43030 + Interview Questions in Mathematics

1.	The values of m for which roots of the quadratic equation −x2+(2m+3)x−m2=0 lies on either side of 3.
Answer» The values of $m$ for which roots of the quadratic equation $- x^{2} + (2 m + 3) x - m^{2} = 0$ lies on either side of $3.$

Discussion

2.	The equation of the ellipse whose foci are ( ±5 , 0 ) and one of its dierctrix is 5x = 36 , is
Answer» The equation of the ellipse whose foci are ( ±5 , 0 ) and one of its dierctrix is 5x = 36 , is

Discussion

3.	Equation of a line which is parallel to the line common to the pair of lines given by 6x2−xy−12y2=0 and 15x2+14xy−8y2=0 and at a distance of 7 units from it, is
Answer» Equation of a line which is parallel to the line common to the pair of lines given by $6 x^{2} - x y - 12 y^{2} = 0$ and $15 x^{2} + 14 x y - 8 y^{2} = 0$ and at a distance of $7$ units from it, is

Discussion

4.	Find area of the triangle with vertices at the point given in each of the following: (i) (1, 0), (6, 0), (4, 3) (ii) (2, 7), (1, 1), (10, 8) (iii) (−2, −3), (3, 2), (−1, −8)
Answer» Find area of the triangle with vertices at the point given in each of the following: (i) (1, 0), (6, 0), (4, 3) (ii) (2, 7), (1, 1), (10, 8) (iii) (−2, −3), (3, 2), (−1, −8)

Discussion

5.	Let (5,6) and (9,−4) be two points on a parabola . The point of intersection of tangents at these points is (1,−2). Then the slope of directrix of the parabola is
Answer» Let $(5, 6)$ and $(9, - 4)$ be two points on a parabola . The point of intersection of tangents at these points is $(1, - 2) .$ Then the slope of directrix of the parabola is

Discussion

6.	Using integration, find the area of the region bounded by the triangle whose vertices are (−1, 2), (1, 5) and (3, 4). [CBSE 2014]
Answer» Using integration, find the area of the region bounded by the triangle whose vertices are (−1, 2), (1, 5) and (3, 4). [CBSE 2014]

Discussion

7.	For the parabola y2+6y−2x+5=0 (i) The vertex is (−2,−3) (ii) The directrix is y+3=0 which of the following is correct?
Answer» For the parabola $y^{2} + 6 y - 2 x + 5 = 0$ (i) The vertex is $(- 2, - 3)$ (ii) The directrix is $y + 3 = 0$ which of the following is correct?

Discussion

8.	The interval in which is increasing is (A) (B) (−2, 0) (C) (D) (0, 2)
Answer» The interval in which is increasing is (A) (B) (−2, 0) (C) (D) (0, 2)

Discussion

9.	Which is the algebraic equation for the statement "a number divided by nine is fifteen"?
Answer» Which is the algebraic equation for the statement "a number divided by nine is fifteen"?

Discussion

10.	In Q. No. 24, Maximum of z occurs at(a) (5, 0)(b) (6, 5)(c) (6, 8)(d) (4, 10)
Answer» In Q. No. 24, Maximum of z occurs at (a) (5, 0) (b) (6, 5) (c) (6, 8) (d) (4, 10)

Discussion

11.	The function f(x)=(tanx11)ex5sgn(x11)[13x2+2] where [⋅] denotes greatest integer function, is:
Answer» The function $f (x) = (t a n x^{11}) e^{x^{5}} s g n (x^{11}) [\frac{1}{3 x^{2} + 2}]$ where $[\cdot]$ denotes greatest integer function, is:

Discussion

12.	If sin \| sin-s-cos-1 x 1 then find the value of xsin+osx-1, then find the value of x14.
Answer» If sin \| sin-s-cos-1 x 1 then find the value of xsin+osx-1, then find the value of x14.

