43030 + Interview Questions in Mathematics

1.	Let matrix A=[12−3−5]. Then inverse of matrix A is
Answer» Let matrix $A = [\begin{matrix} 1 & 2 - 3 & - 5 \end{matrix}] .$ Then inverse of matrix $A$ is

Discussion

2.	Write the relation R = {( x , x 3 ): x is a prime number less than 10} in roster form.
Answer» Write the relation R = {( x , x 3 ): x is a prime number less than 10} in roster form.

Discussion

3.	If cos−1√p+cos−1√1−p+cos−1√1−q=3π4, then the value of q is
Answer» If $c o s^{- 1} \sqrt{p} + c o s^{- 1} \sqrt{1 - p} + c o s^{- 1} \sqrt{1 - q} = \frac{3 π}{4}$ , then the value of q is

Discussion

4.	Find dydx if y=12(1−cost),x=10(t−sint),−π2<t<π2
Answer» Find $\frac{d y}{d x}$ if $y = 12 (1 - cos t), x = 10 (t - sin t), - \frac{π}{2} < t < \frac{π}{2}$

Discussion

5.	Findall the points of discontinuity of fdefined by.
Answer» Find all the points of discontinuity of f defined by.

Discussion

6.	Find the angle between the planes whose vector equations are and .
Answer» Find the angle between the planes whose vector equations are and .

Discussion

7.	If }\operatorname{sin}θ=\operatorname{cos}θ, then find the value of }2\operatorname{tan}θ+\operatorname{cos}^2θ
Answer» If }\operatorname{sin}θ=\operatorname{cos}θ, then find the value of }2\operatorname{tan}θ+\operatorname{cos}^2θ

Discussion

8.	Find the shortest distance between lines and .
Answer» Find the shortest distance between lines and .

Discussion

9.	Two dice of different colours are thrown simultaneously. The probability that the sum of the faces appeared is either 7 or 11 is
Answer» Two dice of different colours are thrown simultaneously. The probability that the sum of the faces appeared is either $7$ or $11$ is

Discussion

10.	Let t1 and t2 be the parameters of 2 points on a parabola. What is the value of t1t2 if tangents at these points are at right angle to each other?___
Answer» Let $t_{1} a n d t_{2}$ be the parameters of 2 points on a parabola. What is the value of $t_{1} t_{2}$ if tangents at these points are at right angle to each other? ___

Discussion

11.	Find a and b such that x=2/3and 3/2 are the roots of ax2-13x+b
Answer» Find a and b such that x=2/3and 3/2 are the roots of ax2-13x+b

Discussion

12.	If f:R->R is defined as f(x)=x2-3x+2 . Find f(f(x))
Answer» If f:R->R is defined as f(x)=x²-3x+2 . Find f(f(x))

12.

If f:R->R is defined as f(x)=x2-3x+2 . Find f(f(x))

Answer»

If f:R->R is defined as f(x)=x²-3x+2 .

Find f(f(x))

Discussion

13.	The value of (cosec θ – sin θ) (secθ – cos θ) (tan θ + cot θ) is _________.
Answer» The value of (cosec θ – sin θ) (secθ – cos θ) (tan θ + cot θ) is _________.

Discussion

14.	limx→−1√π−√cos−1x√x+1
Answer» ${lim}_{x \to - 1} \frac{\sqrt{π} - \sqrt{c o s^{- 1} x}}{\sqrt{x + 1}}$

Discussion

15.	16.Why should we make y coefficient of a line positive before determining position of point with respect to line?
Answer» 16.Why should we make y coefficient of a line positive before determining position of point with respect to line?

Discussion

16.	4.The differential equation of the family of circles of unit radius and Centre lying on the line y = x , is
Answer» 4.The differential equation of the family of circles of unit radius and Centre lying on the line y = x , is

Discussion

17.	if 4 cot inverse(1/(2-√3) = tan inverse(1/3x) + tan inverse(1/5)
Answer» if 4 cot inverse(1/(2-√3) = tan inverse(1/3x) + tan inverse(1/5)

Discussion

18.	The following is the percentage distribution of the revenue split-up of AIRTEL mobile service limited or the years 1999 and 2000. Total revenue in any year = Revenue from local service + Revenue from STD/ISD services. (Use data from previous questions if necessary) Find the percentage by which the total revenue from post-paid STD/ISD services in the year 2000 exceeds that of post-paid local services in the year 2000.
Answer» The following is the percentage distribution of the revenue split-up of AIRTEL mobile service limited or the years 1999 and 2000. Total revenue in any year = Revenue from local service + Revenue from STD/ISD services. (Use data from previous questions if necessary) Find the percentage by which the total revenue from post-paid STD/ISD services in the year 2000 exceeds that of post-paid local services in the year 2000.

