37-x, 2 lt x le 3):}, show that f(x) is increasing in [-1, 2]
Answer» F(x) is INCREASING on [-1,2] f(x) is continous on [-1,3] f(2) doesn 't EXIST f(x)hasthe maximum value at x=2 Answer :A::B::C

Discussion

2927.	Expand (x^2+2/x)^4, x ge 0
Answer» ANSWER :4

Discussion

2928.	The variance of 20observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations.
Answer» ANSWER :`(1)/(20)xx400=20=2^(2)XX5`

Discussion

2929.	If A,B are acute angle, tan A=5/12 , cos B=3/5 , then cos (A+B)=
Answer» `(16)/(65)` `(65)/(16)` `(65)/(63)` `(56)/(65)` ANSWER :A

Discussion

2930.	A force vec(F)= 2vec(i) + 4vec(j) + vec(k) acts on line through a point A(4, 2, -1). Find the moment vector (torque) vec(M) " of" vec(F ) about a point P(0, 1, 2)
Answer» ANSWER :`13 VEC(i)- 10vec(J) + 14vec(K)`

Discussion

2931.	Which of the following sentences are statements? Justify Sky is red.
Answer» ANSWER :It is STATEMENT.

Discussion

2932.	If (3pi)/(4)lt alphaltpi, then sqrt(2cotalpha+(1)/(sin^(2)alpha)) is equal to
Answer» `1f + COT ALPHA` `-1-cot alpha` `1 - cot alpha` `-1 + cot alpha` ANSWER :B

Discussion

2933.	sec h^(2) [tan h^(-1) ((1)/(2))] + "cosec h"^(2) (cot h^(-1) (3)) =
Answer» `(35)/(9)` `(43)/(4)` `(35)/(4)` `(43)/(9)` ANSWER :C

Discussion

2934.	If A=[(2,2,0),(2,1,1),(-7,2,-3)] and if A^(3)-13A+kI=0, then find k.
Answer» ANSWER :12

Discussion

2935.	Solve the general vlaue. cos theta + cos 2 theta+ cos 3 theta =0
Answer» ANSWER :`(N + (1)/(2))`

Discussion

2936.	Statement-I : If two vectors are collinear then those vectors are coplanar Statement-II : For like vectors angle between them is 90^(@) Which of the above statement is true :
Answer» only I only II both I and II Neither I nor II Answer :A

Discussion

2937.	If x^(2)-y^(2)=0, l x+2y=1form an isosceless triangle thenl=
Answer» 0 1 2 `-1` ANSWER :A

Discussion

2938.	Lines bar(OA),bar(OB)are drawn from O with direction cosines proportional to (1,-2,-1), (3,-2,3). Find the direction cosines of the normal to the plane AOB.
Answer» Answer :`((4)/(sqrt(29)),(3)/(sqrt(29)),(-2)/(sqrt(29)))`

Discussion

2939.	If f(x)={:{(x^(2) sin.(pi x)/(2)",",\|x\|lt1,),(x\|x\|",",\|x\|ge1,):} then f(x) is
Answer» an EVEN function an ODD function a PERIODIC function neither even nor odd Answer :B

Discussion

2940.	If the vectors bara = (lambda log_(2) x) bari - 6barj + 3bark and barb = (log_(2) x)bari - 2barj + (2lambda log_(2) x) bark contain an obtuse angle for all xgt0 , " then find the range of "lambda.
Answer» `(0,4/3)` `(-4/3,OO)` `(-4/3,0)` `(-oo,-4/3)` ANSWER :C

Discussion

2941.	Find the multiplicative inverse of 2-3i
Answer» ANSWER :`(2)/(13)+(2)/(13)`

Discussion

2942.	If a is any real number, the number of roots of cot x - tan x = a in the first quadrant is
Answer» 2 0 1 3 Answer :C

Discussion

2943.	Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).
Answer» ANSWER :`X + y = 5`

Discussion

2944.	Find the derivative of the w.r.t.x (x (1+ x ^(2)))/( sqrt (1- x ^(2)))
Answer» Answer :`(1+ 3X ^(2) - 2X ^(4))/( (1- x ^(2)) ^(3//2))`

