43030 + Interview Questions in Mathematics

1.	The value of 10∑r=2 rC2⋅ 10Cr is not divisible by
Answer» The value of $10 \sum r = 2^{r} C_{2} \cdot^{10} C_{r}$ is not divisible by

Discussion

2.	The sum of the values of 'm' for which the equations 3x2+4mx+2=0 and 2x2+3x−2=0 may have a common root, is
Answer» The sum of the values of ' $m$ ' for which the equations $3 x^{2} + 4 m x + 2 = 0$ and $2 x^{2} + 3 x - 2 = 0$ may have a common root, is

Discussion

3.	If p→(q∨r) is false, then the truth values of p,q,r are respectively (where T is true and F is false)
Answer» If $p \to (q \lor r)$ is false, then the truth values of $p, q, r$ are respectively (where $T$ is true and $F$ is false)

Discussion

4.	If z=2+i and z3+3z2−9z+8=a+ib, then the value of a+b is
Answer» If $z = 2 + i$ and $z^{3} + 3 z^{2} - 9 z + 8 = a + i b$ , then the value of $a + b$ is

Discussion

5.	Find the equation of a plane which bisects perpendicularly the line joining the points A(2,3,4) and B(4,5,8) at right angles.
Answer» Find the equation of a plane which bisects perpendicularly the line joining the points A(2,3,4) and B(4,5,8) at right angles.

Discussion

6.	A chord of the parabola y=x2−2x+5 joins the point with the abscissas x1=1,x2=3. Then the equation of the tangent to the parabola parallel to the chord is :
Answer» A chord of the parabola $y = x^{2} - 2 x + 5$ joins the point with the abscissas $x_{1} = 1, x_{2} = 3$ . Then the equation of the tangent to the parabola parallel to the chord is :

Discussion

7.	The vector in the direction of the vector ^i−2^j+2^k that has magnitude 9 is (a) ^i−2^j+2^k (b) ^i−2^j+2^k3 (c) 3(^i−2^j+2^k) (d) 9(^i−2^j+2^k)
Answer» The vector in the direction of the vector $^i - 2^j + 2^k$ that has magnitude 9 is (a) $^i - 2^j + 2^k$ (b) $\frac{^i - 2^j + 2^k}{3}$ (c) $3 (^i - 2^j + 2^k)$ (d) $9 (^i - 2^j + 2^k)$

7.

The vector in the direction of the vector ^i−2^j+2^k that has magnitude 9 is (a) ^i−2^j+2^k (b) ^i−2^j+2^k3 (c) 3(^i−2^j+2^k) (d) 9(^i−2^j+2^k)

Answer»

The vector in the direction of the vector $^i - 2^j + 2^k$ that has magnitude 9 is

(a) $^i - 2^j + 2^k$

(b) $\frac{^i - 2^j + 2^k}{3}$

(c) $3 (^i - 2^j + 2^k)$

(d) $9 (^i - 2^j + 2^k)$

Discussion

8.	A semi-circle of diameter 1 unit sits at the top of a semi-circle of diameter 2 units. The shaded region inside the smaller semi-circle but outside the larger semi-circle is called a lune. The area of the lune is.
Answer» A semi-circle of diameter 1 unit sits at the top of a semi-circle of diameter 2 units. The shaded region inside the smaller semi-circle but outside the larger semi-circle is called a lune. The area of the lune is.

8.

A semi-circle of diameter 1 unit sits at the top of a semi-circle of diameter 2 units. The shaded region inside the smaller semi-circle but outside the larger semi-circle is called a lune. The area of the lune is.

Answer»

A semi-circle of diameter 1 unit sits at the top of a semi-circle of diameter 2 units. The shaded region inside the smaller semi-circle but outside the larger semi-circle is called a lune. The area of the lune is.

