43030 + Interview Questions in Mathematics Page 61 InterviewSolution

3001.	THE VALUE OF LIM X 2 ([2-X]+[X-2]-X) W EAQULA
Answer» THE VALUE OF LIM X 2 ([2-X]+[X-2]-X) W EAQULA

Discussion

3002.	If f(x)=cos−1(1−x1+x); x∈(0,1), then the sum of their possible values of f′(1) is
Answer» If $f (x) = {cos}^{- 1} (\frac{1 - x}{1 + x}); x \in (0, 1),$ then the sum of their possible values of $f^{'} (1)$ is

Discussion

3003.	how slove this interate sin(ax+b)dx
Answer» how slove this interate sin(ax+b)dx

Discussion

3004.	The value of 50∫0[2x21+x2]dx is (where [⋅] denotes the greatest integer function)
Answer» The value of $50 \int 0 [\frac{2 x^{2}}{1 + x^{2}}] d x$ is (where $[\cdot]$ denotes the greatest integer function)

Discussion

3005.	On dividing x2+2x+1 by (x+1), you will getas the quotient.
Answer» On dividing $x^{2} + 2 x + 1$ by (x+1), you will getas the quotient.

Discussion

3006.	If the distance of the point P (1, -2, 1) from the plane x+2y−2z=α where α>0, is 5, then the foot of the perpendicular form P to the plane is
Answer» If the distance of the point P (1, -2, 1) from the plane $x + 2 y - 2 z = α$ where $α > 0$ , is 5, then the foot of the perpendicular form P to the plane is

Discussion

3007.	Let A = { x , y , z} and B = {1, 2}. Find the number of relations from A to B.
Answer» Let A = { x , y , z} and B = {1, 2}. Find the number of relations from A to B.

Discussion

3008.	If tanα=xx+1 and tanβ=12x+1, then α+β is equal to(a) π2 (a) π3 (a) π6 (a) π4
Answer» If $\tan α = \frac{x}{x + 1}$ and $\tan β = \frac{1}{2 x + 1}$ , then $α + β$ is equal to (a) $\frac{π}{2}$ (a) $\frac{π}{3}$ (a) $\frac{π}{6}$ (a) $\frac{π}{4}$

Discussion

3009.	Find the value of 'k' for which the quadratic equation 4x^2 - 2kx + k=0 has real and equal roots.
Answer» Find the value of 'k' for which the quadratic equation 4x^2 - 2kx + k=0 has real and equal roots.

Discussion

3010.	Five friends are standing in a line: John, James, Robert, Mary and Lucy.(i) One of the two persons at the extreme ends is John and other is Lucy. (ii) Robert is to the left of Lucy.(iii) Mary is standing between John and James.Find the position of James.
Answer» Five friends are standing in a line: John, James, Robert, Mary and Lucy. (i) One of the two persons at the extreme ends is John and other is Lucy. (ii) Robert is to the left of Lucy. (iii) Mary is standing between John and James. Find the position of James.

Discussion

3011.	If (1+x)n=C0+C1x+…..+Cnxn, then the value of ∑∑0≤r<s≤n(Cr+Cs) is equal to
Answer» If $(1 + x)^{n} = C_{0} + C_{1} x + \dots . . + C_{n} x^{n},$ then the value of $\sum \sum 0 \leq r < s \leq n (C_{r} + C_{s})$ is equal to

Discussion

3012.	The number of solution(s) of the equation tan2x−sec10x+1=0 in x∈[0,60] is
Answer» The number of solution(s) of the equation ${tan}^{2} x - {sec}^{10} x + 1 = 0$ in $x \in [0, 60]$ is

Discussion

3013.	Prove the following: 12.5+15.8+18.11+⋯+1(3n−1)(3n+2)=n6n+4
Answer» Prove the following: $\frac{1}{2.5} + \frac{1}{5.8} + \frac{1}{8.11} + \dots + \frac{1}{(3 n - 1) (3 n + 2)} = \frac{n}{6 n + 4}$

Discussion

3014.	Which of the following hold true in a Right angled triangle.
Answer» Which of the following hold true in a Right angled triangle.

