43030 + Interview Questions in Mathematics

1.	Consider f(x) =tan−1(√1+sinx1−sinx),xϵ(0,π2). A normal to y=f(x) at x=π6 also passes through the point :
Answer» Consider $f (x)$ $= t a n^{- 1}$ $(\sqrt{\frac{1 + s i n x}{1 - s i n x}})$ , $x ϵ (0, \frac{π}{2})$ . A normal to $y = f (x) a t x = \frac{π}{6}$ also passes through the point :

Discussion

2.	(cos 0° + cos 45° + sin 30°) (sin 90° – cos 45° + cos 60°)
Answer» (cos 0° + cos 45° + sin 30°) (sin 90° – cos 45° + cos 60°)

Discussion

3.	The number of real roots of the equation 5+\|2x−1\|=2x(2x−2) is
Answer» The number of real roots of the equation $5 + \| 2^{x} - 1 \| = 2^{x} (2^{x} - 2)$ is

Discussion

4.	If k=sin π18sin 5π18sin 7π18, then the numerical value of k is __________.
Answer» If $k = \sin \frac{π}{18} \sin \frac{5 π}{18} \sin \frac{7 π}{18},$ then the numerical value of k is __________.

Discussion

5.	Evaluate: ∫1-xx dx
Answer» Evaluate: $\int (1 - x) \sqrt{x} d x$

Discussion

6.	63.Solve the equation ; sin ax +cos bx =0
Answer» 63.Solve the equation ; sin ax +cos bx =0

Discussion

7.	The intergral ∫dxx2(x4+1)3/4 eauals:
Answer» The intergral $\int \frac{d x}{x^{2} (x^{4} + 1)^{3 / 4}}$ eauals:

Discussion

8.	The quadratic polynomial with rational coefficients for which one of the roots is 2+3i is . where 'i' is √−1
Answer» The quadratic polynomial with rational coefficients for which one of the roots is 2+3i is . where 'i' is $\sqrt{- 1}$

Discussion

9.	f(x)+f(2x)+f(2-x)+f(1+x)=x ∀ x∈ R, then the value of f(0) is_________
Answer» f(x)+f(2x)+f(2-x)+f(1+x)=x ∀ x∈ R, then the value of f(0) is_________

Discussion

10.	The equation of auxiliary circle of hyperbola 25y2+250y−16x2−32x+209=0 is
Answer» The equation of auxiliary circle of hyperbola $25 y^{2} + 250 y - 16 x^{2} - 32 x + 209 = 0$ is

Discussion

11.	If log25−4∑k=1log2(sinkπ5)=pq, where p and q are co-prime, then the value of p+q is
Answer» If ${log}_{2} 5 - 4 \sum k = 1 {log}_{2} (sin \frac{k π}{5}) = \frac{p}{q},$ where $p$ and $q$ are co-prime, then the value of $p + q$ is

Discussion

12.	If A and B are the subset of universal set U and n(U) = 100 , n(A) = 40 , n(B) = 30 , n( A cap B ) = 10. than what is the value of n(A' cap B')?
Answer» If A and B are the subset of universal set U and n(U) = 100 , n(A) = 40 , n(B) = 30 , n( A cap B ) = 10. than what is the value of n(A' cap B')?

Discussion

13.	Write the value of cossin-1x+cos-1x, x≤1
Answer» Write the value of $\cos (\sin^{- 1} x + \cos^{- 1} x), \|x\| \leq 1$

Discussion

14.	If →a,→b and→care three vectors such that [→a →b →c]=1, then the value of [→a+→b →b+→c →c+→a]+[→a×→b →b×→c →c×→a]+[→a×(→b×→c) →b×(→c×→a) →c×(→a×→b)] is
Answer» If $\to a, \to b$ and $\to c$ are three vectors such that $[\to a \to b \to c] = 1$ , then the value of $[\to a + \to b \to b + \to c \to c + \to a] + [\to a \times \to b \to b \times \to c \to c \times \to a] + [\to a \times (\to b \times \to c) \to b \times (\to c \times \to a) \to c \times (\to a \times \to b)]$ is

Discussion

15.	The co-ordinates of the points which divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is _____.
Answer» The co-ordinates of the points which divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is _____.

