43030 + Interview Questions in Mathematics

1.	How many non-square numbers are between 9 and 16?
Answer» How many non-square numbers are between 9 and 16?

Discussion

2.	Two sets given such that A={a:a is a prime number<25} &B={b:b∈N,10≤b≤18}, the select the correct statements.
Answer» Two sets given such that $A = {a : a is a prime number < 25} &$ $B = {b : b \in N, 10 \leq b \leq 18},$ the select the correct statements.

Discussion

3.	Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x axis.
Answer» Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x axis.

Discussion

4.	The locus of centroid of the triangle formed by co-ordinate axes and the line segment having midpoint (asinθ,acosθ) is
Answer» The locus of centroid of the triangle formed by co-ordinate axes and the line segment having midpoint $(\frac{a}{sin θ}, \frac{a}{cos θ})$ is

Discussion

5.	The points (5,2,4),(6,-1,2) and (8,-7,K) are collinear if K is equal to
Answer» The points (5,2,4),(6,-1,2) and (8,-7,K) are collinear if K is equal to

Discussion

6.	If tan π/4+x+tan π/4-x=λ sec 2x, then(a) 3(b) 4(c) 1(d) 2
Answer» If $\tan (π / 4 + x) + \tan (π / 4 - x) = λ \sec 2 x, then$ (a) 3 (b) 4 (c) 1 (d) 2

Discussion

7.	Let P=50∑r=150+rCr(2r−1)50Cr(50+r), Q=50∑r=0(50Cr)2 and R=100∑r=0(−1)r(100Cr)2. Then
Answer» Let $P = 50 \sum r = 1 \frac{^{50 + r} C_{r} (2 r - 1)}{^{50} C_{r} (50 + r)}, Q = 50 \sum r = 0 (^{50} C_{r})^{2}$ and $R = 100 \sum r = 0 (- 1)^{r} (^{100} C_{r})^{2}$ . Then

Discussion

8.	∫√x2+2x+5 dx is equal to(where C is integration constant)
Answer» $\int \sqrt{x^{2} + 2 x + 5} d x$ is equal to $($ where $C$ is integration constant $)$

Discussion

9.	Match each of the set on the left in the roster form with the same set on the right described in set-builder form: (i) {1, 2, 3, 6} (a) { x : x is a prime number and a divisor of 6} (ii) {2, 3} (b) { x : x is an odd natural number less than 10} (iii) {M, A,T, H, E, I,C, S} (c) { x : x is natural number and divisor of 6} (iv) {1, 3, 5, 7, 9} (d) { x : x is a letter of the word MATHEMATICS}
Answer» Match each of the set on the left in the roster form with the same set on the right described in set-builder form: (i) {1, 2, 3, 6} (a) { x : x is a prime number and a divisor of 6} (ii) {2, 3} (b) { x : x is an odd natural number less than 10} (iii) {M, A,T, H, E, I,C, S} (c) { x : x is natural number and divisor of 6} (iv) {1, 3, 5, 7, 9} (d) { x : x is a letter of the word MATHEMATICS}

Discussion

10.	The value of p for which the vectors →a=^i−2^j−12^k and →b=−3^i+6^j+p^k are parallel is
Answer» The value of $p$ for which the vectors $\to a =^i - 2^j - 12^k$ and $\to b = - 3^i + 6^j + p^k$ are parallel is

Discussion

11.	An arcade game is such that the probability of any person winning is always 0.3. Then the least number of people play the game to ensure that the probability that atleast one person wins is greater than or equal to 0.96 is
Answer» An arcade game is such that the probability of any person winning is always $0.3.$ Then the least number of people play the game to ensure that the probability that atleast one person wins is greater than or equal to $0.96$ is

Discussion

12.	If a→=4 and -3≤λ≤2, then write the range of λa→.
Answer» If $\|\vec{a}\| = 4$ and $- 3 \leq λ \leq 2$ , then write the range of $\|λ \vec{a}\|$ .

