43030 + Interview Questions in Mathematics

1.	Two card are drawn successively with replacement from a pack of 52 cards. The probability of drawing two aces is [MNR 1988; UPSEAT 2000]
Answer» Two card are drawn successively with replacement from a pack of 52 cards. The probability of drawing two aces is [MNR 1988; UPSEAT 2000]

1.

Two card are drawn successively with replacement from a pack of 52 cards. The probability of drawing two aces is [MNR 1988; UPSEAT 2000]

Answer»

Two card are drawn successively with replacement from a pack of 52 cards. The probability of drawing two aces is

[MNR 1988; UPSEAT 2000]

2.	The value of cos[2cos−115+sin−115] is
Answer» The value of $cos [2 {cos}^{- 1} \frac{1}{5} + {sin}^{- 1} \frac{1}{5}]$ is

Discussion

3.	If y^x = e^(y-x) ,then show that dy/dx=(logey)²/(logy)
Answer» If y^x = e^(y-x) ,then show that dy/dx=(logey)²/(logy)

Discussion

4.	Prove the following by using the principle of mathematical induction for all n ∈ N:
Answer» Prove the following by using the principle of mathematical induction for all n ∈ N:

Discussion

5.	Choose the correct answer in the following question. Matrices A and B will be inverse of each other only if (a)AB=BA (b)AB =BA =O (c)AB=O, BA=I (d)AB=BA =I
Answer» Choose the correct answer in the following question. Matrices A and B will be inverse of each other only if (a)AB=BA (b)AB =BA =O (c)AB=O, BA=I (d)AB=BA =I

Discussion

6.	The equation 2tan2x−5secx=1 holds true for exactly eleven distinct values of x∈[0,nπ2], n∈N. The greatest value of n is
Answer» The equation $2 {tan}^{2} x - 5 sec x = 1$ holds true for exactly eleven distinct values of $x \in [0, \frac{n π}{2}], n \in N$ . The greatest value of $n$ is

Discussion

7.	check weather a*b=(a-b)^2 is commutative or assosiative both
Answer» check weather a*b=(a-b)^2 is commutative or assosiative both

Discussion

8.	A water tank is filled by three pipes with uniformflow. The first two pipes operating simultaneously, fill the tank in the same time during which the tank isfilled by the third pipe alone. The first pipe fills the tank six hours slower than the second pipe andeight hours slower than the third pipe. The time takenby the second pipe to fill the tank is what?
Answer» A water tank is filled by three pipes with uniformflow. The first two pipes operating simultaneously, fill the tank in the same time during which the tank isfilled by the third pipe alone. The first pipe fills the tank six hours slower than the second pipe andeight hours slower than the third pipe. The time takenby the second pipe to fill the tank is what?

Discussion

9.	If tan x=1-cos ysin y, then tan 2x = _____________.
Answer» If $\tan x = \frac{1 - \cos y}{\sin y},$ then tan 2x = _____________.

Discussion

10.	The maximum value of the function f(x)=−\|x+1\|+3 is
Answer» The maximum value of the function $f (x) = - \| x + 1 \| + 3$ is

Discussion

11.	How to solve the indefinite integral of (x^4 +1)/(x^6 +1)
Answer» How to solve the indefinite integral of (x^4 +1)/(x^6 +1)