Discussion

19.	Find the distance between the points −212 and −514 on the number line.
Answer» Find the distance between the points $- 2 \frac{1}{2}$ and $- 5 \frac{1}{4}$ on the number line.

Discussion

20.	If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = αx+β, then find the values of α and β. [NCERT EXEMPLAR]
Answer» If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = $α x + β$ , then find the values of $α$ and $β$ . [NCERT EXEMPLAR]

Discussion

21.	Find the equation of family of circles through the intersection of x2 + y2 − 6x + 2y + 4 = 0 and x2 + y2 + 2x − 4y − 6 = 0 whose center lies on y = x.
Answer» Find the equation of family of circles through the intersection of $x^{2} + y^{2} - 6 x + 2 y + 4 = 0$ and $x^{2} + y^{2} + 2 x - 4 y - 6 = 0$ whose center lies on $y = x .$

Discussion

22.	The value of π/2∫0cosec5xcosec5x+sec5xdx is
Answer» The value of $π / 2 \int 0 \frac{{cosec}^{5} x}{{cosec}^{5} x + {sec}^{5} x} d x$ is

Discussion

23.	all trigonometric formulaes
Answer» all trigonometric formulaes

Discussion

24.	The set of value(s) of k for which x2−kx+sin−1(sin4)>0 for all real x is
Answer» The set of value(s) of $k$ for which $x^{2} - k x + {sin}^{- 1} (sin 4) > 0$ for all real $x$ is

Discussion

25.	Which of the following is INCORRECT for the hyperbola x2−2y2−2x+8y−1=0
Answer» Which of the following is INCORRECT for the hyperbola $x^{2} - 2 y^{2} - 2 x + 8 y - 1 = 0$

Discussion

26.	Evaluate the following integrals:∫1sin4x+sin2x cos2x+cos4xdx
Answer» Evaluate the following integrals: $\int \frac{1}{\sin^{4} x + \sin^{2} x \cos^{2} x + \cos^{4} x} d x$

Discussion

27.	Consider the curve x2a2+y2b2=1. The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of
Answer» Consider the curve $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ . The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of

Discussion

28.	On January 1, 2000, there were 175,000 tons of trash in a landfill that had a capacity of 325,000 tons. Each year since then, the amount of trash in the landfill increased by 7,500 tons. If y represents the time, in years, after January 1, 2000, which of the following inequalities describes the set of years where the landfill is at or above capacity?
Answer» On January 1, 2000, there were 175,000 tons of trash in a landfill that had a capacity of 325,000 tons. Each year since then, the amount of trash in the landfill increased by 7,500 tons. If y represents the time, in years, after January 1, 2000, which of the following inequalities describes the set of years where the landfill is at or above capacity?

Discussion

29.	Find the value of (579−1123)÷56.
Answer» Find the value of $(5 \frac{7}{9} - 11 \frac{2}{3}) \div \frac{5}{6} .$

Discussion

30.	If ey(x+1)=1, show that d2ydx2=(dydx)2.
Answer» $I f e^{y} (x + 1) = 1, s h o w t h a t \frac{d^{2} y}{d x^{2}} = {(\frac{d y}{d x})}^{2} .$

Discussion

31.	18.find the value of k if x square + 2kx - 3 has equal roots
Answer» 18.find the value of k if x square + 2kx - 3 has equal roots

Discussion

32.	HOW TEMP OF BOYELS LAW IS a/bR?
Answer» HOW TEMP OF BOYELS LAW IS a/bR?

Discussion

33.	The derivative of y=loge sin (ex) with respect to x will be
Answer» The derivative of $y = l o g_{e} s i n (e^{x})$ with respect to x will be

Discussion

34.	Find the odds in favor of getting a multiple of 3, when a dice is thrown.
Answer» Find the odds in favor of getting a multiple of 3, when a dice is thrown.