Discussion

13.	For what valuel of m is x3–2mx2+16 is divisible by x +2?
Answer» For what valuel of m is $x^{3} - 2 m x^{2} + 16$ is divisible by x +2?

Discussion

14.	20. If X is the angle between unit Vector a and b, then sin(X/2) equals
Answer» 20. If X is the angle between unit Vector a and b, then sin(X/2) equals

Discussion

15.	If a,b c are in A.P., then the line ax+by+c=0 passes through a fixed point. Write the coordinates of theat point.
Answer» If a,b c are in A.P., then the line $a x + b y + c = 0$ passes through a fixed point. Write the coordinates of theat point.

Discussion

16.	If siny=xsin(a+y); then prove that dy/dx = sina/(1-2xcosa+x²)
Answer» If siny=xsin(a+y); then prove that dy/dx = sina/(1-2xcosa+x²)

Discussion

17.	The value of I=π∫0ln(1+cosx)dx is
Answer» The value of $I = π \int 0 ln (1 + cos x) d x$ is

Discussion

18.	A number is divided by 8 and then 4 is added to it, which of the following expression correctly represent the given data?
Answer» A number is divided by 8 and then 4 is added to it, which of the following expression correctly represent the given data?

Discussion

19.	Find the equation of the straight line intersecting y-axis at a distance of 2 units above the origin and making an angle of 30∘ with the positive direction of the x-axis.
Answer» Find the equation of the straight line intersecting y-axis at a distance of 2 units above the origin and making an angle of $30^{\circ}$ with the positive direction of the x-axis.

Discussion

20.	The largest perfect square that divides 20143−20133+20123−20113+....+23−13 is
Answer» The largest perfect square that divides $2014^{3} - 2013^{3} + 2012^{3} - 2011^{3} + . . . . + 2^{3} - 1^{3}$ is

Discussion

21.	Let n > 1 be an integer. Which of the following sets of numbers necessarily contains a multiple of 3?
Answer» Let n $>$ 1 be an integer. Which of the following sets of numbers necessarily contains a multiple of 3?

Discussion

22.	A straight line through the vertex P of a ΔPQR intersects the side QR at the point S and the circum circle of ΔPQR at the point T. If S is not the centre of the circum circle, then
Answer» A straight line through the vertex $P$ of a $Δ P Q R$ intersects the side $Q R$ at the point $S$ and the circum circle of $Δ P Q R$ at the point $T$ . If $S$ is not the centre of the circum circle, then

Discussion

23.	If z1=24+7i and \|z2\|=6 then \|z1+z2\| lies in
Answer» If $z_{1} = 24 + 7 i$ and $\| z_{2} \| = 6$ then $\| z_{1} + z_{2} \|$ lies in

Discussion

24.	If fx=x2sin1x, where x ≠ 0, then the value of the function f at x = 0, so that the function is continuous at x = 0, is(a) 0(b) –1(c) 1(d) none
Answer» If $f (x) = x^{2} \sin \frac{1}{x},$ where x ≠ 0, then the value of the function f at x = 0, so that the function is continuous at x = 0, is (a) 0 (b) –1 (c) 1 (d) none

Discussion

25.	Find the equation of the line which passes though and is inclined with the x -axis at an angle of 75°.
Answer» Find the equation of the line which passes though and is inclined with the x -axis at an angle of 75°.

Discussion

26.	Find the particular solution of the differntials equation x(1+y2)dx−y(1+x2)dy=0, given that y=1 when x=0.
Answer» Find the particular solution of the differntials equation $x (1 + y^{2}) d x - y (1 + x^{2}) d y = 0$ , given that $y = 1$ when $x = 0$ .

Discussion

27.	Show that the statement "For any real numbers a and b, a2=b2 implies that a = b" is not true by giving a counter example.
Answer» Show that the statement "For any real numbers a and b, $a^{2} = b^{2}$ implies that a = b" is not true by giving a counter example.