Discussion

12.	Find the angle between z and iz in degrees. __
Answer» Find the angle between z and iz in degrees. __

Discussion

13.	Mettez les verbes en couleur au temps qui convient.1. Demain nous aller à la poste.2. Ils se brosser les dents tous les jours.3. Venez manger! La serveuse mettre le couvert.4. Hier Hélène dormir jusq'à onze heures du matin.5. Les animaux rentrer dans 5 minutes.6. Non, je n'ai pas faim. Je manger un sandwich, il y a quelques minutes.7. Thierry offrir une bague à sa petite amie le mois prochain.8. Louis Psteur découvrir le vaccin contre la rage.9. Il n'y a plus de lait. Quelqu'un boire tout le lait.10. Demain nous faire une longue promenade.
Answer» Mettez les verbes en couleur au temps qui convient. 1. Demain nous aller à la poste. 2. Ils se brosser les dents tous les jours. 3. Venez manger! La serveuse mettre le couvert. 4. Hier Hélène dormir jusq'à onze heures du matin. 5. Les animaux rentrer dans 5 minutes. 6. Non, je n'ai pas faim. Je manger un sandwich, il y a quelques minutes. 7. Thierry offrir une bague à sa petite amie le mois prochain. 8. Louis Psteur découvrir le vaccin contre la rage. 9. Il n'y a plus de lait. Quelqu'un boire tout le lait. 10. Demain nous faire une longue promenade.

Discussion

14.	two vectors each of magnitude A have a resul†an t of same magnitude A the angle between the two vectors
Answer» two vectors each of magnitude A have a resul†an t of same magnitude A the angle between the two vectors

Discussion

15.	Solution set of 2x–1>7 and 3x–2≤16 is
Answer» Solution set of $2 x - 1 > 7$ and $3 x - 2 \leq 16$ is

Discussion

16.	The smallest value of x satisfying the equation 3 cot x + tan x=4 is(a) 2π/3(b) π/3(c) π/6(d) π/12
Answer» The smallest value of x satisfying the equation $\sqrt{3} (\cot x + \tan x) = 4$ is (a) $2 π / 3$ (b) $π / 3$ (c) $π / 6$ (d) $π / 12$

Discussion

17.	The graph of a function f(x) in the neighborhood of x = 4 is given. Find the value of limx → 4f(x).
Answer» The graph of a function $f (x)$ in the neighborhood of $x = 4$ is given. Find the value of $lim x \to 4 f (x)$ .

17.

The graph of a function f(x) in the neighborhood of x = 4 is given. Find the value of limx → 4f(x).

Answer»

The graph of a function $f (x)$ in the neighborhood of $x = 4$ is given. Find the value of $lim x \to 4 f (x)$ .

Discussion

18.	If f(x)=tan−11−x1+x−12tan−1x; x≥0, then the value of f′(0) is
Answer» If $f (x) = {tan}^{- 1} \frac{1 - x}{1 + x} - \frac{1}{2} {tan}^{- 1} x; x \geq 0,$ then the value of $f^{'} (0)$ is

Discussion

19.	Probability that A speaks truth is . A coin is tossed. A reports that a head appears. The probability that actually there was head is A. B. C. D.
Answer» Probability that A speaks truth is . A coin is tossed. A reports that a head appears. The probability that actually there was head is A. B. C. D.

Discussion

20.	Let α and β be non zero real numbers such that 2(cosβ−cosα)+cosαcosβ=1. Then which of the following is/are true?
Answer» Let $α$ and $β$ be non zero real numbers such that $2 (c o s β - c o s α) + c o s α c o s β = 1$ . Then which of the following is/are true?

Discussion

21.	The equation of tangent to the parabola y2=6x at point (6,6) is
Answer» The equation of tangent to the parabola $y^{2} = 6 x$ at point $(6, 6)$ is

Discussion

22.	Solve: cossin-1x=16
Answer» Solve: $\cos (\sin^{- 1} x) = \frac{1}{6}$

Discussion

23.	If : A→B and g : B →C be two functions. Then, composition of f and g, gof : A→C is defined as
Answer» If : A→B and g : B →C be two functions. Then, composition of f and g, gof : A→C is defined as