Discussion

9.	Let A and B be two matrices such that A=[aij]=⎡⎢⎣x123x−114x2+1⎤⎥⎦ and B=[bij]=⎡⎢⎢⎢⎣1x21x2x23x⎤⎥⎥⎥⎦, where x>0. If C=[cij]=AB and the minimum value of Δ(x)=∑i≤i≤j≤2cij is pq, where p and q are co-prime numbers, then the value of p+q is
Answer» Let $A$ and $B$ be two matrices such that $A = [a_{i j}] = ⎡ ⎢ ⎣ \begin{matrix} x & 1 & 2 3 x & - 1 & \frac{1}{4 x^{2} + 1} \end{matrix} ⎤ ⎥ ⎦$ and $B = [b_{i j}] = ⎡ ⎢⎢⎢ ⎣ \begin{matrix} \frac{1}{x^{2}} & \frac{1}{x} 2 x & 2 3 & x \end{matrix} ⎤ ⎥⎥⎥ ⎦$ , where $x > 0$ . If $C = [c_{i j}] = A B$ and the minimum value of $Δ (x) = \sum i \leq i \leq j \leq 2 c_{i j}$ is $\frac{p}{q}$ , where $p$ and $q$ are co-prime numbers, then the value of $p + q$ is

Discussion

10.	A balloon which always remains spherical is being inflated by pumping in 10 cubic centimeters of gas per second. Find the rate at which the radius of the balloon is increasing when the radius in 15 cms.
Answer» A balloon which always remains spherical is being inflated by pumping in 10 cubic centimeters of gas per second. Find the rate at which the radius of the balloon is increasing when the radius in 15 cms.

Discussion

11.	If x+√x≥√x−3 then minimum value that x can take is
Answer» If $x + \sqrt{x} \geq \sqrt{x} - 3$ then minimum value that $x$ can take is

Discussion

12.	If the cartesian equation of a line are 3−x5=y+47=2z−64, write the vector equation for the line.
Answer» If the cartesian equation of a line are $\frac{3 - x}{5} = \frac{y + 4}{7} = \frac{2 z - 6}{4}$ , write the vector equation for the line.

Discussion

13.	If the point (5, 2) bisects the intercept of a line between the axes, then its equation is
Answer» If the point $(5, 2)$ bisects the intercept of a line between the axes, then its equation is

Discussion

14.	Evaluate limx→0(1+x)6−1(1+x)5−1
Answer» Evaluate $l i m x \to 0 \frac{(1 + x)^{6} - 1}{(1 + x)^{5} - 1}$

Discussion

15.	Which of the following is true about (√3+1)2n, where n is a positive integer
Answer» Which of the following is true about $(\sqrt{3} + 1)^{2 n}$ , where n is a positive integer

Discussion

16.	The value of 12∞∑r=112r2+164r6−48r4+12r2−1 is
Answer» The value of $12 \infty \sum r = 1 \frac{12 r^{2} + 1}{64 r^{6} - 48 r^{4} + 12 r^{2} - 1}$ is

Discussion

17.	Find the equation of an ellipse whose major axis lies on the x-axis and which passes through the points (4, 3) and (6, 2).
Answer» Find the equation of an ellipse whose major axis lies on the x-axis and which passes through the points (4, 3) and (6, 2).

Discussion

18.	Evaluate limn→∞5.2n+2−8.5n+23.2n+8.5n
Answer» Evaluate $lim n \to \infty \frac{{5.2}^{n + 2} - {8.5}^{n + 2}}{{3.2}^{n} + {8.5}^{n}}$

Discussion

19.	Find the equation for the ellipse that satisfies the given conditions, Ends of major axis (0,±√5), ends of minor axis
Answer» Find the equation for the ellipse that satisfies the given conditions, Ends of major axis $(0, \pm \sqrt{5}),$ ends of minor axis

Discussion

20.	The expression nCr+2 nCr−1+ nCr−2 is equal to
Answer» The expression $^{n} C_{r} + 2^{n} C_{r - 1} +^{n} C_{r - 2}$ is equal to

Discussion

21.	The probability that a bulb produced by a factory will fuse after 150 days of used is 0.05. Find the probability that out of 5 such bulbs not more than one will fuse after 150 days
Answer» The probability that a bulb produced by a factory will fuse after 150 days of used is 0.05. Find the probability that out of 5 such bulbs not more than one will fuse after 150 days

Discussion

22.	in combination problems why are we adding the total number of combinations if 'or' is given in the question and multiplying if 'and' is given.explain please.
Answer» in combination problems why are we adding the total number of combinations if 'or' is given in the question and multiplying if 'and' is given.explain please.

Discussion

23.	If z=reiθ, then find the value of \|eiz\|
Answer» If $z = r e^{i θ}$ , then find the value of $\| e^{i z} \|$

Discussion

24.	Which of the following statements is/are correct about identity function?
Answer» Which of the following statements is/are correct about identity function?

