14949 + Interview Questions in Maths in Class 11 Page 63 InterviewSolution

3101.	Series 1^(2) + 2.2^(2) + 3^(2) + 2.4^(2)+ 5^(2) + 2.6^(2)+ ……are given. The sum of its first 20 terms is A and that of first 40 terms is B. If B- 2A = 100 lamda, " then" lamda=…….
Answer» 232 248 464 496 Answer :B

Discussion

3102.	Evaluate the following limits : Lim_(x to a) (log x - log a )/(x - a)
Answer» ANSWER :`1/a`

Discussion

3103.	If the normals drawn at the points t_(1) & t_(2) on the parabola y^(2)=4axmeet the parabola again at its point t_(3), then t_(1)t_(2) equals:
Answer» 2 `-1` `-2` `t_(3)-(2)/(t_(3))` Solution :LET NORMAL at t meets the parabola again at `t_(3)` `:.t_(3)= -t-(2)/(t) "" :.t^(2)+t_(3)*t+2=0` `t_(1)&t_(2)` are the roots of the EQUATION `:.t_(1)t_(2)=2 `

Discussion

3104.	Let f: R to R be a continuousfunction defined by f(x)=(1)/(e^(x)+2e^(-x)) Statement -1 : f(x)=(1)/(3), for some c in R. Statement -2, 0 ltf(x) le (1)/(2sqrt(2))AAx in R.
Answer» Statement-1 is TRUE, statement-2 is true, Statement-2 is CORRECT EXPLANATION for Statement-1. Statement-1 is true, statement-2 is not a correct explanation for Statement-1. Satement-1 is true, Statement-2 is FALSE Statement-1 is false, Statement-2 is true Answer :A

Discussion

3105.	If (1 + tan alpha) (1 + tan 4 alpha) = 2, alpha in (0, (pi)/(16)), then alpha =
Answer» `(PI)/(20)` `(pi)/(30)` `(pi)/(40)` `(pi)/(60)` Answer :A

Discussion

3106.	The three concurrent edges of a parallelopiped represents the vectors bara, barb, barc such that [bara barb barc] = lamda.Then the volume of the parallelopiped whose three concurrent ed2es are the three concurrent diagonals of three faces of the given parallelopiped is
Answer» `LAMDA` `2lamda` `3lamda` `4lamda` ANSWER :B

Discussion

3107.	In the isosceles triangle OAB, O is the origin, OA=OB=6. If the equation of side AB is x-y+1=0, then the area of the triangle OAB is (in square units)
Answer» `SQRT(71)` `1/2sqrt(71)` `3sqrt(71)` `4sqrt(71)` ANSWER :B

Discussion

3108.	Let f: X rarrY , f(x)= sin x + cos x + 2 sqrt(2) beinvertible. Thenwhich X rarr Y is not possible ?
Answer» `[ PI/4, (5 pi)/(4)] RARR [ SQRT(2), 3 sqrt(2)]` `[ - (3PI)/(4), pi/4] rarr [ sqrt(2), 3 sqrt(2)]` `[ - (3pi)/(4), (3 pi)/(4) ] rarr [ sqrt(2), 3 sqrt(2)]` none of these Answer :B

Discussion

3109.	Consider the sets X and Y of Example 14. Find X ∩ Y.
Answer» ANSWER :{GEETA}

Discussion

3110.	Height of the cylinder of maximum volume that can be inscribed in a sphere of radius 12 cm is
Answer» `8sqrt(3)CM` `8 cm` `12sqrt(3)cm` 24 cm Answer :A

Discussion

3111.	There are 100 students in a class of which 36 are boys studying science and 13 are girls not studying science. If there are 55 girls in all, probability that a boy picked up at random is not studying science is
Answer» `3/5` `2/5` `1/5` `1/3` ANSWER :C

Discussion

3112.	A line passing through (3,4) meets the axes bar(OX) and bar(OY) at A and B respectively. The minimum area of triangle OAB in square units is
Answer» 12 10 24 36 Answer :C