Discussion

28.	If y = tan−1(sinx+cosxcosx−sinx) , then dydx is equal to
Answer» If $y = {tan}^{- 1} (\frac{sin x + cos x}{cos x - sin x})$ , then $\frac{d y}{d x}$ is equal to

Discussion

29.	Solve the following:y²(xdy+ydx)+xdy-ydx=0
Answer» Solve the following: y²(xdy+ydx)+xdy-ydx=0

Discussion

30.	The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.
Answer» The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.

Discussion

31.	∫√x+1dx
Answer» $\int \sqrt{x + 1} d x$

Discussion

32.	The value of sin−1x+sin−11x+cos−1x+cos−11x where ever defined is
Answer» The value of ${sin}^{- 1} x + {sin}^{- 1} \frac{1}{x} + {cos}^{- 1} x + {cos}^{- 1} \frac{1}{x}$ where ever defined is

Discussion

33.	The equation of the focal chord of the parabola y2=8x whose sum of ordinates of the endpoints of the chord is 8, is
Answer» The equation of the focal chord of the parabola $y^{2} = 8 x$ whose sum of ordinates of the endpoints of the chord is $8$ , is

Discussion

34.	If α,β,γ are the roots of x3−3x2+3x+7=0 and ω is a cube root of unity, then α−1β−1+β−1γ−1+γ−1α−1=
Answer» If $α, β, γ$ are the roots of $x^{3} - 3 x^{2} + 3 x + 7 = 0$ and $ω$ is a cube root of unity, then $\frac{α - 1}{β - 1} + \frac{β - 1}{γ - 1} + \frac{γ - 1}{α - 1} =$

Discussion

35.	Write the following in the simplest form. tan−1√1+x2−1x,x≠0
Answer» Write the following in the simplest form. $t a n^{- 1} \frac{\sqrt{1 + x^{2}} - 1}{x}, x \neq 0$

35.

Write the following in the simplest form. tan−1√1+x2−1x,x≠0

Answer»

Write the following in the simplest form.

$t a n^{- 1} \frac{\sqrt{1 + x^{2}} - 1}{x}, x \neq 0$

Discussion

36.	If x1+x2+x3=0,y1+y2+y3=0 and x1y1+x2y2+x3y3=0, then the value of x21x21+x22+x23+y21y21+y22+y23 is (correct answer + 2, wrong answer - 0.50)
Answer» If $x_{1} + x_{2} + x_{3} = 0, y_{1} + y_{2} + y_{3} = 0$ and $x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3} = 0,$ then the value of $\frac{x_{1}^{2}}{x_{1}^{2} + x_{2}^{2} + x_{3}^{2}} + \frac{y_{1}^{2}}{y_{1}^{2} + y_{2}^{2} + y_{3}^{2}}$ is (correct answer + 2, wrong answer - 0.50)

Discussion

37.	Find the sum to nterms in the geometric progression
Answer» Find the sum to n terms in the geometric progression

Discussion

38.	for positive numbers p q and r the minimum value of ((p^(2)+1)(q^(2)+1)(r^(2)+1))/(pqr) is
Answer» for positive numbers p q and r the minimum value of ((p^(2)+1)(q^(2)+1)(r^(2)+1))/(pqr) is

Discussion

39.	A well of diameter 20 cm fully penetrates a confined aquifer. After a long period of pumping at a rate of 2720 L/min, the observations of drawdown taken at 10 m and 100 m distances from the centre of the well are found to be 3 m and 0.5 m respectively. The transmissivity of the aquifer is ________.
Answer» A well of diameter $20 cm$ fully penetrates a confined aquifer. After a long period of pumping at a rate of $2720 L/min$ , the observations of drawdown taken at $10 m$ and $100 m$ distances from the centre of the well are found to be $3 m$ and $0.5 m$ respectively. The transmissivity of the aquifer is ________.