Discussion

35.	Consider a F=4i-3j.Another vector perpendicular of F is (1) 3i-4j or (2) k cap
Answer» Consider a F=4i-3j.Another vector perpendicular of F is (1) 3i-4j or (2) k cap

Discussion

36.	The value of cos15∘+sin15∘cos15∘−sin15∘ is
Answer» The value of $\frac{cos 15^{\circ} + sin 15^{\circ}}{cos 15^{\circ} - sin 15^{\circ}}$ is

Discussion

37.	if A and B are any two non empty sets and A is proper subset of B. If n(A)=5 then minimum possible value of n(AB) IS?=SYMMETRIC DIFFERENCE.
Answer» if A and B are any two non empty sets and A is proper subset of B. If n(A)=5 then minimum possible value of n(AB) IS? =SYMMETRIC DIFFERENCE.

Discussion

38.	If Z=3x+4y, subject to the constraints: x+y≤4, x≥0, y≥0, then Zmax is equal to
Answer» If $Z = 3 x + 4 y,$ subject to the constraints: $x + y \leq 4,$ $x \geq 0,$ $y \geq 0,$ then $Z_{max}$ is equal to

Discussion

39.	The number of solutions of the equation tanx + secx= 2cosx lying in the Internal [0,2π] is
Answer» The number of solutions of the equation tanx + secx= 2cosx lying in the Internal [0,2 $π$ ] is

39.

The number of solutions of the equation tanx + secx= 2cosx lying in the Internal [0,2π] is

Answer»

The number of solutions of the equation tanx + secx= 2cosx lying in the

Internal [0,2 $π$ ] is

Discussion

40.	The maximum value of 11111+sinθ1111+cosθ is ___________.
Answer» The maximum value of $\|\begin{matrix} 1 & 1 & 1 \\ 1 & 1 + \sin θ & 1 \\ 1 & 1 & 1 + \cos θ \end{matrix}\|$ is ___________.

Discussion

41.	Solve the trigonometric equation - Sin+ tan - sin 2 = 0
Answer» Solve the trigonometric equation - Sin+ tan - sin 2 = 0

Discussion

42.	If the tangents are drawn from (3, 2) to the hyperbola x2−9y2=9. Find the area of the triangle (in sq. unit) that these tangents form with their chord of contact.
Answer» If the tangents are drawn from (3, 2) to the hyperbola $x^{2} - 9 y^{2} = 9$ . Find the area of the triangle (in sq. unit) that these tangents form with their chord of contact.

Discussion

43.	The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.
Answer» The 4^th term of a G.P. is square of its second term, and the first term is –3. Determine its 7^th term.

Discussion

44.	cos[cos−1(−17)+sin−1(−17)]=
Answer» $c o s [c o s^{- 1} (\frac{- 1}{7}) + s i n^{- 1} (\frac{- 1}{7})] =$

Discussion

45.	limx→1x-1, where [.] is the greatest integer function, is equal to(a) 1 (b) 2 (c) 0 (d) does not exist
Answer» $\lim_{x \to 1} [x - 1]$ , where [.] is the greatest integer function, is equal to (a) 1 (b) 2 (c) 0 (d) does not exist

Discussion

46.	The last digit of 17256 is
Answer» The last digit of $17^{256}$ is

Discussion

47.	Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.
Answer» Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.

Discussion

48.	The smaller angle (in degrees) between the planes x + y + z = 1, and 2x -y + 2z = 0 is_______54.73
Answer» The smaller angle (in degrees) between the planes x + y + z = 1, and 2x -y + 2z = 0 is_______ 54.73

Discussion

49.	If O is the origin and Q is a variable point on y2=x.Fin the locus of the mid-point of OQ.
Answer» $If O is the origin and Q is a variable point on y^{2} = x . Fin the locus of the mid-point of OQ.$

Discussion

50.	If α,β,γ are the roots of x3+64=0, then the equation whose roots are (αβ)2and(αγ)2 is
Answer» If $α, β, γ$ are the roots of $x^{3} + 64 = 0$ , then the equation whose roots are ${(\frac{α}{β})}^{2} a n d {(\frac{α}{γ})}^{2}$ is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let matrix A=[12−3−5]. Then inverse of matrix A is

Write the relation R = {( x , x 3 ): x is a prime number less than 10} in roster form.

