14949 + Interview Questions in Maths in Class 11 Page 83 InterviewSolution

4101.	Find the distance of the point (3, -5) from the line 3x - 4y - 26 = 0.
Answer» ANSWER :`(3)/(5)`.

Discussion

4102.	Find the co-ordinates of the foot of the perpendicular drawn from the point (2, 3) on the line x+y-9=0.
Answer» ANSWER :M=(4,5)

Discussion

4103.	Draw the graph of the function f: R to R defined by f(x)=x^(3), x in R.
Answer» ANSWER :`F: {(X, x^(3)); x in R}`

Discussion

4104.	A party of n men is to be seated round a circular table . Find the odds against the event two particular men sit together .
Answer» ANSWER :`=(n-3):2`.

Discussion

4105.	Match the items of Column I with the items Column II
Answer» ANSWER :A-c,B-r,C-p,D-q

Discussion

4106.	Assertion (A) : Suppose f is differentiable on R such that 1le f'(x ) le2 for x in Rand that f(0 ) = 0 .Then x le f(x) le2x for all xge 0. Reason (R ) : f is an increasing function on R. Then
Answer» Both A and R are trueand R is a correct EXPLANATION of A. Both A and R are true and R is not a correct explanation of A. A is false and R is true A is true and R is false Answer :B

Discussion

4107.	If \|2 sin theta-cosec theta\|ge1 and thea!=(npi)/2, n in Z then
Answer» `COS 2 THETA GE 1//2` `cos 2 theta ge 1//4` `cos 2 le 1//2` `cos 2 theta 1//4` Answer :A

Discussion

4108.	Determine whether p,q and "If p, then q " are true or false in each case given below : 3(5 -: 6 ) lt 1
Answer» <P> ANSWER :`{:(p,Q,p =>q),(F,F,T):}`

Discussion

4109.	.........is the remainder if P (n) : 3^(2n+2) - 8nis divided by 64.
Answer» ANSWER :9

Discussion

4110.	Given n_(1) = 50, n_(2) = 40, sigma_(1) = 9, sigma_(2) = 6, d_(1) = 4, d_(2) = 5 Find the combined standard deviation.
Answer» ANSWER :9

Discussion

4111.	If f(x)= 64 x^(3)+ (1)/(x^(3)) and alpha and beta are roots of the equation 4x + (1)/(x)=3 then………
Answer» `f(alpha)= f(BETA)= -9` `f(alpha) = f(beta)= 63` `f(alpha ) ne f(beta)` None of these Answer :A

Discussion

4112.	The minute hand of a watch is 1.5cm long. How far does it tip move in 40 minute?
Answer» ANSWER :`6.28 CM`

Discussion

4113.	Find y if the slope of the line joining (-8, 11), (2, y) is -4/(3).
Answer» ANSWER : `(-7)/(3)`

Discussion

4114.	Let f(x)={{:(e^(x)",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):} , g(x)=int_(0)^(x)f(t)dt, x in[1,3] then g(x) has
Answer» LOCAL maximum at`x=1 +LN 2 and localminima at x=e local MAXIMA at x=1 and local MINIMA at x=2 no local maxima no local minima Answer :A::B

Discussion

4115.	Let f(x) and g(x) be two differentiable functions in R such that f(2) = 8, g(2)=0 f(4) = 10, g(4) = 8 and for atleast one x in ( 2,4), g' (x) = kf'(x) , then k is
Answer» 2 3 4 1 Answer :C

Discussion

4116.	Find the derivative of the function 2 ^(log _(2) sec x)+ log _(3) (27^(x))
Answer» ANSWER :`SEC X TAN +3`

Discussion

4117.	Two arcs of same length of two differen circles subtended angles of 25^(@) and 75^(@) at their centres respectively. Then the ratio of theradii of the circles is
Answer» `3 : 1` `1 : 3 ` `1 : 2` `2 : 1` ANSWER :A

Discussion

4118.	(( cos alpha - cos 3 alpha ) ( sin 8 alpha + sin 2 alpha ))/( ( sin 5 alpha - sin alpha ) ( cos 4 alpha - cos 6 alpha ))=
Answer» 1 `-1` 2 `-2` ANSWER :A