Discussion

2945.	Find the co-ordinates of the points lying on parabola y^(2)=16x whose focal distance is 8.
Answer» ANSWER :(4,8) , (4,-8)

Discussion

2946.	Find the value of (sqrt(1+sin 2A)+sqrt(1-sin 2 A))/(sqrt(1 + sin 2A)-sqrt(1-sin 2 A)), When \|tan A\| lt 1 and \|A\| is acute.
Answer» `TANA` `COTA` `-tanA` `-cotA` ANSWER :B

Discussion

2947.	If the period of the function f(x) = sin ( sqrt([n]) x), where [n] denotes the greatest integer less than or equal to n, is 2pi, then
Answer» `1 LE n le 2` `1 LT n lt 2` `1 le n le 2` `1 lt n le 2` ANSWER :A

Discussion

2948.	A line perpendicular to the line 5x-y=0 forms a triangle with the coordinate axes. If the area of the triangle is 5 sq. units, then its equation is
Answer» `x+5y PM 5sqrt(2)=0` `x-5y pm 5sqrt(2)=0` `5x+y pm 5sqrt(2)=0` `5x-y pm 5sqrt(2)=0` ANSWER :A

Discussion

2949.	If Delta_(1)=\|{:(a_(1)^(2)+b_(1)+c_(1),a_(1)a_(2)\|b_(2)\|c_(2),a_(1)a_(3)+b_(3)+c_(3)),(b_(1)b_(2)+c_(1),b_(2)^(2)+c_(2),b_(2)b_(3)+c_(3)),(c_(1)c_(3),c_(2)c_(3),c_(3)^(2)):}\|" and " Delta_(2)=\|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}\|, then find the value of (Delta_(1))/(Delta_(2)).
Answer» ANSWER :`a_(1)b_(2)c_(3)`

Discussion

2950.	If bara=bari+barj-bark,barb=bari-barj+bark,barc is a unit vector perpendicular to bara and coplanar with bara and barb, then barc =
Answer» `1/(SQRT6)(2bari+barj+bark)` `PM(1/(sqrt6)(2bari-barj+bark)` `1/(sqrt6)(2bari+barj-bark)` `1/(sqrt6)(2bari-barj-bark)` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

The value of expression (lambda tan + beta cot lambda + beta lambda)-4alpha beta cot^(2)-2lambda depends on

Find the solution set of (tan 2x - tan x)/(1+tan 2x tan x) = 1.

Arun draws a circle with centre at (-1,-2) and radius sqrt5. What may be its algebric equation?

If an error of 0.05 is made while measruing the side 10 cm of a cube, then find the error, the relative error and the percentage error in the surface area and volume.

A particle is moving along a line according to s=f(t) =4t^(3)-3t^(2)+5t-1 where s is measured in meter and t is measured in seconds. Find the velocity and acceleration at time t. At what time the acceleration is zero.

Let tanx-tan^(2)xgt0 and |2sinx|lt1. Then the intersection of which of the following two sets satisfies both the inequalities?

Translate the following statements into symbolic form: Students can take Hindi or English as an optional paper.

A man saved Rs 66,000 in 20yr. In each succeeding year after the first year, he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?

If in the expansion of (a+b)^(n) , (T_(2))/(T_(3)) is equalto (T_(3))/(T_(4))in the expansion of (a+b)^(n+3) then n = ……….

Given that lim_(x rarr 0) (a^x - 1)/x = log a and lim_(x rarr 0) (tan x)/x = 1 Evaluate lim_(x rarr 0) (2^x - 1)/x

The periodof3 cos 3x+ 3 tan 3xis

If y=(1+tanA)(1-tanB)andA-B=(pi)/(4) then (y+1)^(y+1) = …………

Find the number of permutations of n distinct things taken r together, in which 3 parritcular things must occur together.

Let f(x) be a function defined as follows : f(x)=sin(x^(2)-3x),xle0,and at 6x+5x^(2),xgt0 then at x=0,f(x)

Find the real numbers x and y if (x-iy)(3+5i) is the conjugate of -6-24i.