Discussion

3113.	The value of alpha such that sin^(-1)""2/sqrt(5), sin^(-1)""3/sqrt(10), sin^(-1)alpha are the angles of a triangle is
Answer» `(-1)/2` `1/2` `1/sqrt(3)` `1/sqrt(2)` ANSWER :D

Discussion

3114.	If tan theta, 2 tan theta + 2, 3 tan theta + 3 are in G.P then the value of(7-5cottheta)/(9-4sqrt(sec^(2)theta-1))s is
Answer» `(12)/(5)` `(-33)/(28)` `(33)/(100)` `(12)/(13)` Answer :B

Discussion

3115.	Solve the following equations for which solution lies in the interval 0^(@) le theta lt 360^(@). (i) sin^(4) x=sin^(2)x (ii) 2 cos x+1=-3 cos x (iii) 2 sin^(2) x+1=3 sin x (iv) cos 2x=1-3x sin x.
Answer» Answer :(i) `0,pi/2, pi, (3pi)/(2),2pi` (ii) `(4pi)/(3) and x=pi` (III) 1 (IV) `pi`

Discussion

3116.	If f(x) = 2x+5 ifxge1
Answer» 2 3 7 1 Answer :A

Discussion

3117.	Out of the following which is not function?
Answer» `{(x,y): x, y in R "" x^(2)= y}` `{(x,y ): x, y in R " " y^(2)=x}` `{(x,y): x, y in R " " x= y^(3)}` `{(x,y) : x, y in R " " y= x^(3)}` Answer :B

Discussion

3118.	Without finding point of intersection obtain the equation of line passes from point of intersection of lines 5x + y + 4 = 0 and 2x + 3y - 1 = 0. which is parallel to the line 4x - 2y- 1 = 0.
Answer» ANSWER :`2X - y + 3 = 0`

Discussion

3119.	The point on the line 3x+4y-5 which is equidistant from (1,2) and (3,4) is :
Answer» (7,-4) (15,-10) `(1//7,8//7)` `(0,5//4)` ANSWER :B

Discussion

3120.	For what value of k is this function f(x)={(x^3 -8)/(x-2) if xne 2kif x=2 is continuous on(-infty,infty):
Answer» 2 8 4 12 Answer :D

Discussion

3121.	Reduce the equation sqrt(3) x + y- 8=0 into normal form. Find the value of p and omega.
Answer» <P> ANSWER :`P = 4, OMEGA = 30^(@)`.

Discussion

3122.	A (0,a) ,B(0,b) be fixed points , P(x,0) a variable point. The angle angle APB is maximum if
Answer» ANSWER :`SQRT5`

Discussion

3123.	cos((pi)/(7))cos((2pi)/(7))cos((4pi)/(7))= ………..
Answer» 0 `(1)/(2)` `(1)/(4)` `-(1)/(8)` ANSWER :D

Discussion

3124.	(ii) Eliminate 'theta' from the equations x= tan theta + cot theta, y = sec theta - cos theta
Answer» ANSWER :`(X^(2)-y^(2))^(2)=16XY`

Discussion

3125.	Let S= {x in R : x ge 0" and "2\|sqrt(x)-3\|+sqrt(x)(sqrt(x)-6)+6=0}. Then S : "…………"
Answer» is an EMPTY set has only ONE element has only TWO element has only FOUR element Answer :C

Discussion

3126.	Compute lim_(x to infty)(x^(2)+5x+2)/(2x^(2)-5x+1)
Answer» ANSWER :`1//2`

Discussion

3127.	A variable plane makes with the coordinate planes, a tetrahedron of constant volume 64k^(3). Then the locus of the centroid of tetrahedron is the surface
Answer» `xyz=6k^(3)` `xy+yz+zx=6k^(2)` `X^(2)+y^(2)+Z^(2)=8k^(2)` `x^(-2)+y^(-2) +z^(-2) =8k^(2)` ANSWER :a

Discussion

3128.	Let f:R rarr R be a continuous function such that f(x)-2 f(x/2) + f(x/4)=x^(2). Now answer the following f(3)=
Answer» `F(0)` `4+f(0)` `9+f(0)` `16+f(0)` ANSWER :D