Discussion

4119.	If sin A= sin B and cos A= cos B, then show that A = 2n pi + B, n in Z
Answer» ANSWER :`2NPI + B, N in Z`

Discussion

4120.	Consider the expansion of ((4x)/5-5/(2x))^9 Find the general term in the expansion
Answer» Solution :`T_(x+1)=(-1)^(R9)C_r((4X)/5)^(9-r)(5/(2X))^r`

Discussion

4121.	If for real values of x, costheta=x+(1)/(x), then
Answer» `THETA` is an acute ANGLE `theta` is right angle `theta` is an OBTUSE angle No values of `theta` is possible Answer :D

Discussion

4122.	Find the derivativ of the function from first principles : cos ^(2) x
Answer» ANSWER :`therefore f' (X) =- SIN 2X,`

Discussion

4123.	If bara,barb and barc are non zero non-collinear vectors and theta(ne0,pi) is the angle between barb and barc if (baraxxbarb)xxbarc=1/3abs(barb)abs(barc)bara, then find sin theta
Answer» ANSWER :`(2SQRT2)/3`

Discussion

4124.	Trigonometric point P((101pi)/(3)) lies in………quadrant.
Answer» FIRST SECOND THIRD Fourth Answer :D

Discussion

4125.	Find the moment of force vec(F) = 4vec(i) + 2vec(j) + vec(k) through the point 5vec(i) + 2vec(j) + 4vec(k) about the point 3vec(i) - vec(j) + 3vec(k).
Answer» ANSWER :`VEC(i)+ 2vec(J)- 8vec(K)`

Discussion

4126.	If the point A, B, C, D are collinear asnd C, D divide AB in the ratios 2:3, -2:3 respectively, then the ratio in which AS divides CD is
Answer» `5:1` `2:3` `3:2 ` `1:5` ANSWER :d

Discussion

4127.	Evaluate the following limits : Lim_( x to a) (x^(a) - a^(a))/(a^(x) - a^(a))
Answer» ANSWER :`1/(LOG a)`

Discussion

4128.	If the set A has 3 elements and the set B= {3, 4, 5}, then find the number of elements in (A xx B)
Answer» ANSWER :9

Discussion

4129.	At what points the slopes of the tangents to the curve y = (x^(3))/(6) - (3x^(2))/(2) + (11x)/(2) + 12 increase ?
Answer» ANSWER :`(3, OO)`

Discussion

4130.	f(x) = {{:(((27- 2x )^(1//3)-3)/(9-3 (243 + 5x)^(1//5)) " if " x ne 0),(k "if "x = 0 ):}continuous atx = 0 then k =
Answer» 1 2 3 4 Answer :B

Discussion

4131.	One of the roots of 4x^(3)-3x=(1)/(2) is ………
Answer» `sin70^(@)` `SIN10^(@)` `SIN20^(@)` `COS70^(@)` ANSWER :A

Discussion

4132.	Two verticess of a Triangle are (1,3) and (4,7) the orthocentre lies on the line x+y=3. the locus of third vertx is
Answer» `x^2-2xy+2y^2-3x-4y+36=0` `2x^2-4xy+3y^2-4x-y+42=0` `3x^2+xy-4y^2-2x+24y-40=0` `x^2-4xy+3y^2-2x-4y-40=0` ANSWER :C

Discussion

4133.	If a,b,c arein HP, then prove that (a+b)/(2a-b)+(c+b)/(2c-b)gt4.
Answer» `(2)/(BC)-(1)/(b^(2))` `(1)/(4) ((3)/(c^(2))+ (2)/(ca)-(1)/(a^(2)))` `(3)/(b^(2))-(2)/(ab)` NONE of these Answer :D

Discussion

4134.	Find the term independent of x in ((3x^(2))/(2)-(1)/(3x))^(9)
Answer» ANSWER :`7^(TH)" TERM " , (7)/(8)`

Discussion

4135.	The coordinates of points in the XY-plane are of the form ______
Answer» ANSWER :(X,o,Z)

Discussion

4136.	x = a sin^(2)theta , y = b cos^(2)theta then dy/dx:
Answer» `a/b` `-a/b` `b/a` `-b/a` ANSWER :D