Discussion

3015.	Question 36A carton of 24 bulbs contains 6 defective bulbs. One bulb is drawn at random. What is the probability that the bulb is not defective? If the bulb selected is defective and it is not replaced and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective?
Answer» Question 36 A carton of 24 bulbs contains 6 defective bulbs. One bulb is drawn at random. What is the probability that the bulb is not defective? If the bulb selected is defective and it is not replaced and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective?

Discussion

3016.	Find the general solution of the equation
Answer» Find the general solution of the equation

Discussion

3017.	If ∫sinxsin(x−α)dx=Ax+Bln\|sin(x−α)\|+C, then value of (A,B) is(where A,B are fixed constants and C is constant of integration)
Answer» If $\int \frac{sin x}{sin (x - α)} d x = A x + B ln \| sin (x - α) \| + C,$ then value of $(A, B)$ is (where $A, B$ are fixed constants and $C$ is constant of integration)

Discussion

3018.	Minimum number of 2 micro farad capacitors required to obtain 7 micro farad capacitor is- (a)6 (b)3 (c)7 (d)5
Answer» Minimum number of 2 micro farad capacitors required to obtain 7 micro farad capacitor is- (a)6 (b)3 (c)7 (d)5

Discussion

3019.	The equation xn=1,n>1,n∈N has roots 1,a1,a2,...,an−1. Then which of the following are correct?
Answer» The equation $x^{n} = 1, n > 1, n \in N$ has roots $1, a_{1}, a_{2}, . . ., a_{n - 1}$ . Then which of the following are correct?

Discussion

3020.	In the given equilateral triangle ABC, AP is the median in triangle ABC. Find the value of angle PAC.
Answer» In the given equilateral triangle ABC, AP is the median in triangle ABC. Find the value of angle PAC.

Discussion

3021.	The total number of reflexive relations on a finite set having n elements is __________.
Answer» The total number of reflexive relations on a finite set having n elements is __________.

Discussion

3022.	Equation of tangent having slope '1' to the circle x2 + y2 -10x-8y+50
Answer» Equation of tangent having slope '1' to the circle x2 + y2 -10x-8y+50

Discussion

3023.	Let fk(x)=1k(sinkx+coskx) where xϵR and k⩾1 Then f4(x)−f6(x) equals
Answer» Let $f_{k} (x) = \frac{1}{k} (s i n^{k} x + c o s^{k} x)$ where $x ϵ R$ and $k ⩾ 1$ Then $f_{4} (x) - f_{6} (x)$ equals

Discussion

3024.	Solve sin2x−sin4x+sin6x=0
Answer» Solve $sin 2 x - sin 4 x + sin 6 x = 0$

Discussion

3025.	If alpha, beta and gamma are the roots of the equation x^3+4x+1=0, then (alpha+beta)^-1 + (beta+gamma)^-1 + (gamma+alpha)^-1 is
Answer» If alpha, beta and gamma are the roots of the equation x^3+4x+1=0, then (alpha+beta)^-1 + (beta+gamma)^-1 + (gamma+alpha)^-1 is

Discussion

3026.	Which of the following lines subtends chords of equal lengths on intersecting with the circle, x2+y2−2x+4y=0?
Answer» Which of the following lines subtends chords of equal lengths on intersecting with the circle, $x^{2} + y^{2} - 2 x + 4 y = 0$ ?