Discussion

25.	The expression tan(iloge(2−3i2+3i)) is equal to
Answer» The expression $tan (i {log}_{e} (\frac{2 - 3 i}{2 + 3 i}))$ is equal to

Discussion

26.	Let f(x)=15−\|x−10\|;x∈R. Then the set of all values of x, at which the function, g(x)=f(f(x)) is not differentiable is:
Answer» Let $f (x) = 15 - \| x - 10 \|; x \in R$ . Then the set of all values of $x$ , at which the function, $g (x) = f (f (x))$ is not differentiable is:

Discussion

27.	The area enclosed between the parabola y2=4ax and the lines x = a, x = 9a is
Answer» The area enclosed between the parabola $y^{2} = 4 a x$ and the lines x = a, x = 9a is

Discussion

28.	If the sides fo a triangle are in A.P. as well as in G.P. Then the value of r1r2−r2r3
Answer» If the sides fo a triangle are in A.P. as well as in G.P. Then the value of $\frac{r_{1}}{r_{2}} - \frac{r_{2}}{r_{3}}$

Discussion

29.	The maximum value of f(x)=89x2−6x+5 in its domain is
Answer» The maximum value of $f (x) = \frac{8}{9 x^{2} - 6 x + 5}$ in its domain is

Discussion

30.	The distance of the point P (3,8,2) from the line 12(x−1)=14(y−3)=13(z−2) measured parallel to the plane 3x+2y−2z+15=0 is
Answer» The distance of the point P (3,8,2) from the line $\frac{1}{2} (x - 1) = \frac{1}{4} (y - 3) = \frac{1}{3} (z - 2)$ measured parallel to the plane $3 x + 2 y - 2 z + 15 = 0 i s$

Discussion

31.	∫etan−1x(1+x+x2).d(cot−1x) is equal to
Answer» $\int e^{t a n^{- 1} x} (1 + x + x^{2}) . d (c o t^{- 1} x)$ is equal to

Discussion

32.	One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is:
Answer» One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is:

Discussion

33.	If ax2 +bx+c=0 has no real roots and a+b+c<0, then
Answer» If $a x^{2}$ +bx+c=0 has no real roots and a+b+c<0, then

Discussion

34.	In the first two lines, what images does the speaker use to describe love?
Answer» In the first two lines, what images does the speaker use to describe love?

Discussion

35.	The number of points on the line 3x + 4y = 5, which are at a distance of sec2θ+2cosec2θ, θϵR, form the point (1,3), is
Answer» The number of points on the line 3x + 4y = 5, which are at a distance of $s e c^{2} θ + 2 c o s e c^{2} θ, θ ϵ R,$ form the point (1,3), is

Discussion

36.	limx→01−cos2x+tan2xxsinx
Answer» ${lim}_{x \to 0} \frac{1 - c o s 2 x + t a n^{2} x}{x s i n x}$

Discussion

37.	A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30∘. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60∘. Then the time taken (in minutes) by him, from B to reach the pillar, is:
Answer» A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is $30^{\circ}$ . After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is $60^{\circ}$ . Then the time taken (in minutes) by him, from B to reach the pillar, is:

Discussion

38.	A bag contains 3 white and 7 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red
Answer» A bag contains 3 white and 7 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

38.

A bag contains 3 white and 7 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

Answer»

A bag contains 3 white and 7 red balls. If a ball is drawn at random, then

what is the probability that the drawn ball is either white or red

Discussion

39.	If In=∫tannxdx,then I0+I1+2(I2+...I8)+I9+I10, is equal to
Answer» If $I_{n} = \int t a n^{n} x d x, t h e n I_{0} + I_{1} + 2 (I_{2} + . . . I_{8}) + I_{9} + I_{10}$ , is equal to

Discussion

40.	Let S be a sample space. A and B are two mutually exclusive events such that A∪B=S. If P(.) denotes the probability of the event, then the maximum value of P(A)P(B) is
Answer» Let $S$ be a sample space. $A$ and $B$ are two mutually exclusive events such that $A \cup B = S$ . If $P (.)$ denotes the probability of the event, then the maximum value of $P (A) P (B)$ is

Discussion

41.	If a curve passes through the point (1,−2) and has slope of the tangent at any point (x,y) on it as x2−2yx, then the curve also passes through the point :
Answer» If a curve passes through the point $(1, - 2)$ and has slope of the tangent at any point $(x, y)$ on it as $\frac{x^{2} - 2 y}{x}$ , then the curve also passes through the point :

Discussion

42.	How many three letter words can be made using the letters of the word 'ORIENTAL' ?
Answer» How many three letter words can be made using the letters of the word 'ORIENTAL' ?