Discussion

3129.	Let n(A)=5 and n(B)=3 then find the number of injective functions and onto functions from Ato B.
Answer» ANSWER :FALSE STATEMENT

Discussion

3130.	The number of values of k for which the equation x^(3)-3x+k=0 has two distinct roots lying I the interval (0,1) is
Answer» three two infinitely many zero Answer :D

Discussion

3131.	A wire given 'l' is cut into two portions which are bent into the shapes of a circle and a squarerespectively . If the sum of the areas of the circle and square will be least when sideof square is lambda then 8lambda =
Answer» ANSWER :8

Discussion

3132.	Find the multiplicative inverse of the following complex number. 3-2i
Answer» ANSWER :`(3)/(13)+(2)/(13)i`

Discussion

3133.	If A and B are coefficient of x^(n)in the expansions of (1+x)^(2n) and (1+x)^(2n-1) respectively , then A/Bequals to
Answer» 1 2 `1/2` `1/n` ANSWER :B

Discussion

3134.	If f (x +y) = 2 f (x) .f(y) such that f '(0) 3 and (4) = 2find d'(4).
Answer» ANSWER :12

Discussion

3135.	A variable triangle is inscribed in a circle of radius R. If the rate of change of a side is R times the rate of change of he opposite angle, then the opposite angle is
Answer» `(pi)/(6)` `(pi)/(4)` `(pi)/(3)` `(pi)/(2)` Answer :C

Discussion

3136.	Determine the value of k if the rank of [(1,-2,3,1),(2,3,1,1),(4,-1,7,3),(5,4,5,k)] is 2.
Answer» ANSWER :`k=3`

Discussion

3137.	A stick of length I rests against the floor and a wall of a room. If the stick begins to slide on the floor, then the locus of its middle point is
Answer» `3X^(2)+3y^(2)=1^(2)` `4X^(2)+4y^(2)=1^(2)` `2x^(2)+2y^(2)=1^(2)` `X^(2)+y^(2)=1^(2)` Answer :B

Discussion

3138.	Which of the following pairs of sets are disjoint : {x : x is a letter in the word july} {x : x a letter in the word March}
Answer» ANSWER :it is not DISJOINT SET

Discussion

3139.	The tangent of angle between the lines whose intercepts on the axes are a, -b and b, -a, respectively, is
Answer» `(a^2 - b^2)/ (AB)` `( b^2 - a^2)/( 2)` `( b^2 - a^2)/( 2 ab)` NONE of these Answer :C

Discussion

3140.	if ((77),( r)) is maximum then r = …… .
Answer» 35 38.5 39 4 Answer :C

Discussion

3141.	A, B, C are three pointsvec(ox),vec(oy),vec(oz) respectively at a distances of a, b, c (a ne 0, b ne 0, c ne 0) from the origin O. Find the coordinates of the point which is equidistant from A, B, C and O.
Answer» ANSWER :`((a)/(2),(B)/(2),( C )/(2))`

Discussion

3142.	A basket contains 15 guava and 12 banana. Out of which 5 guava and 7 banana are defective. If a person takes out 3 at random, then what is the probability that either all are guava or all are good?
Answer» ANSWER :0.27

Discussion

3143.	If ainR then \|{:(a^(2),(a+1)^(2),(a+2)^(2)),((a+1)^(2),(a+2)^(2),(a+3)^(2)),((a+2)^(2),(a+3)^(2),(a+4)^(2)):}\| is
Answer» DEPENDS on a independent of a of DEGREE 6 0 Answer :B

Discussion

3144.	For what values of x 2Cos^(-1)x=Sin^(-1)2xsqrt(1-x^(2)) is valid
Answer» ANSWER :`[1/(SQRT(2)),1]`

Discussion

3145.	State whether the following statements are negation to each other ? (i) p: ram is a good boy. q : ram is not a good boy. (ii) p: sqrt(5) is a rational number. q : sqrt(5) is an irational number. (iii) p: australia is a continent. q: australia is not a continent. (iv) p: a multiple of 2 is 16. q : a multiple of 2 is 12.
Answer» SOLUTION :(i) YES (II) yes (III) yes (IV) No.