Discussion

24.	Draw the graph of y = root (2- x^2)
Answer» Draw the graph of y = root (2- x^2)

Discussion

25.	intreation of Sin^2 X/2
Answer» intreation of Sin^2 X/2

Discussion

26.	If area of the triangle formed by the line x+y=3 and the angle bisectors of the pair of lines x2−y2+4y−4=0 is A unit2, then the value of 16A is
Answer» If area of the triangle formed by the line $x + y = 3$ and the angle bisectors of the pair of lines $x^{2} - y^{2} + 4 y - 4 = 0$ is $A {unit}^{2}$ , then the value of $16 A$ is

Discussion

27.	what is th dw=∫_0^1(20+10y)dy
Answer» what is th dw=∫_0^1(20+10y)dy

Discussion

28.	A box contains 4 blue, 5 green and 4 yellow balls. Two balls are drawn with replacement. Find the probability that the first ball is blue and the second ball is yellow.
Answer» A box contains 4 blue, 5 green and 4 yellow balls. Two balls are drawn with replacement. Find the probability that the first ball is blue and the second ball is yellow.

Discussion

29.	If f(x) = 2x + 1, what is f(-5)?
Answer» If f(x) = 2x + 1, what is f(-5)?

Discussion

30.	10.Vertices(+5, 0), foci (±4,0)
Answer» 10.Vertices(+5, 0), foci (±4,0)

Discussion

31.	The lengths of the sides of a right triangle are the integers a,c and c and these integers have no common factor. If a
Answer» The lengths of the sides of a right triangle are the integers a,c and c and these integers have no common factor. If a

Discussion

32.	If the lines x=ay+b,z=cy+d and x=a′z+b′,y=c′z+d′ are perpendicular, then :
Answer» If the lines $x = a y + b, z = c y + d$ and $x = a^{'} z + b^{'}, y = c^{'} z + d^{'}$ are perpendicular, then :

Discussion

33.	Write the value of i592+i590+i588+i586+i584i582+i580+i578+i576+i574.
Answer» Write the value of $\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} .$

33.

Write the value of i592+i590+i588+i586+i584i582+i580+i578+i576+i574.

Answer»

Write the value of

$\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} .$

Discussion

34.	Value of S1Sn+S2Sn−1+...+SnS1 is
Answer» Value of $S_{1} S_{n} + S_{2} S_{n - 1} + . . . + S_{n} S_{1}$ is

Discussion

35.	How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
Answer» How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Discussion

36.	Evaluate the following integrals:∫x2x4+x2-2dx
Answer» Evaluate the following integrals: $\int \frac{x^{2}}{x^{4} + x^{2} - 2} d x$

Discussion

37.	Let the tangent at point P(8,4) to the curve y3=x2 meets the curve again at Q and PQ=a√10. Then the value of a is
Answer» Let the tangent at point $P (8, 4)$ to the curve $y^{3} = x^{2}$ meets the curve again at $Q$ and $P Q = a \sqrt{10} .$ Then the value of $a$ is

Discussion

38.	28. Let a variable line drawn from A(h,k) intersects the ellipse x+2y=1 at P and Q. The tangents at P and Q intersects at R and the locus of R is βx+(β+1)y=1. Find the values of β such that point A lies inside the ellipse
Answer» 28. Let a variable line drawn from A(h,k) intersects the ellipse x+2y=1 at P and Q. The tangents at P and Q intersects at R and the locus of R is βx+(β+1)y=1. Find the values of β such that point A lies inside the ellipse

Discussion

39.	Express 2−i3+i in the form a + ib
Answer» Express $\frac{2 - i}{3 + i}$ in the form a + ib

Discussion

40.	The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be(a) 9(b) 3(c) –9(d) 6
Answer» The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be (a) 9 (b) 3 (c) –9 (d) 6

Discussion

41.	46. If a,b and c are positive integers such that abc=2018, then the largest possible value of the sum of a,b and c is?
Answer» 46. If a,b and c are positive integers such that abc=2018, then the largest possible value of the sum of a,b and c is?