Discussion

3027.	For an ap if tm =1/n and tn=1/m then a-d=
Answer» For an ap if tm =1/n and tn=1/m then a-d=

Discussion

3028.	41. Prove that 10 raise to n +34 raise to n+2 +5 is divisible by 9, n belong to N
Answer» 41. Prove that 10 raise to n +34 raise to n+2 +5 is divisible by 9, n belong to N

Discussion

3029.	d/dx(a^x^2+1/log(tanx) )
Answer» d/dx(a^x^2+1/log(tanx) )

Discussion

3030.	If P=⎡⎢⎣04−2x0−y2−80⎤⎥⎦ is a skew-symmetric matrix, then x−y is
Answer» If $P = ⎡ ⎢ ⎣ \begin{matrix} 0 & 4 & - 2 x & 0 & - y 2 & - 8 & 0 \end{matrix} ⎤ ⎥ ⎦$ is a skew-symmetric matrix, then $x - y$ is

Discussion

3031.	Given a non empty set X, consider P(X) which is the set of all subsets of X. Define the relation R in P(X) as follows: For subsets A, B in P(X), ARB if and only if A ⊂ B. Is R an equivalence relation on P(X)? Justify you answer:
Answer» Given a non empty set X, consider P(X) which is the set of all subsets of X. Define the relation R in P(X) as follows: For subsets A, B in P(X), ARB if and only if A ⊂ B. Is R an equivalence relation on P(X)? Justify you answer:

3031.

Given a non empty set X, consider P(X) which is the set of all subsets of X. Define the relation R in P(X) as follows: For subsets A, B in P(X), ARB if and only if A ⊂ B. Is R an equivalence relation on P(X)? Justify you answer:

Answer»

Given a
non empty set X, consider P(X) which is the set of all
subsets of X.

Define the
relation R in P(X) as follows:

For
subsets A, B in P(X), ARB if and
only if A ⊂ B.
Is R an equivalence relation on P(X)? Justify you answer:

Discussion

3032.	Let a be an integer such that all the real roots of the polynomial 2x5+5x4+10x3+10x2+10x+10 lie in the interval a,a+1. Then, \|a\| is equal to
Answer» Let $a$ be an integer such that all the real roots of the polynomial $2 x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 10 x + 10$ lie in the interval $a, a + 1$ . Then, $\| a \|$ is equal to

Discussion

3033.	The area (in sq. units) of the region in first quadrant in which points are nearer to the origin than to the line x=3 is
Answer» The area (in sq. units) of the region in first quadrant in which points are nearer to the origin than to the line $x = 3$ is

Discussion

3034.	Events A and B are such that . State whether A and B are independent?
Answer» Events A and B are such that . State whether A and B are independent?

Discussion

3035.	Solve the equation x2+3x+9=0
Answer» Solve the equation $x^{2} + 3 x + 9 = 0$

Discussion

3036.	If A and B are two events such that P(A) = 12 and P(B) = 23, then
Answer» If A and B are two events such that P(A) = $\frac{1}{2}$ and P(B) = $\frac{2}{3}$ , then

Discussion

3037.	if cot 20=p then [tan 160-tan110/]/1+tan 160*tan 110
Answer» if cot 20=p then [tan 160-tan110/]/1+tan 160*tan 110

Discussion

3038.	If point P(3,8) lies on the line segment joining A(2,10) and B(6,2), then:[1 mark]
Answer» If point $P (3, 8)$ lies on the line segment joining $A (2, 10)$ and $B (6, 2),$ then: [1 mark]

Discussion

3039.	Question 17If the points A(2,9), B(a,5) and C(5,5) are the vertices of a Δ ABC right angled at B, then find the values of a and hence the area of Δ ABC.
Answer» Question 17 If the points A(2,9), B(a,5) and C(5,5) are the vertices of a $Δ$ ABC right angled at B, then find the values of a and hence the area of $Δ$ ABC.

Discussion

3040.	How many positive and negative real roots are there for the equation x^2-\|x\|-2=0?
Answer» How many positive and negative real roots are there for the equation x^2-\|x\|-2=0?

Discussion

3041.	Let us consider a square matrix of order n ×n. Every element of this matrix is either 1 or - 1 and the product of entries in each row and each column is equal to - 1. Find out the number of such possible matrices for n = n.
Answer» Let us consider a square matrix of order n ×n. Every element of this matrix is either 1 or - 1 and the product of entries in each row and each column is equal to - 1. Find out the number of such possible matrices for n = n.