Discussion

16.	find the range of f(x)=2 sin^8 x - 3 sin^4 x + 2
Answer» find the range of f(x)=2 sin^8 x - 3 sin^4 x + 2

Discussion

17.	The set of point where the function f(x) = \|2x – 1\| is differentiable, is ____________.
Answer» The set of point where the function f(x) = \|2x – 1\| is differentiable, is ____________.

Discussion

18.	If u = 3^i−5^j+9^k and v = 3^i+4^j+0k; What is the component of u along the direction of v?
Answer» If $u = 3^i - 5^j + 9^k a n d v = 3^i + 4^j + 0 k;$ What is the component of u along the direction of v?

Discussion

19.	If coordinates of two points A and B are (3,4) and (5,-2), find coordinates of P is PA=PB and area of triangle PAB =10
Answer» If coordinates of two points A and B are (3,4) and (5,-2), find coordinates of P is PA=PB and area of triangle PAB =10

Discussion

20.	The lines whose vector equations are →r=→a+t→b and →r=→c+s→d are coplanar if..
Answer» The lines whose vector equations are $\to r = \to a + t \to b$ and $\to r = \to c + s \to d$ are coplanar if..

Discussion

21.	Given vectors →a=12^i+√32^j, →b=√32^j+12^k and →c=^i+2^j+3^k. Then the volume of a parallelepiped with three coterminous edges as →u=(→a⋅→a)→a+(→a⋅→b)→b+(→a⋅→c)→c, →v=(→a⋅→b)→a+(→b⋅→b)→b+(→b⋅→c)→c and →w=(→a⋅→c)→a+(→b⋅→c)→b+(→c⋅→c)→c equals
Answer» Given vectors $\to a = \frac{1}{2}^i + \frac{\sqrt{3}}{2}^j,$ $\to b = \frac{\sqrt{3}}{2}^j + \frac{1}{2}^k$ and $\to c =^i + 2^j + 3^k .$ Then the volume of a parallelepiped with three coterminous edges as $\to u = (\to a \cdot \to a) \to a + (\to a \cdot \to b) \to b + (\to a \cdot \to c) \to c,$ $\to v = (\to a \cdot \to b) \to a + (\to b \cdot \to b) \to b + (\to b \cdot \to c) \to c$ and $\to w = (\to a \cdot \to c) \to a + (\to b \cdot \to c) \to b + (\to c \cdot \to c) \to c$ equals

Discussion

22.	A random variable X has the following probability distribution:X01234567P(X)0k2k2k3kk22k27k2+kThen value of k is:
Answer» A random variable $X$ has the following probability distribution: $\begin{matrix} X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 P(X) & 0 & k & 2k & 2k & 3k & k^{2} & 2 k^{2} & 7 k^{2} + k \end{matrix}$ Then value of $k$ is:

Discussion

23.	Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax2 + sin x) (p + q cos x)
Answer» Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax² + sin x) (p + q cos x)

Discussion

24.	If f(x)=∣∣∣∣∣x2x2−(y−z)2yzy2y2−(z−x)2zxz2z2−(x−y)2xy∣∣∣∣∣, then which of the following is/are factor of f(x)
Answer» If $f (x) = ∣ ∣∣∣ ∣ \begin{matrix} x^{2} & x^{2} - (y - z)^{2} & y z y^{2} & y^{2} - (z - x)^{2} & z x z^{2} & z^{2} - (x - y)^{2} & x y \end{matrix} ∣ ∣∣∣ ∣,$ then which of the following is/are factor of $f (x)$

Discussion

25.	Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola
Answer» Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola

Discussion

26.	The range of x for which the formula 3sin−1x=sin−1[x(3−4x2)] holds is :
Answer» The range of $x$ for which the formula $3 {sin}^{- 1} x = {sin}^{- 1} [x (3 - 4 x^{2})]$ holds is :

Discussion

27.	The modulus and argument of sinπ5+i1-cosπ5 are _______ and _______ respectively.
Answer» The modulus and argument of $\sin \frac{π}{5} + i (1 - \cos \frac{π}{5})$ are _______ and _______ respectively.