Discussion

42.	Evaluate the given limit :limx→0sinax+bxax+sinbx,a,b,a+b≠0
Answer» Evaluate the given limit : $lim x \to 0 \frac{sin a x + b x}{a x + sin b x}, a, b, a + b \neq 0$

Discussion

43.	The number of pair solution (x, y) of the equation 1+x2+2x sin(cos−1y)=0 is ___ .
Answer» The number of pair solution (x, y) of the equation $1 + x^{2} + 2 x s i n (c o s^{- 1} y) = 0$ is ___ .

Discussion

44.	If tan(cotx)=cot(tanx), then the least positive value of cotx+tanx is
Answer» If $tan (cot x) = cot (tan x)$ , then the least positive value of $cot x + tan x$ is

Discussion

45.	If the vectors →a,→b and →c form the sides BC, CA and AB respectively of a Δ ABC, then
Answer» If the vectors $\to a, \to b$ and $\to c$ form the sides BC, CA and AB respectively of a $Δ A B C$ , then

Discussion

46.	Ram’s gardener is not dependable, the probability that he will forget to water the rose bush is23. The probability of its withering if watered is 12and the probability of withering if not watered is 34. Ram went out of station and upon returning, he finds that the rose bush has withered. If the probability that the gardener did not water the bush is p, then the value of 16p = ___
Answer» Ram’s gardener is not dependable, the probability that he will forget to water the rose bush is $\frac{2}{3}$ . The probability of its withering if watered is $\frac{1}{2}$ and the probability of withering if not watered is $\frac{3}{4}$ . Ram went out of station and upon returning, he finds that the rose bush has withered. If the probability that the gardener did not water the bush is p, then the value of 16p = ___

Discussion

47.	A ray originating from the point (5, 0) is incident on the hyperbola 9x2 − 16y2 = 144 at the point P with abscissa 8. Find the equation of the reflected ray after first reflection and point P lying in first quadrant.
Answer» A ray originating from the point (5, 0) is incident on the hyperbola $9 x^{2} - 16 y^{2} = 144$ at the point P with abscissa 8. Find the equation of the reflected ray after first reflection and point P lying in first quadrant.

Discussion

48.	9.Find the derivative ofG) 2r-34(in (5x3. 3x-1) (x-1)(iv) r 3-6x(vi)-9x-"(5+3x)(iii)(v) x4(3-4x-x3x-1
Answer» 9.Find the derivative ofG) 2r-34(in (5x3. 3x-1) (x-1)(iv) r 3-6x(vi)-9x-"(5+3x)(iii)(v) x4(3-4x-x3x-1

Discussion

49.	3. x. cos x
Answer» 3. x. cos x

Discussion

50.	Two points A and B have coordinates (1, 0) and (-1, 0) respectively and Q is a point which satisfies the relationAQ - BQ = ± 1. The locus of Q is
Answer» Two points A and B have coordinates (1, 0) and (-1, 0) respectively and Q is a point which satisfies the relation AQ - BQ = $\pm$ 1. The locus of Q is

50.

Two points A and B have coordinates (1, 0) and (-1, 0) respectively and Q is a point which satisfies the relationAQ - BQ = ± 1. The locus of Q is

Answer»

Two points A and B have coordinates (1, 0) and (-1, 0) respectively and Q is a point which satisfies the relation

AQ - BQ = $\pm$ 1. The locus of Q is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Two card are drawn successively with replacement from a pack of 52 cards. The probability of drawing two aces is [MNR 1988; UPSEAT 2000]

The value of cos[2cos−115+sin−115] is

If y^x = e^(y-x) ,then show that dy/dx=(logey)²/(logy)

Prove the following by using the principle of mathematical induction for all n ∈ N:

Choose the correct answer in the following question. Matrices A and B will be inverse of each other only if (a)AB=BA (b)AB =BA =O (c)AB=O, BA=I (d)AB=BA =I

The equation 2tan2x−5secx=1 holds true for exactly eleven distinct values of x∈[0,nπ2], n∈N. The greatest value of n is

check weather a*b=(a-b)^2 is commutative or assosiative both

If tan x=1-cos ysin y, then tan 2x = _____________.