Discussion

3146.	Find the valuesof other five trigonometric functions Sinx=(3)/(5),x lies in second quadrant.
Answer» Answer :`COSEC X = 5/3, cos x =-4/5 , sec x =- 5/4 , TAN x=- 3/4, COT x =- 4/3`

Discussion

3147.	If ""^((n+2))C_(7):^((n-1))P_(4)=13:24 find n.
Answer» ANSWER :N = 13

Discussion

3148.	Arrange the following matrices in ascending order of their determinant values. (A) [(costheta,sintheta),(-sintheta,costheta)] (B) [(1,w,w^(2)),(w,w^(2),1),(w^(2),1,w)] (C) [(0,i),(-i,0)]
Answer» C,A,B B,C,A C,B,A B,A,C Answer :C

Discussion

3149.	If bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k), bar(c)=bar(i)+bar(k), then the unit vector in the opposite direction of bar(a)-2bar(b)+3bar(c) is
Answer» `1/(3sqrt(2))(4bar(i)-BAR(J)+bar(K))` `-1/(3sqrt(2))(4bar(i)-bar(j)+bar(k))` `1/(3sqrt(2))(bar(i)-4bar(j)+bar(k))` `1/(3sqrt(2))(bar(i)+bar(j)-4bar(k))` Answer :B

Discussion

3150.	Statemant I : If f is continuous , then \|f\| is continuous Statement II : If \|f\| is continuous, then f is also continuous Which one of the following is true
Answer» only I only II both I & II Neither I or II ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

Series 1^(2) + 2.2^(2) + 3^(2) + 2.4^(2)+ 5^(2) + 2.6^(2)+ ……are given. The sum of its first 20 terms is A and that of first 40 terms is B. If B- 2A = 100 lamda, " then" lamda=…….

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

If the normals drawn at the points t_(1) & t_(2) on the parabola y^(2)=4axmeet the parabola again at its point t_(3), then t_(1)t_(2) equals:

Let f: R to R be a continuousfunction defined by f(x)=(1)/(e^(x)+2e^(-x)) Statement -1 : f(x)=(1)/(3), for some c in R. Statement -2, 0 ltf(x) le (1)/(2sqrt(2))AAx in R.

If (1 + tan alpha) (1 + tan 4 alpha) = 2, alpha in (0, (pi)/(16)), then alpha =

The three concurrent edges of a parallelopiped represents the vectors bara, barb, barc such that [bara barb barc] = lamda.Then the volume of the parallelopiped whose three concurrent ed2es are the three concurrent diagonals of three faces of the given parallelopiped is

In the isosceles triangle OAB, O is the origin, OA=OB=6. If the equation of side AB is x-y+1=0, then the area of the triangle OAB is (in square units)

Let f: X rarrY , f(x)= sin x + cos x + 2 sqrt(2) beinvertible. Thenwhich X rarr Y is not possible ?

Consider the sets X and Y of Example 14. Find X ∩ Y.

Height of the cylinder of maximum volume that can be inscribed in a sphere of radius 12 cm is

There are 100 students in a class of which 36 are boys studying science and 13 are girls not studying science. If there are 55 girls in all, probability that a boy picked up at random is not studying science is

A line passing through (3,4) meets the axes bar(OX) and bar(OY) at A and B respectively. The minimum area of triangle OAB in square units is

The value of alpha such that sin^(-1)""2/sqrt(5), sin^(-1)""3/sqrt(10), sin^(-1)alpha are the angles of a triangle is

If tan theta, 2 tan theta + 2, 3 tan theta + 3 are in G.P then the value of(7-5cottheta)/(9-4sqrt(sec^(2)theta-1))s is

Solve the following equations for which solution lies in the interval 0^(@) le theta lt 360^(@). (i) sin^(4) x=sin^(2)x (ii) 2 cos x+1=-3 cos x (iii) 2 sin^(2) x+1=3 sin x (iv) cos 2x=1-3x sin x.

If f(x) = 2x+5 ifxge1

Out of the following which is not function?