Discussion

13.	If fx=x, x>1x2, x<1, then lim x→2fx=____________________________________.
Answer» $If f (x) = \{\begin{cases} x, x > 1 \\ x^{2}, x < 1 \end{cases}, then \lim_{x \to 2} f (x) =____________________________________.$

Discussion

14.	If A is a 3×3 matrix such that \|5⋅adjA\|=5, then \|A\| is equal to
Answer» If $A$ is a $3 \times 3$ matrix such that $\| 5 \cdot a d j A \| = 5,$ then $\| A \|$ is equal to

Discussion

15.	The lines tangent to the curve x3+2y3+3x2y−2yx2+3x−2y=0 and x7−y4+2x+3y=0 at the origin intersect at an angle θ, then the value of θ is equal to
Answer» The lines tangent to the curve $x^{3} + 2 y^{3} + 3 x^{2} y - 2 y x^{2} + 3 x - 2 y = 0 and x^{7} - y^{4} + 2 x + 3 y = 0$ at the origin intersect at an angle $θ$ , then the value of $θ$ is equal to

Discussion

16.	How many of the following are functions ? (i) f(x) = x5;{−1,0,1}→{0,1,2} (ii) f(x) = ∓√x;{0,4,9}→{0,2,−2,3,−3} (iii) f(x) = √x;{0,4,9}→{0,2,−2,3,−3} (iv) f(x) = x2;{0,1,2}→{0,1,2,3,4}
Answer» How many of the following are functions ? (i) f(x) = $x^{5}; {- 1, 0, 1} \to {0, 1, 2}$ (ii) f(x) = $\mp \sqrt{x}; {0, 4, 9} \to {0, 2, - 2, 3, - 3}$ (iii) f(x) = $\sqrt{x}; {0, 4, 9} \to {0, 2, - 2, 3, - 3}$ (iv) f(x) = $x^{2}; {0, 1, 2} \to {0, 1, 2, 3, 4}$

16.

How many of the following are functions ? (i) f(x) = x5;{−1,0,1}→{0,1,2} (ii) f(x) = ∓√x;{0,4,9}→{0,2,−2,3,−3} (iii) f(x) = √x;{0,4,9}→{0,2,−2,3,−3} (iv) f(x) = x2;{0,1,2}→{0,1,2,3,4}

Answer»

How many of the following are functions ?

(i) f(x) = $x^{5}; {- 1, 0, 1} \to {0, 1, 2}$

(ii) f(x) = $\mp \sqrt{x}; {0, 4, 9} \to {0, 2, - 2, 3, - 3}$

(iii) f(x) = $\sqrt{x}; {0, 4, 9} \to {0, 2, - 2, 3, - 3}$

(iv) f(x) = $x^{2}; {0, 1, 2} \to {0, 1, 2, 3, 4}$

Discussion

17.	Probability of n heads in 2n tosses of a fair coin can be given by
Answer» Probability of $n$ heads in $2 n$ tosses of a fair coin can be given by

Discussion

18.	Let Z be the set of all integers andA = {(x, y); x4y4 = 175, x, y E Z}B = {(x, y); xy, x, y EZ}Then, the number of elements in An B is
Answer» Let Z be the set of all integers and A = {(x, y); x4y4 = 175, x, y E Z} B = {(x, y); xy, x, y EZ} Then, the number of elements in An B is

Discussion

19.	In ΔABC, If a=13 cm,b=12 cm,c=5 cm, then sinA2=
Answer» In $Δ A B C,$ If $a = 13 c m, b = 12 c m, c = 5 c m,$ then $sin \frac{A}{2} =$

Discussion

20.	2. Find the value of }\operatorname{cos}2θ\operatorname{cos}2ϕ+\operatorname{sin}^2(θ-ϕ)-\operatorname{sin}^2(θ+ϕ)
Answer» 2. Find the value of }\operatorname{cos}2θ\operatorname{cos}2ϕ+\operatorname{sin}^2(θ-ϕ)-\operatorname{sin}^2(θ+ϕ)

Discussion

21.	Let a1,a2,a3⋯ be terms of A.P.If a1+a2+⋯apa1+a2+⋯+aq=p2q2,p≠q, then a6a21 equal
Answer» Let $a_{1}, a_{2}, a_{3} \dots$ be terms of A.P. $I f \frac{a_{1} + a_{2} + \dots a_{p}}{a_{1} + a_{2} + \dots + a_{q}} = \frac{p^{2}}{q^{2}}, p \neq q,$ then $\frac{a_{6}}{a_{21}}$ equal

Discussion

22.	If the mean and median of a unimodal data are 34.5 and 32.5 respectively, then mode of the data is __________.
Answer» If the mean and median of a unimodal data are 34.5 and 32.5 respectively, then mode of the data is __________.