Discussion

28.	{0.3^(1/3)(1/27)^(1/4)9^(1/6)0.81^(2/3)}/{0.9^(2/3)3^(-1/2)(1/3)^(-2)243^(-1/4)
Answer» {0.3^(1/3)(1/27)^(1/4)9^(1/6)0.81^(2/3)}/{0.9^(2/3)3^(-1/2)(1/3)^(-2)243^(-1/4)

Discussion

29.	The miniumum number of 2×1 MUX required to implement a half-subtractor circuit when only basic inputs 0,1 A and B are available is
Answer» The miniumum number of $2 \times 1$ MUX required to implement a half-subtractor circuit when only basic inputs $0, 1$ $A$ and $B$ are available is

Discussion

30.	What is real numbers
Answer» What is real numbers

Discussion

31.	Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5) and C (6, 3)
Answer» Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5) and C (6, 3)

Discussion

32.	A real-valued function f(x) satisfies the functional equation f(x−y)=f(x)f(y)−f(a−x)f(a+y) ∀ x,y ∈R, where a is a given constant and f(0)=1. Then, f(2a−x) is equal to
Answer» A real-valued function $f (x)$ satisfies the functional equation $f (x - y) = f (x) f (y) - f (a - x) f (a + y) \forall x, y \in R$ , where $a$ is a given constant and $f (0) = 1$ . Then, $f (2 a - x)$ is equal to

Discussion

33.	PQ is a double ordinate of the hyperbola x2a2−y2b2=1 such that OPQ is an equilateral triangle, O being the centre of the hyperbola, then the range of the eccentricity e of the hyperbola is
Answer» $P Q$ is a double ordinate of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ such that $O P Q$ is an equilateral triangle, $O$ being the centre of the hyperbola, then the range of the eccentricity $e$ of the hyperbola is

Discussion

34.	What is the differentiation of x^2/2 ?
Answer» What is the differentiation of x^2/2 ?

Discussion

35.	Prove that sin x sin π3-x sin π3+x≤14 for all values of x
Answer» Prove that $\|\sin x \sin (\frac{π}{3} - x) \sin (\frac{π}{3} + x)\| \leq \frac{1}{4}$ for all values of x

Discussion

36.	PM and PN are the perpendiculars from any point P on the rectangular hyperbola xy = 8 to the asymptotes. If the locus of the mid point of MN is a conic, then the least distance of (1, 1) to director circle of the conic is
Answer» PM and PN are the perpendiculars from any point P on the rectangular hyperbola xy = 8 to the asymptotes. If the locus of the mid point of MN is a conic, then the least distance of (1, 1) to director circle of the conic is

Discussion

37.	What are the 17 topics that can assure me seat in top 5 IIT's in all subjects
Answer» What are the 17 topics that can assure me seat in top 5 IIT's in all subjects

Discussion

38.	If there are 12 points in a plane out of which only 5 are collinear, then the number of quadrilaterals that can be formed using these points is
Answer» If there are $12$ points in a plane out of which only $5$ are collinear, then the number of quadrilaterals that can be formed using these points is

Discussion

39.	If the angles made by a straight line with the coordinate axes are α,π/2−α,β then β=
Answer» If the angles made by a straight line with the coordinate axes are $α, π / 2 - α, β t h e n β =$

Discussion

40.	Let O be the vertex and Q be any point on the parabola x2=8y. If the point P divides the line segement OQ internally in the ratio 1 : 3, then the locus of P is
Answer» Let O be the vertex and Q be any point on the parabola $x^{2} = 8 y$ . If the point P divides the line segement OQ internally in the ratio 1 : 3, then the locus of P is

Discussion

41.	The complex number Z satisfies the equation Z +\|Z\| = 2+8i, then the value of \|Z\| - 8 is ___
Answer» The complex number Z satisfies the equation Z + $\| Z \|$ = 2+8i, then the value of $\| Z \|$ - 8 is ___

Discussion

42.	If r2−13r+40=0, then the value of 7Cr is
Answer» If $r^{2} - 13 r + 40 = 0$ , then the value of $^{7} C_{r}$ is

Discussion

43.	20. If y=e to the power ax.sinbx Prove that : y"-2ay'+(a square+ b square) y=0
Answer» 20. If y=e to the power ax.sinbx Prove that : y"-2ay'+(a square+ b square) y=0