Discussion

3042.	The value of limx→0x(ex−1)1−cosx is
Answer» The value of $lim x \to 0 \frac{x (e^{x} - 1)}{1 - cos x}$ is

Discussion

3043.	The number of tetrahedral and octahedral voidsformed by one half of a sphere with its adjacernt layer in close packing are respectively(1) 8 and 6 (2) 4 and 6 (3) 4 and 3 (4) 2 and 3 explain als
Answer» The number of tetrahedral and octahedral voidsformed by one half of a sphere with its adjacernt layer in close packing are respectively(1) 8 and 6 (2) 4 and 6 (3) 4 and 3 (4) 2 and 3 explain als

Discussion

3044.	(1-i) (1-2i)..... (1-ni) =x-iy then 2.5.10.••••(1+n^2)
Answer» (1-i) (1-2i)..... (1-ni) =x-iy then 2.5.10.••••(1+n^2)

Discussion

3045.	For all positive integers n, show that 2nCn+2nCn−1=12(2n+2Cn+1)
Answer» For all positive integers n, show that $^{2 n} C_{n} +^{2 n} C_{n - 1} = \frac{1}{2} (^{2 n + 2} C_{n + 1})$

3045.

For all positive integers n, show that 2nCn+2nCn−1=12(2n+2Cn+1)

Answer»

For all positive integers n, show that

$^{2 n} C_{n} +^{2 n} C_{n - 1} = \frac{1}{2} (^{2 n + 2} C_{n + 1})$

Discussion

3046.	What is Snell's law?
Answer» What is Snell's law?

Discussion

3047.	If x and y are connected parametrically by the equation, without eliminating the parameter, find .
Answer» If x and y are connected parametrically by the equation, without eliminating the parameter, find .

Discussion

3048.	26. 2[a.sin(C/2) + c.sin(A/2)] = c + k, then k = ? (1) a + b (2) a - b (3) b - a (4) s + a
Answer» 26. 2[a.sin(C/2) + c.sin(A/2)] = c + k, then k = ? (1) a + b (2) a - b (3) b - a (4) s + a

Discussion

3049.	What are the points on the y -axis whose distance from the line is 4 units.
Answer» What are the points on the y -axis whose distance from the line is 4 units.

Discussion

3050.	The tangents to the curve y=sin(x+y),−2π≤x≤2π that are parallel to the line x+2y=0 is
Answer» The tangents to the curve $y = sin (x + y), - 2 π \leq x \leq 2 π$ that are parallel to the line $x + 2 y = 0$ is

Discussion

Explore topic-wise InterviewSolutions in .

THE VALUE OF LIM X 2 ([2-X]+[X-2]-X) W EAQULA

If f(x)=cos−1(1−x1+x); x∈(0,1), then the sum of their possible values of f′(1) is

how slove this interate sin(ax+b)dx

The value of 50∫0[2x21+x2]dx is (where [⋅] denotes the greatest integer function)

On dividing x2+2x+1 by (x+1), you will getas the quotient.

If the distance of the point P (1, -2, 1) from the plane x+2y−2z=α where α&gt;0, is 5, then the foot of the perpendicular form P to the plane is

Let A = { x , y , z} and B = {1, 2}. Find the number of relations from A to B.

If tanα=xx+1 and tanβ=12x+1, then α+β is equal to(a) π2 (a) π3 (a) π6 (a) π4

Find the value of 'k' for which the quadratic equation 4x^2 - 2kx + k=0 has real and equal roots.

Five friends are standing in a line: John, James, Robert, Mary and Lucy.(i) One of the two persons at the extreme ends is John and other is Lucy. (ii) Robert is to the left of Lucy.(iii) Mary is standing between John and James.Find the position of James.

If (1+x)n=C0+C1x+…..+Cnxn, then the value of ∑∑0≤r&lt;s≤n(Cr+Cs) is equal to

The number of solution(s) of the equation tan2x−sec10x+1=0 in x∈[0,60] is

Prove the following: 12.5+15.8+18.11+⋯+1(3n−1)(3n+2)=n6n+4

Which of the following hold true in a Right angled triangle.