If cos−1√p+cos−1√1−p+cos−1√1−q=3π4, then the value of q is

Find dydx if y=12(1−cost),x=10(t−sint),−π2&lt;t&lt;π2

Findall the points of discontinuity of fdefined by.

Find the angle between the planes whose vector equations are and .

If }\operatorname{sin}θ=\operatorname{cos}θ, then find the value of }2\operatorname{tan}θ+\operatorname{cos}^2θ

Find the shortest distance between lines and .

Two dice of different colours are thrown simultaneously. The probability that the sum of the faces appeared is either 7 or 11 is

Let t1 and t2 be the parameters of 2 points on a parabola. What is the value of t1t2 if tangents at these points are at right angle to each other?___

Find a and b such that x=2/3and 3/2 are the roots of ax2-13x+b

If f:R-&gt;R is defined as f(x)=x2-3x+2 . Find f(f(x))

The value of (cosec θ – sin θ) (secθ – cos θ) (tan θ + cot θ) is _________.

limx→−1√π−√cos−1x√x+1

16.Why should we make y coefficient of a line positive before determining position of point with respect to line?

4.The differential equation of the family of circles of unit radius and Centre lying on the line y = x , is

if 4 cot inverse(1/(2-√3) = tan inverse(1/3x) + tan inverse(1/5)

Find the distance between the points −212 and −514 on the number line.

If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = αx+β, then find the values of α and β. [NCERT EXEMPLAR]

Find the equation of family of circles through the intersection of x2 + y2 − 6x + 2y + 4 = 0 and x2 + y2 + 2x − 4y − 6 = 0 whose center lies on y = x.

The value of π/2∫0cosec5xcosec5x+sec5xdx is

all trigonometric formulaes

The set of value(s) of k for which x2−kx+sin−1(sin4)&gt;0 for all real x is

Which of the following is INCORRECT for the hyperbola x2−2y2−2x+8y−1=0

Evaluate the following integrals:∫1sin4x+sin2x cos2x+cos4xdx

Consider the curve x2a2+y2b2=1. The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of

Find the value of (579−1123)÷56.

If ey(x+1)=1, show that d2ydx2=(dydx)2.

18.find the value of k if x square + 2kx - 3 has equal roots

HOW TEMP OF BOYELS LAW IS a/bR?

The derivative of y=loge sin (ex) with respect to x will be

Find the odds in favor of getting a multiple of 3, when a dice is thrown.

Consider a F=4i-3j.Another vector perpendicular of F is (1) 3i-4j or (2) k cap

The value of cos15∘+sin15∘cos15∘−sin15∘ is

if A and B are any two non empty sets and A is proper subset of B. If n(A)=5 then minimum possible value of n(A*B) IS?*=SYMMETRIC DIFFERENCE.

If Z=3x+4y, subject to the constraints: x+y≤4, x≥0, y≥0, then Zmax is equal to

The number of solutions of the equation tanx + secx= 2cosx lying in the Internal [0,2π] is

The maximum value of 11111+sinθ1111+cosθ is ___________.

Solve the trigonometric equation - Sin+ tan - sin 2 = 0

If the tangents are drawn from (3, 2) to the hyperbola x2−9y2=9. Find the area of the triangle (in sq. unit) that these tangents form with their chord of contact.

The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.

cos[cos−1(−17)+sin−1(−17)]=

limx→1x-1, where [.] is the greatest integer function, is equal to(a) 1 (b) 2 (c) 0 (d) does not exist

The last digit of 17256 is

Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.

The smaller angle (in degrees) between the planes x + y + z = 1, and 2x -y + 2z = 0 is_______54.73

If O is the origin and Q is a variable point on y2=x.Fin the locus of the mid-point of OQ.

If α,β,γ are the roots of x3+64=0, then the equation whose roots are (αβ)2and(αγ)2 is

Find dydx if y=12(1−cost),x=10(t−sint),−π2<t<π2

If f:R->R is defined as f(x)=x2-3x+2 . Find f(f(x))

The set of value(s) of k for which x2−kx+sin−1(sin4)>0 for all real x is

if A and B are any two non empty sets and A is proper subset of B. If n(A)=5 then minimum possible value of n(AB) IS?=SYMMETRIC DIFFERENCE.