The maximum value of the function f(x)=−|x+1|+3 is

How to solve the indefinite integral of (x^4 +1)/(x^6 +1)

Find the angle between z and iz in degrees. __

two vectors each of magnitude A have a resul†an t of same magnitude A the angle between the two vectors

Solution set of 2x–1&gt;7 and 3x–2≤16 is

The smallest value of x satisfying the equation 3 cot x + tan x=4 is(a) 2π/3(b) π/3(c) π/6(d) π/12

The graph of a function f(x) in the neighborhood of x = 4 is given. Find the value of limx → 4f(x).

If f(x)=tan−11−x1+x−12tan−1x; x≥0, then the value of f′(0) is

Probability that A speaks truth is . A coin is tossed. A reports that a head appears. The probability that actually there was head is A. B. C. D.

Let α and β be non zero real numbers such that 2(cosβ−cosα)+cosαcosβ=1. Then which of the following is/are true?

The equation of tangent to the parabola y2=6x at point (6,6) is

Solve: cossin-1x=16

If : A→B and g : B →C be two functions. Then, composition of f and g, gof : A→C is defined as

Draw the graph of y = root (2- x^2)

intreation of Sin^2 X/2

If area of the triangle formed by the line x+y=3 and the angle bisectors of the pair of lines x2−y2+4y−4=0 is A unit2, then the value of 16A is

what is th dw=∫_0^1(20+10y)dy

A box contains 4 blue, 5 green and 4 yellow balls. Two balls are drawn with replacement. Find the probability that the first ball is blue and the second ball is yellow.

If f(x) = 2x + 1, what is f(-5)?

10.Vertices(+5, 0), foci (±4,0)

The lengths of the sides of a right triangle are the integers a,c and c and these integers have no common factor. If a

If the lines x=ay+b,z=cy+d and x=a′z+b′,y=c′z+d′ are perpendicular, then :

Write the value of i592+i590+i588+i586+i584i582+i580+i578+i576+i574.

Value of S1Sn+S2Sn−1+...+SnS1 is

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Evaluate the following integrals:∫x2x4+x2-2dx​

Let the tangent at point P(8,4) to the curve y3=x2 meets the curve again at Q and PQ=a√10. Then the value of a is

28. Let a variable line drawn from A(h,k) intersects the ellipse x+2y=1 at P and Q. The tangents at P and Q intersects at R and the locus of R is βx+(β+1)y=1. Find the values of β such that point A lies inside the ellipse

Express 2−i3+i in the form a + ib

The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be(a) 9(b) 3(c) –9(d) 6

46. If a,b and c are positive integers such that abc=2018, then the largest possible value of the sum of a,b and c is?

Evaluate the given limit :limx→0sinax+bxax+sinbx,a,b,a+b≠0

The number of pair solution (x, y) of the equation 1+x2+2x sin(cos−1y)=0 is ___ .

If tan(cotx)=cot(tanx), then the least positive value of cotx+tanx is

If the vectors →a,→b and →c form the sides BC, CA and AB respectively of a Δ ABC, then

A ray originating from the point (5, 0) is incident on the hyperbola 9x2 − 16y2 = 144 at the point P with abscissa 8. Find the equation of the reflected ray after first reflection and point P lying in first quadrant.

9.Find the derivative ofG) 2r-34(in (5x3. 3x-1) (x-1)(iv) r 3-6x(vi)-9x-"(5+3x)(iii)(v) x4(3-4x-x3x-1

3. x. cos x

Two points A and B have coordinates (1, 0) and (-1, 0) respectively and Q is a point which satisfies the relationAQ - BQ = ± 1. The locus of Q is

Solution set of 2x–1>7 and 3x–2≤16 is

Evaluate the following integrals:∫x2x4+x2-2dx