Discussion

44.	Find the sum to n terms of each of the series in Exercises 1 to 7 1: 1x2+2x3+3 x4 4 x5+2. 1 x2 x 3+2 x3 4+34 3. 3 x 1 +5 x 22 +7 x3 +... 5. 5+6+72 + 20 Ix2 2x3 3x4 3x8+6x11+9x14 + 6,
Answer» Find the sum to n terms of each of the series in Exercises 1 to 7 1: 1x2+2x3+3 x4 4 x5+2. 1 x2 x 3+2 x3 4+34 3. 3 x 1 +5 x 22 +7 x3 +... 5. 5+6+72 + 20 Ix2 2x3 3x4 3x8+6x11+9x14 + 6,

Discussion

45.	To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A1, A2, A3, ... are located at equal distances on the ray AX and the point B is joined to(a) A12(b) A11(c) A10(d) A9
Answer» To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A₁, A₂, A₃, ... are located at equal distances on the ray AX and the point B is joined to (a) A₁₂ (b) A₁₁ (c) A₁₀ (d) A₉

Discussion

46.	If x, y, z ∈ R, the value of the determinant 2x+2-x22x-2-x213x+3-x23x-3-x214x+4-x24x-4-x21 is equal to ________________.
Answer» If x, y, z ∈ R, the value of the determinant $\|\begin{matrix} {(2^{x} + 2^{- x})}^{2} & {(2^{x} - 2^{- x})}^{2} & 1 \\ {(3^{x} + 3^{- x})}^{2} & {(3^{x} - 3^{- x})}^{2} & 1 \\ {(4^{x} + 4^{- x})}^{2} & {(4^{x} - 4^{- x})}^{2} & 1 \end{matrix}\|$ is equal to ________________.

Discussion

47.	The number of constant functions possible from R to B where B={2,4,6,8,...24} are
Answer» The number of constant functions possible from $R$ to $B$ where $B = {2, 4, 6, 8, . . .24}$ are

Discussion

48.	If A=[abcd] (where bc≠0) satisfies the equation x2+k=0, then
Answer» $I f A = [\begin{matrix} a & b c & d \end{matrix}] (w h e r e b c \neq 0) s a t i s f i e s t h e e q u a t i o n x^{2} + k = 0, t h e n$

Discussion

49.	Check whether the following are quadratic equations:(x−2)(x+1)=(x−1)(x+3)
Answer» Check whether the following are quadratic equations: $(x - 2) (x + 1) = (x - 1) (x + 3)$

Discussion

50.	Why is ∇\cdot(∇×\overrightarrow{A)} equal to 0 for any random vector field \overrightarrow A Also why is curl of a gradient always zero mathematically?
Answer» Why is ∇\cdot(∇×\overrightarrow{A)} equal to 0 for any random vector field \overrightarrow A Also why is curl of a gradient always zero mathematically?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Consider f(x) =tan−1(√1+sinx1−sinx),xϵ(0,π2). A normal to y=f(x) at x=π6 also passes through the point :

(cos 0° + cos 45° + sin 30°) (sin 90° – cos 45° + cos 60°)

The number of real roots of the equation 5+|2x−1|=2x(2x−2) is

If k=sin π18sin 5π18sin 7π18, then the numerical value of k is __________.

Evaluate: ∫1-xx dx

63.Solve the equation ; sin ax +cos bx =0

The intergral ∫dxx2(x4+1)3/4 eauals:

The quadratic polynomial with rational coefficients for which one of the roots is 2+3i is . where 'i' is √−1

f(x)+f(2x)+f(2-x)+f(1+x)=x ∀ x∈ R, then the value of f(0) is_________

The equation of auxiliary circle of hyperbola 25y2+250y−16x2−32x+209=0 is

If log25−4∑k=1log2(sinkπ5)=pq, where p and q are co-prime, then the value of p+q is

If A and B are the subset of universal set U and n(U) = 100 , n(A) = 40 , n(B) = 30 , n( A cap B ) = 10. than what is the value of n(A' cap B')?

Write the value of cossin-1x+cos-1x, x≤1

If →a,→b and→care three vectors such that [→a →b →c]=1, then the value of [→a+→b →b+→c →c+→a]+[→a×→b →b×→c →c×→a]+[→a×(→b×→c) →b×(→c×→a) →c×(→a×→b)] is

The co-ordinates of the points which divides the line joining (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is _____.

find the range of f(x)=2 sin^8 x - 3 sin^4 x + 2

The set of point where the function f(x) = |2x – 1| is differentiable, is ____________.