Discussion

40.	The equation of the normal to the curve x216−y29=1 at (8,3√3) is
Answer» The equation of the normal to the curve $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$ at $(8, 3 \sqrt{3})$ is

Discussion

41.	If f(x)=cos2x+sin4xcos4x+sin2x for all real x, then f(2016) =
Answer» If $f (x) = \frac{c o s^{2} x + s i n^{4} x}{c o s^{4} x + s i n^{2} x}$ for all real x, then f(2016) =

Discussion

42.	Solve the equation: √(116+cos4x−12cos2x)+√(916+cos4x−32cos2x)=12
Answer» Solve the equation: $\sqrt{(\frac{1}{16} + c o s^{4} x - \frac{1}{2} c o s^{2} x)} + \sqrt{(\frac{9}{16} + c o s^{4} x - \frac{3}{2} c o s^{2} x)} = \frac{1}{2}$

Discussion

43.	If the lengths of each of the segments of a focal chord of the parabola y2=8x, which are divided by the focus of the parabola are integers, then the length of the focal chord may be
Answer» If the lengths of each of the segments of a focal chord of the parabola $y^{2} = 8 x,$ which are divided by the focus of the parabola are integers, then the length of the focal chord may be

Discussion

44.	The value(s) of x satisfying \|x+3\|=x2−4x−3 is/are
Answer» The value(s) of $x$ satisfying $\| x + 3 \| = x^{2} - 4 x - 3$ is/are

Discussion

45.	In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.
Answer» In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.

Discussion

46.	Find the equation of a sphere, whose centre is (1,1,1) and radius is 5 units
Answer» Find the equation of a sphere, whose centre is $(1, 1, 1)$ and radius is $5$ units

Discussion

47.	If the domain of the function f(x)=loge(log\|cosx\|(x2−7x+26)−4log2\|cosx\|) is set A, then A contains the interval(s)
Answer» If the domain of the function $f (x) = {log}_{e} ({log}_{\| cos x \|} (x^{2} - 7 x + 26) - \frac{4}{{log}_{2} \| cos x \|})$ is set $A,$ then $A$ contains the interval(s)

Discussion

48.	Let x2−ax+b=0, where a,b∈R be a quadratic equation such that the roots are opposite in sign and the magnitude of one root is twice the other. Then which of the following options is/are always true ?
Answer» Let $x^{2} - a x + b = 0$ , where $a, b \in R$ be a quadratic equation such that the roots are opposite in sign and the magnitude of one root is twice the other. Then which of the following options is/are always true ?

Discussion

49.	11. If xcube+1/xcube=110 then x+1/x=?
Answer» 11. If xcube+1/xcube=110 then x+1/x=?

Discussion

50.	Evaluate ∫9x+27x3+3x2+16x+48dx(where C is constant of integration)
Answer» Evaluate $\int \frac{9 x + 27}{x^{3} + 3 x^{2} + 16 x + 48} d x$ (where $C$ is constant of integration)

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

How many non-square numbers are between 9 and 16?

Two sets given such that A={a:a is a prime number&lt;25} &amp;B={b:b∈N,10≤b≤18}, the select the correct statements.

Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x axis.

The locus of centroid of the triangle formed by co-ordinate axes and the line segment having midpoint (asinθ,acosθ) is

The points (5,2,4),(6,-1,2) and (8,-7,K) are collinear if K is equal to

If tan π/4+x+tan π/4-x=λ sec 2x, then(a) 3(b) 4(c) 1(d) 2

Let P=50∑r=150+rCr(2r−1)50Cr(50+r), Q=50∑r=0(50Cr)2 and R=100∑r=0(−1)r(100Cr)2. Then

∫√x2+2x+5 dx is equal to(where C is integration constant)

The value of p for which the vectors →a=^i−2^j−12^k and →b=−3^i+6^j+p^k are parallel is

An arcade game is such that the probability of any person winning is always 0.3. Then the least number of people play the game to ensure that the probability that atleast one person wins is greater than or equal to 0.96 is

If a→=4 and -3≤λ≤2, then write the range of λa→.

For what valuel of m is x3–2mx2+16 is divisible by x +2?