Discussion

23.	Let AB is a normal chord of parabola y2=4x, with foot of normal as A(1,−2). If AB=p√q, where p is a natural number and q is a prime number, then pq is equal to
Answer» Let $A B$ is a normal chord of parabola $y^{2} = 4 x$ , with foot of normal as $A (1, - 2)$ . If $A B = p \sqrt{q}$ , where $p$ is a natural number and $q$ is a prime number, then $\frac{p}{q}$ is equal to

Discussion

24.	A rectangle ABCD has area 200.Sq.units and an ellipse with area 200π Sq.units having foci at B and D passes through A and C . If the perimeter of the rectangle is P units then the value of P20 is
Answer» A rectangle $A B C D$ has area $200.$ Sq.units and an ellipse with area $200 π$ Sq.units having foci at $B$ and $D$ passes through $A$ and $C$ . If the perimeter of the rectangle is $P$ units then the value of $\frac{P}{20}$ is

Discussion

25.	If y=x sin x square, then the value of dy/dx is
Answer» If y=x sin x square, then the value of dy/dx is

Discussion

26.	A square of side "a" lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle α where 0<α<90with the positive direction of x - axis. The equation of its diagonal not passing through the origin is
Answer» A square of side "a" lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle α where 0<α<90with the positive direction of x - axis. The equation of its diagonal not passing through the origin is

Discussion

27.	The area of the region, enclosed by the circle x2+y2=2 which is not common to the region bounded by the parabola y2=x and the straight line y=x, is
Answer» The area of the region, enclosed by the circle $x^{2} + y^{2} = 2$ which is not common to the region bounded by the parabola $y^{2} = x$ and the straight line $y = x$ , is

Discussion

28.	A line passes through . If slope of the line is m , show that .
Answer» A line passes through . If slope of the line is m , show that .

Discussion

29.	Find the equations of the tangent and normal to the parabola y 2 = 4 ax at the point ( at 2 , 2 at ).
Answer» Find the equations of the tangent and normal to the parabola y 2 = 4 ax at the point ( at 2 , 2 at ).

Discussion

30.	If the local maximum of f(x) = sin2x - xϵ(0,π) is at x = a, then find the value of 36 aπ___
Answer» If the local maximum of f(x) = sin2x - xϵ(0,π) is at x = a, then find the value of 36 $\frac{a}{π}$ ___

Discussion

31.	Find the 20th and nth terms of the G.P. 52,54,58,...
Answer» Find the $20^{t h}$ and $n^{t h}$ terms of the G.P. $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, . . .$

Discussion

32.	Solve the equation 9x2−155x−500 using quadratic method.
Answer» Solve the equation $9 x^{2} - 155 x - 500$ using quadratic method.

Discussion

33.	Find the domain and range of the following real function:(i) f(x)= –\|x\| (ii)
Answer» Find the domain and range of the following real function: (i) f(x) = –\|x\| (ii)

33.

Find the domain and range of the following real function:(i) f(x)= –|x| (ii)

Answer»

Find the domain and range of the following real function:

(i) f(x)
= –|x| (ii)

Discussion

34.	If 2p2−3q2+4pq−p=0 and a variable line px+qy=1 always touches a parabola whose axis is parallel to X-axis, then equation of the parabola is
Answer» If $2 p^{2} - 3 q^{2} + 4 p q - p = 0$ and a variable line px+qy=1 always touches a parabola whose axis is parallel to X-axis, then equation of the parabola is

Discussion

35.	The common tangent to the circles x2+y2=4 and x2+y2+6x+8y−24=0 also passes through the point :
Answer» The common tangent to the circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} + 6 x + 8 y - 24 = 0$ also passes through the point :

Discussion

36.	If 5,5r,5r2 are the side lengths of a triangle, then the possible value(s) of r is/are
Answer» If $5, 5 r, 5 r^{2}$ are the side lengths of a triangle, then the possible value(s) of $r$ is/are

Discussion

37.	The value of 3(sinx−cosx)4+6(sinx+cosx)2+4(sin6x+cos6x) is
Answer» The value of $3 (sin x - cos x)^{4} + 6 (sin x + cos x)^{2} + 4 ({sin}^{6} x + {cos}^{6} x)$ is

Discussion

38.	If a root of the equation ax2+bx+c=0 be reciprocal of the equation then a′x2+b′x+c′=0, then
Answer» If a root of the equation $a x^{2} + b x + c = 0$ be reciprocal of the equation then $a^{'} x^{2} + b^{'} x + c^{'} = 0$ , then

Discussion

39.	The area of the region bounded by the curve x = 2y + 3, y-axis and the line y = 1 and y = -1 is(a) 4 sq. units (b) 32 sq. units (c) 6 sq. units (d) 8 sq. units
Answer» The area of the region bounded by the curve x = 2y + 3, y-axis and the line y = 1 and y = -1 is (a) 4 sq. units (b) $\frac{3}{2}$ sq. units (c) 6 sq. units (d) 8 sq. units