Discussion

43.	If a cos 2θ+b sin 2θ=c has α and β as its solution, then the value of tan α+tan β is
Answer» If $a c o s 2 θ + b s i n 2 θ = c h a s α a n d β$ as its solution, then the value of $t a n α + t a n β$ is

Discussion

44.	131+13+231+3+13+23+331+3+5+.... to 16 terms =
Answer» $\frac{1^{3}}{1} + \frac{1^{3} + 2^{3}}{1 + 3} + \frac{1^{3} + 2^{3} + 3^{3}}{1 + 3 + 5} + . . . .$ to 16 terms =

Discussion

45.	A particle is projected up on an incline at t=0 with a speed of 14 ms−1 as shown in the figure. At the same moment, a box starts sliding down. The box has two small windows at a height of 2 m on opposite walls. The particle enters from 1st window and leaves through the other. The width of the box is 7α√3 m. The value of α is . (Assume friction to be absent everywhere and answer upto two digit after decimal point)
Answer» A particle is projected up on an incline at $t = 0$ with a speed of $14 m s^{- 1}$ as shown in the figure. At the same moment, a box starts sliding down. The box has two small windows at a height of $2 m$ on opposite walls. The particle enters from $1^{st}$ window and leaves through the other. The width of the box is $\frac{7 α}{\sqrt{3}} m$ . The value of $α$ is . (Assume friction to be absent everywhere and answer upto two digit after decimal point)

Discussion

46.	The negation of ∼ s∨(∼ r∨s) is
Answer» The negation of $\sim s \lor (\sim r \lor s)$ is

Discussion

47.	The set of all x in (−π,π) satisying \|4cosx−1\|<√5 is
Answer» The set of all $x$ in $(- π, π)$ satisying $\| 4 cos x - 1 \| < \sqrt{5}$ is

Discussion

48.	Let p,q,r be relative prime number such that p⋅q⋅r=1800, then p+q+r=
Answer» Let $p, q, r$ be relative prime number such that $p \cdot q \cdot r = 1800$ , then $p + q + r =$

Discussion

49.	If the sum of the ordinate and the abscissa of a point P (x, y) is 2n, where x and y are natural numbers, then probability that the point does not lie on y = x is:
Answer» If the sum of the ordinate and the abscissa of a point P (x, y) is 2n, where x and y are natural numbers, then probability that the point does not lie on y = x is:

Discussion

50.	The maximum value of f(x)=−\|log(x−3)\|+3 is
Answer» The maximum value of $f (x) = - \| log (x - 3) \| + 3$ is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The value of 10∑r=2 rC2⋅ 10Cr is not divisible by

The sum of the values of 'm' for which the equations 3x2+4mx+2=0 and 2x2+3x−2=0 may have a common root, is

If p→(q∨r) is false, then the truth values of p,q,r are respectively (where T is true and F is false)

If z=2+i and z3+3z2−9z+8=a+ib, then the value of a+b is

Find the equation of a plane which bisects perpendicularly the line joining the points A(2,3,4) and B(4,5,8) at right angles.

A chord of the parabola y=x2−2x+5 joins the point with the abscissas x1=1,x2=3. Then the equation of the tangent to the parabola parallel to the chord is :

The vector in the direction of the vector ^i−2^j+2^k that has magnitude 9 is (a) ^i−2^j+2^k (b) ^i−2^j+2^k3 (c) 3(^i−2^j+2^k) (d) 9(^i−2^j+2^k)

A semi-circle of diameter 1 unit sits at the top of a semi-circle of diameter 2 units. The shaded region inside the smaller semi-circle but outside the larger semi-circle is called a lune. The area of the lune is.