Find the general solution of the equation

If ∫sinxsin(x−α)dx=Ax+Bln|sin(x−α)|+C, then value of (A,B) is(where A,B are fixed constants and C is constant of integration)

Minimum number of 2 micro farad capacitors required to obtain 7 micro farad capacitor is- (a)6 (b)3 (c)7 (d)5

The equation xn=1,n&gt;1,n∈N has roots 1,a1,a2,...,an−1. Then which of the following are correct?

In the given equilateral triangle ABC, AP is the median in triangle ABC. Find the value of angle PAC.

The total number of reflexive relations on a finite set having n elements is __________.

Equation of tangent having slope '1' to the circle x2 + y2 -10x-8y+50

Let fk(x)=1k(sinkx+coskx) where xϵR and k⩾1 Then f4(x)−f6(x) equals

Solve sin2x−sin4x+sin6x=0

If alpha, beta and gamma are the roots of the equation x^3+4x+1=0, then (alpha+beta)^-1 + (beta+gamma)^-1 + (gamma+alpha)^-1 is

Which of the following lines subtends chords of equal lengths on intersecting with the circle, x2+y2−2x+4y=0?

For an ap if tm =1/n and tn=1/m then a-d=

41. Prove that 10 raise to n +34 raise to n+2 +5 is divisible by 9, n belong to N

d/dx(a^x^2+1/log(tanx) )

If P=⎡⎢⎣04−2x0−y2−80⎤⎥⎦ is a skew-symmetric matrix, then x−y is

Given a non empty set X, consider P(X) which is the set of all subsets of X. Define the relation R in P(X) as follows: For subsets A, B in P(X), ARB if and only if A ⊂ B. Is R an equivalence relation on P(X)? Justify you answer:

Let a be an integer such that all the real roots of the polynomial 2x5+5x4+10x3+10x2+10x+10 lie in the interval a,a+1. Then, |a| is equal to

The area (in sq. units) of the region in first quadrant in which points are nearer to the origin than to the line x=3 is

Events A and B are such that . State whether A and B are independent?

Solve the equation x2+3x+9=0

If A and B are two events such that P(A) = 12 and P(B) = 23, then

if cot 20=p then [tan 160-tan110/]/1+tan 160*tan 110

If point P(3,8) lies on the line segment joining A(2,10) and B(6,2), then:[1 mark]

Question 17If the points A(2,9), B(a,5) and C(5,5) are the vertices of a Δ ABC right angled at B, then find the values of a and hence the area of Δ ABC.

How many positive and negative real roots are there for the equation x^2-|x|-2=0?

Let us consider a square matrix of order n ×n. Every element of this matrix is either 1 or - 1 and the product of entries in each row and each column is equal to - 1. Find out the number of such possible matrices for n = n.

The value of limx→0x(ex−1)1−cosx is

The number of tetrahedral and octahedral voidsformed by one half of a sphere with its adjacernt layer in close packing are respectively(1) 8 and 6 (2) 4 and 6 (3) 4 and 3 (4) 2 and 3 explain als

(1-i) (1-2i)..... (1-ni) =x-iy then 2.5.10.••••(1+n^2)

For all positive integers n, show that 2nCn+2nCn−1=12(2n+2Cn+1)

What is Snell's law?

If x and y are connected parametrically by the equation, without eliminating the parameter, find .

26. 2[a.sin(C/2) + c.sin(A/2)] = c + k, then k = ? (1) a + b (2) a - b (3) b - a (4) s + a

What are the points on the y -axis whose distance from the line is 4 units.

The tangents to the curve y=sin(x+y),−2π≤x≤2π that are parallel to the line x+2y=0 is

If the distance of the point P (1, -2, 1) from the plane x+2y−2z=α where α>0, is 5, then the foot of the perpendicular form P to the plane is

If (1+x)n=C0+C1x+…..+Cnxn, then the value of ∑∑0≤r<s≤n(Cr+Cs) is equal to

The equation xn=1,n>1,n∈N has roots 1,a1,a2,...,an−1. Then which of the following are correct?