Without finding point of intersection obtain the equation of line passes from point of intersection of lines 5x + y + 4 = 0 and 2x + 3y - 1 = 0. which is parallel to the line 4x - 2y- 1 = 0.

The point on the line 3x+4y-5 which is equidistant from (1,2) and (3,4) is :

For what value of k is this function f(x)={(x^3 -8)/(x-2) if xne 2kif x=2 is continuous on(-infty,infty):

Reduce the equation sqrt(3) x + y- 8=0 into normal form. Find the value of p and omega.

A (0,a) ,B(0,b) be fixed points , P(x,0) a variable point. The angle angle APB is maximum if

cos((pi)/(7))cos((2pi)/(7))cos((4pi)/(7))= ………..

(ii) Eliminate 'theta' from the equations x= tan theta + cot theta, y = sec theta - cos theta

Let S= {x in R : x ge 0" and "2|sqrt(x)-3|+sqrt(x)(sqrt(x)-6)+6=0}. Then S : "…………"

Compute lim_(x to infty)(x^(2)+5x+2)/(2x^(2)-5x+1)

A variable plane makes with the coordinate planes, a tetrahedron of constant volume 64k^(3). Then the locus of the centroid of tetrahedron is the surface

Let f:R rarr R be a continuous function such that f(x)-2 f(x/2) + f(x/4)=x^(2). Now answer the following f(3)=

Let n(A)=5 and n(B)=3 then find the number of injective functions and onto functions from Ato B.

The number of values of k for which the equation x^(3)-3x+k=0 has two distinct roots lying I the interval (0,1) is

A wire given 'l' is cut into two portions which are bent into the shapes of a circle and a squarerespectively . If the sum of the areas of the circle and square will be least when sideof square is lambda then 8lambda =

Find the multiplicative inverse of the following complex number. 3-2i

If A and B are coefficient of x^(n)in the expansions of (1+x)^(2n) and (1+x)^(2n-1) respectively , then A/Bequals to

If f (x +y) = 2 f (x) .f(y) such that f '(0) 3 and (4) = 2find d'(4).

A variable triangle is inscribed in a circle of radius R. If the rate of change of a side is R times the rate of change of he opposite angle, then the opposite angle is

Determine the value of k if the rank of [(1,-2,3,1),(2,3,1,1),(4,-1,7,3),(5,4,5,k)] is 2.

A stick of length I rests against the floor and a wall of a room. If the stick begins to slide on the floor, then the locus of its middle point is

Which of the following pairs of sets are disjoint : {x : x is a letter in the word july} {x : x a letter in the word March}

The tangent of angle between the lines whose intercepts on the axes are a, -b and b, -a, respectively, is

if ((77),( r)) is maximum then r = …… .

A, B, C are three pointsvec(ox),vec(oy),vec(oz) respectively at a distances of a, b, c (a ne 0, b ne 0, c ne 0) from the origin O. Find the coordinates of the point which is equidistant from A, B, C and O.

A basket contains 15 guava and 12 banana. Out of which 5 guava and 7 banana are defective. If a person takes out 3 at random, then what is the probability that either all are guava or all are good?

If ainR then |{:(a^(2),(a+1)^(2),(a+2)^(2)),((a+1)^(2),(a+2)^(2),(a+3)^(2)),((a+2)^(2),(a+3)^(2),(a+4)^(2)):}| is

For what values of x 2Cos^(-1)x=Sin^(-1)2xsqrt(1-x^(2)) is valid

Find the valuesof other five trigonometric functions Sinx=(3)/(5),x lies in second quadrant.

If ""^((n+2))C_(7):^((n-1))P_(4)=13:24 find n.

Arrange the following matrices in ascending order of their determinant values. (A) [(costheta,sintheta),(-sintheta,costheta)] (B) [(1,w,w^(2)),(w,w^(2),1),(w^(2),1,w)] (C) [(0,i),(-i,0)]

If bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k), bar(c)=bar(i)+bar(k), then the unit vector in the opposite direction of bar(a)-2bar(b)+3bar(c) is

Statemant I : If f is continuous , then |f| is continuous Statement II : If |f| is continuous, then f is also continuous Which one of the following is true