Discussion

40.	If f(x)=(1+x)n then the value of f(0)+f′(0)+...+fn(0)n! is
Answer» If $f (x) = (1 + x)^{n}$ then the value of $f (0) + f^{'} (0) + . . . + \frac{f^{n} (0)}{n!}$ is

Discussion

41.	4·49-25-
Answer» 4·49-25-

Discussion

42.	If f: R → R is defined by f(x) =xx2+1find f(f(2))
Answer» If f: R $\to$ R is defined by f(x) $= \frac{x}{x^{2} + 1}$ find f(f(2))

Discussion

43.	Sinar+bx20. lima,b, a + b#0
Answer» Sinar+bx20. lima,b, a + b#0

Discussion

44.	Find the area of the region bounded by the curve y 2 = 4 x and the line x = 3
Answer» Find the area of the region bounded by the curve y 2 = 4 x and the line x = 3

Discussion

45.	If }\operatorname{cos}A=n\operatorname{cos}B and }\operatorname{sin}A=m\operatorname{sin}B then show that }(m^2-n^2)\operatorname{sin}^2B=1-n^2
Answer» If }\operatorname{cos}A=n\operatorname{cos}B and }\operatorname{sin}A=m\operatorname{sin}B then show that }(m^2-n^2)\operatorname{sin}^2B=1-n^2

Discussion

46.	Which of the following dot plots has a mean of 66 and a median of 70?
Answer» Which of the following dot plots has a mean of 66 and a median of 70?

Discussion

47.	From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Answer» From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

Discussion

48.	3. If x2(0 + sine) and y = 2(1 - cosθ), then value of- dy/dx is (1) tanθ/2 (2) cotθ/2(3) sinθ/2(4) cosθ/
Answer» 3. If x2(0 + sine) and y = 2(1 - cosθ), then value of- dy/dx is (1) tanθ/2 (2) cotθ/2(3) sinθ/2(4) cosθ/

Discussion

49.	The equation of the common tangent to the circles x2 + y2 − 4x + 6y − 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 at their point of contact.
Answer» The equation of the common tangent to the circles $x^{2} + y^{2} - 4 x + 6 y - 12 = 0$ and $x^{2} + y^{2} + 6 x + 18 y + 26 = 0$ at their point of contact.

Discussion

50.	A game consists of tossing a one-rupee coin three times, and noting its outcome each time. If getting the same result in all the tosses is a success, find the probability of losing the game.
Answer» A game consists of tossing a one-rupee coin three times, and noting its outcome each time. If getting the same result in all the tosses is a success, find the probability of losing the game.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The values of m for which roots of the quadratic equation −x2+(2m+3)x−m2=0 lies on either side of 3.

The equation of the ellipse whose foci are ( ±5 , 0 ) and one of its dierctrix is 5x = 36 , is

Equation of a line which is parallel to the line common to the pair of lines given by 6x2−xy−12y2=0 and 15x2+14xy−8y2=0 and at a distance of 7 units from it, is

Find area of the triangle with vertices at the point given in each of the following: (i) (1, 0), (6, 0), (4, 3) (ii) (2, 7), (1, 1), (10, 8) (iii) (−2, −3), (3, 2), (−1, −8)

Let (5,6) and (9,−4) be two points on a parabola . The point of intersection of tangents at these points is (1,−2). Then the slope of directrix of the parabola is

Using integration, find the area of the region bounded by the triangle whose vertices are (−1, 2), (1, 5) and (3, 4). [CBSE 2014]

For the parabola y2+6y−2x+5=0 (i) The vertex is (−2,−3) (ii) The directrix is y+3=0 which of the following is correct?

The interval in which is increasing is (A) (B) (−2, 0) (C) (D) (0, 2)

Which is the algebraic equation for the statement "a number divided by nine is fifteen"?

In Q. No. 24, Maximum of z occurs at(a) (5, 0)(b) (6, 5)(c) (6, 8)(d) (4, 10)

The function f(x)=(tanx11)ex5sgn(x11)[13x2+2] where [⋅] denotes greatest integer function, is:

If sin | sin-s-cos-1 x 1 then find the value of xsin+osx-1, then find the value of x14.

If fx=x, x&gt;1x2, x&lt;1, then lim x→2fx=____________________________________.