A, B and C are mutually exclusive and exhaustive events. P(A) = 0.40, P(B) = P(C), then P(B) = ……..

Sin^(2)50^(@)+Sin^(2)70^(@)+Sin^(2)170^(@)=

The tw geometric means between the numbers 1 and 64 are

If the difference between the roots of the equation x^(2)+ax+1=0 is less than sqrt(5), then the set of possible values of a is(i) (3,oo)(ii) (-oo,-3)(iii) (-3,3)(iv) (-3,oo)

Evaluate the following limits : Lim_( x to 0) e^(x)

For the above n, if (n,r) =136, find r

sin^(2) ( 60^(@) + x) sin^(2) ( 60^(@) - x) in [ - (k)/(2) , (k)/(2) ] rArr k =

A die is thrown twice. What is the probability that at least one of the two throws comes up with the number 4 ?

How many 5-digit numbers can be formed by using the digits 5, 4, 3, 3, 0 ?

If alpha, beta , gamma do not differ by a multiple of a pi and if ( cos (alpha + theta))/( sin (beta + gamma)) = (cos (bega + theta))/( sin (gamma + alpha )) = (cos (gamma + theta))/( sin (alpha + beta)) = k. Then k equals

If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(""37-x, 2 lt x le 3):}, show that f(x) is increasing in [-1, 2]

Expand (x^2+2/x)^4, x ge 0

The variance of 20observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations.

If A,B are acute angle, tan A=5/12 , cos B=3/5 , then cos (A+B)=

A force vec(F)= 2vec(i) + 4vec(j) + vec(k) acts on line through a point A(4, 2, -1). Find the moment vector (torque) vec(M) " of" vec(F ) about a point P(0, 1, 2)

Which of the following sentences are statements? Justify Sky is red.

If (3pi)/(4)lt alphaltpi, then sqrt(2cotalpha+(1)/(sin^(2)alpha)) is equal to

sec h^(2) [tan h^(-1) ((1)/(2))] + "cosec h"^(2) (cot h^(-1) (3)) =

If A=[(2,2,0),(2,1,1),(-7,2,-3)] and if A^(3)-13A+kI=0, then find k.

Solve the general vlaue. cos theta + cos 2 theta+ cos 3 theta =0

Statement-I : If two vectors are collinear then those vectors are coplanar Statement-II : For like vectors angle between them is 90^(@) Which of the above statement is true :

If x^(2)-y^(2)=0, l x+2y=1form an isosceless triangle thenl=

Lines bar(OA),bar(OB)are drawn from O with direction cosines proportional to (1,-2,-1), (3,-2,3). Find the direction cosines of the normal to the plane AOB.

If f(x)={:{(x^(2) sin.(pi x)/(2)",",|x|lt1,),(x|x|",",|x|ge1,):} then f(x) is

If the vectors bara = (lambda log_(2) x) bari - 6barj + 3bark and barb = (log_(2) x)bari - 2barj + (2lambda log_(2) x) bark contain an obtuse angle for all xgt0 , " then find the range of "lambda.

Find the multiplicative inverse of 2-3i

If a is any real number, the number of roots of cot x - tan x = a in the first quadrant is

Find the equation of a line that cuts off equal intercepts on the coordinate axes and﻿ passes﻿ through the point (2, 3).

Find the derivative of the w.r.t.x (x (1+ x ^(2)))/( sqrt (1- x ^(2)))

Find the co-ordinates of the points lying on parabola y^(2)=16x whose focal distance is 8.

Find the value of (sqrt(1+sin 2A)+sqrt(1-sin 2 A))/(sqrt(1 + sin 2A)-sqrt(1-sin 2 A)), When |tan A| lt 1 and |A| is acute.

If the period of the function f(x) = sin ( sqrt([n]) x), where [n] denotes the greatest integer less than or equal to n, is 2pi, then

A line perpendicular to the line 5x-y=0 forms a triangle with the coordinate axes. If the area of the triangle is 5 sq. units, then its equation is

If bara=bari+barj-bark,barb=bari-barj+bark,barc is a unit vector perpendicular to bara and coplanar with bara and barb, then barc =

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).