Discussion

4137.	The sum of probabilities of two students getting distinction in their final examinations is 1.2.
Answer» ANSWER :A

Discussion

4138.	A lamp post is situated at the middle point M of the side AC of a triangular plot ABC with BC=7m, CA=8m and AB=9m. Lamp post subtends an angle 15^(@) at the point B. Determine the height of the lamp post.
Answer» ANSWER :`h=7(2-sqrt(3)m)`

Discussion

4139.	The sides of a Delta^("le") ABC " are " a = 4, b = 5, c = 6 The length of the external bisector of angle A is
Answer» `12 SQRT2` `15 sqrt2` `10 sqrt3` `15 sqrt3` ANSWER :b

Discussion

4140.	Find the radius of a circle in which a central angle of 60^(@) intercepts an arc of 37.4 cm
Answer» ANSWER :35-7 CM

Discussion

4141.	The mean and variance of eight observations are 9 and 9.25 , respectively . If six of the observations are 6,7,10,12,12 and 13, find the remaining two observations.
Answer» ANSWER :4, 8

Discussion

4142.	A wheel rotates so that the angle of rotation is proportional to the square of the time. The first revolution was performed by the wheel for 8 seconds the angular velocity at this time is
Answer» `PI` rad/sec `2PI` rad/sec `(pi)/(2)` rad/sec `(pi)/(3)`rad/sec Answer :C

Discussion

4143.	((12),(1))+((12),(3))+((12),(5))+.....+((12),(11))=2^(12).
Answer» ANSWER :FALSE STATEMENT

Discussion

4144.	Find the multiplicative inverse of each of the following complex numbers when it exists. (6+ 5i)^(2)
Answer» ANSWER :`(11)/(3721) - (60)/(3721)i`

Discussion

4145.	Find the point to which theorigin is to be shifted so that the point (3,0) my change to (2, -3).
Answer» ANSWER :(1,3)

Discussion

4146.	A die is tossed. The probability that the number on a die is divisible by 3 is …….
Answer» `(1)/(6)` `(2)/(3)` `(1)/(3)` `(5)/(6)` Answer :C

Discussion

4147.	A rectangle of the greatest area is inscribed in a trapezium ABCD , one of whose non - parallel sides AB is perpendicular to the base , so that one of the rectangle 's side lies on the larger base of the trapezium . The base of trapezium are 6 cm and 10 cm and AB is 8 cm longThen the maximum area of the rectangle is
Answer» `24CM^(2)` `48CM^(2)` `36CM^(2)` `70cm^(2)` ANSWER :B

Discussion

4148.	If the sides of a triangle are 13,14,15 , then find circum diameter .
Answer» ANSWER :` (65)/(4) ` UNITS

Discussion

4149.	Write the conjugate of (1-i)/(1+i)
Answer» ANSWER :i

Discussion

4150.	If a cos B = b cos A then the triangle is
Answer» Scalene Equilateral RIGHT ANGLED ISOSCELES Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

Find the distance of the point (3, -5) from the line 3x - 4y - 26 = 0.

Find the co-ordinates of the foot of the perpendicular drawn from the point (2, 3) on the line x+y-9=0.

Draw the graph of the function f: R to R defined by f(x)=x^(3), x in R.

A party of n men is to be seated round a circular table . Find the odds against the event two particular men sit together .

Match the items of Column I with the items Column II

Assertion (A) : Suppose f is differentiable on R such that 1le f'(x ) le2 for x in Rand that f(0 ) = 0 .Then x le f(x) le2x for all xge 0. Reason (R ) : f is an increasing function on R. Then

If |2 sin theta-cosec theta|ge1 and thea!=(npi)/2, n in Z then

Determine whether p,q and "If p, then q " are true or false in each case given below : 3(5 -: 6 ) lt 1

.........is the remainder if P (n) : 3^(2n+2) - 8nis divided by 64.

Given n_(1) = 50, n_(2) = 40, sigma_(1) = 9, sigma_(2) = 6, d_(1) = 4, d_(2) = 5 Find the combined standard deviation.

If f(x)= 64 x^(3)+ (1)/(x^(3)) and alpha and beta are roots of the equation 4x + (1)/(x)=3 then………

The minute hand of a watch is 1.5cm long. How far does it tip move in 40 minute?