If A is a 3×3 matrix such that |5⋅adjA|=5, then |A| is equal to

The lines tangent to the curve x3+2y3+3x2y−2yx2+3x−2y=0 and x7−y4+2x+3y=0 at the origin intersect at an angle θ, then the value of θ is equal to

How many of the following are functions ? (i) f(x) = x5;{−1,0,1}→{0,1,2} (ii) f(x) = ∓√x;{0,4,9}→{0,2,−2,3,−3} (iii) f(x) = √x;{0,4,9}→{0,2,−2,3,−3} (iv) f(x) = x2;{0,1,2}→{0,1,2,3,4}

Probability of n heads in 2n tosses of a fair coin can be given by

Let Z be the set of all integers andA = {(x, y); x4y4 = 175, x, y E Z}B = {(x, y); xy, x, y EZ}Then, the number of elements in An B is

In ΔABC, If a=13 cm,b=12 cm,c=5 cm, then sinA2=

2. Find the value of }\operatorname{cos}2θ\operatorname{cos}2ϕ+\operatorname{sin}^2(θ-ϕ)-\operatorname{sin}^2(θ+ϕ)

Let a1,a2,a3⋯ be terms of A.P.If a1+a2+⋯apa1+a2+⋯+aq=p2q2,p≠q, then a6a21 equal

If the mean and median of a unimodal data are 34.5 and 32.5 respectively, then mode of the data is __________.

Let AB is a normal chord of parabola y2=4x, with foot of normal as A(1,−2). If AB=p√q, where p is a natural number and q is a prime number, then pq is equal to

A rectangle ABCD has area 200.Sq.units and an ellipse with area 200π Sq.units having foci at B and D passes through A and C . If the perimeter of the rectangle is P units then the value of P20 is

If y=x sin x square, then the value of dy/dx is

A square of side "a" lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle α where 0&lt;α&lt;90with the positive direction of x - axis. The equation of its diagonal not passing through the origin is

The area of the region, enclosed by the circle x2+y2=2 which is not common to the region bounded by the parabola y2=x and the straight line y=x, is

A line passes through . If slope of the line is m , show that .

Find the equations of the tangent and normal to the parabola y 2 = 4 ax at the point ( at 2 , 2 at ).

If the local maximum of f(x) = sin2x - xϵ(0,π) is at x = a, then find the value of 36 aπ___

Find the 20th and nth terms of the G.P. 52,54,58,...

Solve the equation 9x2−155x−500 using quadratic method.

Find the domain and range of the following real function:(i) f(x)= –|x| (ii)

If 2p2−3q2+4pq−p=0 and a variable line px+qy=1 always touches a parabola whose axis is parallel to X-axis, then equation of the parabola is

The common tangent to the circles x2+y2=4 and x2+y2+6x+8y−24=0 also passes through the point :

If 5,5r,5r2 are the side lengths of a triangle, then the possible value(s) of r is/are

The value of 3(sinx−cosx)4+6(sinx+cosx)2+4(sin6x+cos6x) is

If a root of the equation ax2+bx+c=0 be reciprocal of the equation then a′x2+b′x+c′=0, then

The area of the region bounded by the curve x = 2y + 3, y-axis and the line y = 1 and y = -1 is(a) 4 sq. units (b) 32 sq. units (c) 6 sq. units (d) 8 sq. units

If f(x)=(1+x)n then the value of f(0)+f′(0)+...+fn(0)n! is

4·49-25-

If f: R → R is defined by f(x) =xx2+1find f(f(2))

Sinar+bx20. lima,b, a + b#0

Find the area of the region bounded by the curve y 2 = 4 x and the line x = 3

If }\operatorname{cos}A=n\operatorname{cos}B and }\operatorname{sin}A=m\operatorname{sin}B then show that }(m^2-n^2)\operatorname{sin}^2B=1-n^2

Which of the following dot plots has a mean of 66 and a median of 70?

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

3. If x2(0 + sine) and y = 2(1 - cosθ), then value of- dy/dx is (1) tanθ/2 (2) cotθ/2(3) sinθ/2(4) cosθ/

The equation of the common tangent to the circles x2 + y2 − 4x + 6y − 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 at their point of contact.

A game consists of tossing a one-rupee coin three times, and noting its outcome each time. If getting the same result in all the tosses is a success, find the probability of losing the game.

If fx=x, x>1x2, x<1, then lim x→2fx=____________________________________.

A square of side "a" lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle α where 0<α<90with the positive direction of x - axis. The equation of its diagonal not passing through the origin is