Let A and B be two matrices such that A=[aij]=⎡⎢⎣x123x−114x2+1⎤⎥⎦ and B=[bij]=⎡⎢⎢⎢⎣1x21x2x23x⎤⎥⎥⎥⎦, where x&gt;0. If C=[cij]=AB and the minimum value of Δ(x)=∑i≤i≤j≤2cij is pq, where p and q are co-prime numbers, then the value of p+q is

A balloon which always remains spherical is being inflated by pumping in 10 cubic centimeters of gas per second. Find the rate at which the radius of the balloon is increasing when the radius in 15 cms.

If x+√x≥√x−3 then minimum value that x can take is

If the cartesian equation of a line are 3−x5=y+47=2z−64, write the vector equation for the line.

If the point (5, 2) bisects the intercept of a line between the axes, then its equation is

Evaluate limx→0(1+x)6−1(1+x)5−1

Which of the following is true about (√3+1)2n, where n is a positive integer

The value of 12∞∑r=112r2+164r6−48r4+12r2−1 is

Find the equation of an ellipse whose major axis lies on the x-axis and which passes through the points (4, 3) and (6, 2).

Evaluate limn→∞5.2n+2−8.5n+23.2n+8.5n

Find the equation for the ellipse that satisfies the given conditions, Ends of major axis (0,±√5), ends of minor axis

The expression nCr+2 nCr−1+ nCr−2 is equal to

The probability that a bulb produced by a factory will fuse after 150 days of used is 0.05. Find the probability that out of 5 such bulbs not more than one will fuse after 150 days

in combination problems why are we adding the total number of combinations if 'or' is given in the question and multiplying if 'and' is given.explain please.

If z=reiθ, then find the value of |eiz|

Which of the following statements is/are correct about identity function?

The expression tan(iloge(2−3i2+3i)) is equal to

Let f(x)=15−|x−10|;x∈R. Then the set of all values of x, at which the function, g(x)=f(f(x)) is not differentiable is:

The area enclosed between the parabola y2=4ax and the lines x = a, x = 9a is

If the sides fo a triangle are in A.P. as well as in G.P. Then the value of r1r2−r2r3

The maximum value of f(x)=89x2−6x+5 in its domain is

The distance of the point P (3,8,2) from the line 12(x−1)=14(y−3)=13(z−2) measured parallel to the plane 3x+2y−2z+15=0 is

∫etan−1x(1+x+x2).d(cot−1x) is equal to

One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 &lt; p &lt; 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is:

If ax2 +bx+c=0 has no real roots and a+b+c&lt;0, then

In the first two lines, what images does the speaker use to describe love?

The number of points on the line 3x + 4y = 5, which are at a distance of sec2θ+2cosec2θ, θϵR, form the point (1,3), is

limx→01−cos2x+tan2xxsinx

A bag contains 3 white and 7 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

If In=∫tannxdx,then I0+I1+2(I2+...I8)+I9+I10, is equal to

Let S be a sample space. A and B are two mutually exclusive events such that A∪B=S. If P(.) denotes the probability of the event, then the maximum value of P(A)P(B) is

If a curve passes through the point (1,−2) and has slope of the tangent at any point (x,y) on it as x2−2yx, then the curve also passes through the point :

How many three letter words can be made using the letters of the word 'ORIENTAL' ?

If a cos 2θ+b sin 2θ=c has α and β as its solution, then the value of tan α+tan β is

131+13+231+3+13+23+331+3+5+.... to 16 terms =

The negation of ∼ s∨(∼ r∨s) is

The set of all x in (−π,π) satisying |4cosx−1|&lt;√5 is

Let p,q,r be relative prime number such that p⋅q⋅r=1800, then p+q+r=

If the sum of the ordinate and the abscissa of a point P (x, y) is 2n, where x and y are natural numbers, then probability that the point does not lie on y = x is:

The maximum value of f(x)=−|log(x−3)|+3 is

Let A and B be two matrices such that A=[aij]=⎡⎢⎣x123x−114x2+1⎤⎥⎦ and B=[bij]=⎡⎢⎢⎢⎣1x21x2x23x⎤⎥⎥⎥⎦, where x>0. If C=[cij]=AB and the minimum value of Δ(x)=∑i≤i≤j≤2cij is pq, where p and q are co-prime numbers, then the value of p+q is

One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is:

If ax2 +bx+c=0 has no real roots and a+b+c<0, then

The set of all x in (−π,π) satisying |4cosx−1|<√5 is