Find y if the slope of the line joining (-8, 11), (2, y) is -4/(3).

Let f(x)={{:(e^(x)",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):} , g(x)=int_(0)^(x)f(t)dt, x in[1,3] then g(x) has

Let f(x) and g(x) be two differentiable functions in R such that f(2) = 8, g(2)=0 f(4) = 10, g(4) = 8 and for atleast one x in ( 2,4), g' (x) = kf'(x) , then k is

Find the derivative of the function 2 ^(log _(2) sec x)+ log _(3) (27^(x))

Two arcs of same length of two differen circles subtended angles of 25^(@) and 75^(@) at their centres respectively. Then the ratio of theradii of the circles is

(( cos alpha - cos 3 alpha ) ( sin 8 alpha + sin 2 alpha ))/( ( sin 5 alpha - sin alpha ) ( cos 4 alpha - cos 6 alpha ))=

If sin A= sin B and cos A= cos B, then show that A = 2n pi + B, n in Z

Consider the expansion of ((4x)/5-5/(2x))^9 Find the general term in the expansion

If for real values of x, costheta=x+(1)/(x), then

Find the derivativ of the function from first principles : cos ^(2) x

If bara,barb and barc are non zero non-collinear vectors and theta(ne0,pi) is the angle between barb and barc if (baraxxbarb)xxbarc=1/3abs(barb)abs(barc)bara, then find sin theta

Trigonometric point P((101pi)/(3)) lies in………quadrant.

Find the moment of force vec(F) = 4vec(i) + 2vec(j) + vec(k) through the point 5vec(i) + 2vec(j) + 4vec(k) about the point 3vec(i) - vec(j) + 3vec(k).

If the point A, B, C, D are collinear asnd C, D divide AB in the ratios 2:3, -2:3 respectively, then the ratio in which AS divides CD is

Evaluate the following limits : Lim_( x to a) (x^(a) - a^(a))/(a^(x) - a^(a))

If the set A has 3 elements and the set B= {3, 4, 5}, then find the number of elements in (A xx B)

At what points the slopes of the tangents to the curve y = (x^(3))/(6) - (3x^(2))/(2) + (11x)/(2) + 12 increase ?

f(x) = {{:(((27- 2x )^(1//3)-3)/(9-3 (243 + 5x)^(1//5)) " if " x ne 0),(k "if "x = 0 ):}continuous atx = 0 then k =

One of the roots of 4x^(3)-3x=(1)/(2) is ………

Two verticess of a Triangle are (1,3) and (4,7) the orthocentre lies on the line x+y=3. the locus of third vertx is

If a,b,c arein HP, then prove that (a+b)/(2a-b)+(c+b)/(2c-b)gt4.

Find the term independent of x in ((3x^(2))/(2)-(1)/(3x))^(9)

The coordinates of points in the XY-plane are of the form ______

x = a sin^(2)theta , y = b cos^(2)theta then dy/dx:

The sum of probabilities of two students getting distinction in their final examinations is 1.2.

A lamp post is situated at the middle point M of the side AC of a triangular plot ABC with BC=7m, CA=8m and AB=9m. Lamp post subtends an angle 15^(@) at the point B. Determine the height of the lamp post.

The sides of a Delta^("le") ABC " are " a = 4, b = 5, c = 6 The length of the external bisector of angle A is

Find the radius of a circle in which a central angle of 60^(@) intercepts an arc of 37.4 cm

The mean and variance of eight observations are 9 and 9.25 , respectively . If six of the observations are 6,7,10,12,12 and 13, find the remaining two observations.

A wheel rotates so that the angle of rotation is proportional to the square of the time. The first revolution was performed by the wheel for 8 seconds the angular velocity at this time is

((12),(1))+((12),(3))+((12),(5))+.....+((12),(11))=2^(12).

Find the multiplicative inverse of each of the following complex numbers when it exists. (6+ 5i)^(2)

Find the point to which theorigin is to be shifted so that the point (3,0) my change to (2, -3).

A die is tossed. The probability that the number on a die is divisible by 3 is …….

If the sides of a triangle are 13,14,15 , then find circum diameter .

Write the conjugate of (1-i)/(1+i)

If a cos B = b cos A then the triangle is