20. If X is the angle between unit Vector a and b, then sin(X/2) equals

If a,b c are in A.P., then the line ax+by+c=0 passes through a fixed point. Write the coordinates of theat point.

If siny=xsin(a+y); then prove that dy/dx = sina/(1-2xcosa+x²)

The value of I=π∫0ln(1+cosx)dx is

A number is divided by 8 and then 4 is added to it, which of the following expression correctly represent the given data?

Find the equation of the straight line intersecting y-axis at a distance of 2 units above the origin and making an angle of 30∘ with the positive direction of the x-axis.

The largest perfect square that divides 20143−20133+20123−20113+....+23−13 is

Let n &gt; 1 be an integer. Which of the following sets of numbers necessarily contains a multiple of 3?

A straight line through the vertex P of a ΔPQR intersects the side QR at the point S and the circum circle of ΔPQR at the point T. If S is not the centre of the circum circle, then

If z1=24+7i and |z2|=6 then |z1+z2| lies in

If fx=x2sin1x, where x ≠ 0, then the value of the function f at x = 0, so that the function is continuous at x = 0, is(a) 0(b) –1(c) 1(d) none

Find the equation of the line which passes though and is inclined with the x -axis at an angle of 75°.

Find the particular solution of the differntials equation x(1+y2)dx−y(1+x2)dy=0, given that y=1 when x=0.

Show that the statement "For any real numbers a and b, a2=b2 implies that a = b" is not true by giving a counter example.

If y = tan−1(sinx+cosxcosx−sinx) , then dydx is equal to

Solve the following:y²(xdy+ydx)+xdy-ydx=0

The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.

∫√x+1dx

The value of sin−1x+sin−11x+cos−1x+cos−11x where ever defined is

The equation of the focal chord of the parabola y2=8x whose sum of ordinates of the endpoints of the chord is 8, is

If α,β,γ are the roots of x3−3x2+3x+7=0 and ω is a cube root of unity, then α−1β−1+β−1γ−1+γ−1α−1=

Write the following in the simplest form. tan−1√1+x2−1x,x≠0

If x1+x2+x3=0,y1+y2+y3=0 and x1y1+x2y2+x3y3=0, then the value of x21x21+x22+x23+y21y21+y22+y23 is (correct answer + 2, wrong answer - 0.50)

Find the sum to nterms in the geometric progression

for positive numbers p q and r the minimum value of ((p^(2)+1)(q^(2)+1)(r^(2)+1))/(pqr) is

A well of diameter 20 cm fully penetrates a confined aquifer. After a long period of pumping at a rate of 2720 L/min, the observations of drawdown taken at 10 m and 100 m distances from the centre of the well are found to be 3 m and 0.5 m respectively. The transmissivity of the aquifer is ________.

The equation of the normal to the curve x216−y29=1 at (8,3√3) is

If f(x)=cos2x+sin4xcos4x+sin2x for all real x, then f(2016) =

Solve the equation: √(116+cos4x−12cos2x)+√(916+cos4x−32cos2x)=12

If the lengths of each of the segments of a focal chord of the parabola y2=8x, which are divided by the focus of the parabola are integers, then the length of the focal chord may be

The value(s) of x satisfying |x+3|=x2−4x−3 is/are

In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.

Find the equation of a sphere, whose centre is (1,1,1) and radius is 5 units

If the domain of the function f(x)=loge(log|cosx|(x2−7x+26)−4log2|cosx|) is set A, then A contains the interval(s)

Let x2−ax+b=0, where a,b∈R be a quadratic equation such that the roots are opposite in sign and the magnitude of one root is twice the other. Then which of the following options is/are always true ?

11. If xcube+1/xcube=110 then x+1/x=?

Evaluate ∫9x+27x3+3x2+16x+48dx(where C is constant of integration)

Two sets given such that A={a:a is a prime number<25} &B={b:b∈N,10≤b≤18}, the select the correct statements.

Let n > 1 be an integer. Which of the following sets of numbers necessarily contains a multiple of 3?