If u = 3^i−5^j+9^k and v = 3^i+4^j+0k; What is the component of u along the direction of v?

If coordinates of two points A and B are (3,4) and (5,-2), find coordinates of P is PA=PB and area of triangle PAB =10

The lines whose vector equations are →r=→a+t→b and →r=→c+s→d are coplanar if..

A random variable X has the following probability distribution:X01234567P(X)0k2k2k3kk22k27k2+kThen value of k is:

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax2 + sin x) (p + q cos x)

If f(x)=∣∣∣∣∣x2x2−(y−z)2yzy2y2−(z−x)2zxz2z2−(x−y)2xy∣∣∣∣∣, then which of the following is/are factor of f(x)

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola

The range of x for which the formula 3sin−1x=sin−1[x(3−4x2)] holds is :

The modulus and argument of sinπ5+i1-cosπ5 are _______ and _______ respectively.

{0.3^(1/3)*(1/27)^(1/4)*9^(1/6)*0.81^(2/3)}/{0.9^(2/3)*3^(-1/2)*(1/3)^(-2)*243^(-1/4)

The miniumum number of 2×1 MUX required to implement a half-subtractor circuit when only basic inputs 0,1 A and B are available is

What is real numbers

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5) and C (6, 3)

A real-valued function f(x) satisfies the functional equation f(x−y)=f(x)f(y)−f(a−x)f(a+y) ∀ x,y ∈R, where a is a given constant and f(0)=1. Then, f(2a−x) is equal to

PQ is a double ordinate of the hyperbola x2a2−y2b2=1 such that OPQ is an equilateral triangle, O being the centre of the hyperbola, then the range of the eccentricity e of the hyperbola is

What is the differentiation of x^2/2 ?

Prove that sin x sin π3-x sin π3+x≤14 for all values of x

PM and PN are the perpendiculars from any point P on the rectangular hyperbola xy = 8 to the asymptotes. If the locus of the mid point of MN is a conic, then the least distance of (1, 1) to director circle of the conic is

What are the 17 topics that can assure me seat in top 5 IIT's in all subjects

If there are 12 points in a plane out of which only 5 are collinear, then the number of quadrilaterals that can be formed using these points is

If the angles made by a straight line with the coordinate axes are α,π/2−α,β then β=

Let O be the vertex and Q be any point on the parabola x2=8y. If the point P divides the line segement OQ internally in the ratio 1 : 3, then the locus of P is

The complex number Z satisfies the equation Z +|Z| = 2+8i, then the value of |Z| - 8 is ___

If r2−13r+40=0, then the value of 7Cr is

20. If y=e to the power ax.sinbx Prove that : y"-2ay'+(a square+ b square) y=0

Find the sum to n terms of each of the series in Exercises 1 to 7 1: 1x2+2x3+3 x4 4 x5+2. 1 x2 x 3+2 x3 4+34 3. 3 x 1 +5 x 22 +7 x3 +... 5. 5+6+72 + 20 Ix2 2x3 3x4 3x8+6x11+9x14 + 6,

To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A1, A2, A3, ... are located at equal distances on the ray AX and the point B is joined to(a) A12(b) A11(c) A10(d) A9

If x, y, z ∈ R, the value of the determinant 2x+2-x22x-2-x213x+3-x23x-3-x214x+4-x24x-4-x21 is equal to ________________.

The number of constant functions possible from R to B where B={2,4,6,8,...24} are

If A=[abcd] (where bc≠0) satisfies the equation x2+k=0, then

Check whether the following are quadratic equations:(x−2)(x+1)=(x−1)(x+3)

Why is ∇\cdot(∇×\overrightarrow{A)} equal to 0 for any random vector field \overrightarrow A Also why is curl of a gradient always zero mathematically?

The modulus and argument of sinπ5+i1-cosπ5 are _ and _ respectively.

{0.3^(1/3)(1/27)^(1/4)9^(1/6)0.81^(2/3)}/{0.9^(2/3)3^(-1/2)(1/3)^(-2)243^(-1/4)