43030 + Interview Questions in Mathematics

1.	sinx31. (1+cos x
Answer» sinx31. (1+cos x

Discussion

2.	The number of real solution(s) of the equation ex+x=0 is
Answer» The number of real solution(s) of the equation $e^{x} + x = 0$ is

Discussion

3.	Let N=26.55.76.107, then the total number of even factors of N is
Answer» Let $N = 2^{6} {.5}^{5} {.7}^{6} {.10}^{7}$ , then the total number of even factors of $N$ is

Discussion

4.	find the slope of the tangent to the curve y = 3x^2+2x+1 at x=2
Answer» find the slope of the tangent to the curve y = 3x^2+2x+1 at x=2

Discussion

5.	J 04(x e2X)dx
Answer» J 04(x e2X)dx

Discussion

6.	Find the equation of the normal at thepoint (am2, am3) for the curveay2 = x3.
Answer» Find the equation of the normal at the point (am², am³) for the curve ay² = x³.

Discussion

7.	If A and B are two events, then the probability of occurrence of A only is _______________.
Answer» If A and B are two events, then the probability of occurrence of A only is _______________.

Discussion

8.	Who is Jenifer's aunt?
Answer» Who is Jenifer's aunt?

8.

Who is Jenifer's aunt?

Answer»

Who is Jenifer's aunt?

Discussion

9.	Differentiate sin xx using the first principle.
Answer» Differentiate $\frac{s i n x}{x}$ using the first principle.

Discussion

10.	How to take antilog?
Answer» How to take antilog?

Discussion

11.	Solve 3-4x≥9 [NCERT EXEMPLAR]
Answer» Solve $\|3 - 4 x\| \geq 9$ [NCERT EXEMPLAR]

Discussion

12.	20. If f(x) is thrice differentiable function such that f(k)=-2, f(m)=-2 , f(l)=1,f(n)=3 and f(p)=-2,where k
Answer» 20. If f(x) is thrice differentiable function such that f(k)=-2, f(m)=-2 , f(l)=1,f(n)=3 and f(p)=-2,where k

Discussion

13.	38. Sin1by2cos inverse x equals 1 find x
Answer» 38. Sin1by2cos inverse x equals 1 find x

Discussion

14.	The centers of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the midpoint of the line segment joining the centers of C1 and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then find the radius of circle C.___
Answer» The centers of two circles $C_{1} a n d C_{2}$ each of unit radius are at a distance of 6 units from each other. Let P be the midpoint of the line segment joining the centers of $C_{1}$ and $C_{2}$ and $C$ be a circle touching circles $C_{1}$ and $C_{2}$ externally. If a common tangent to $C_{1} a n d C$ passing through P is also a common tangent to $C_{2} a n d C$ , then find the radius of circle C.___

Discussion

15.	There are three coins. One is two-headed coin (having head on both faces), another is biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tail 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin? [CBSE 2014]
Answer» There are three coins. One is two-headed coin (having head on both faces), another is biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tail 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin? [CBSE 2014]

Discussion

16.	If cosec x+cot x=112, then tan x =(a) 2122(b) 1516(c) 44117(d) 11744
Answer» If $cosec x + \cot x = \frac{11}{2}$ , then tan x = (a) $\frac{21}{22}$ (b) $\frac{15}{16}$ (c) $\frac{44}{117}$ (d) $\frac{117}{44}$

Discussion

17.	The focal distances of points on the parabola y2 = 16x whose ordinate is twice the abscissa, is __________.
Answer» The focal distances of points on the parabola y² = 16x whose ordinate is twice the abscissa, is __________.

Discussion

18.	If f(9)=9 and f′(9)=4, then limx→9√f(x)−3√x−3=
Answer» If $f (9) = 9$ and $f^{'} (9) = 4,$ then $lim x \to 9 \frac{\sqrt{f (x)} - 3}{\sqrt{x} - 3} =$

Discussion

19.	Y = f( 1 /x) and f'(x) = sin( x ^2) then dy/dx is
Answer» Y = f( 1 /x) and f'(x) = sin( x ^2) then dy/dx is

Discussion

20.	The value of 3∫2dxx2−1 is:
Answer» The value of $3 \int 2 \frac{d x}{x^{2} - 1}$ is:

Discussion

21.	Let ABC and PQR be any two triangles in the same plane. Assume that the perpendiculars from the points A,B,C to the sides QR,RP,PQ respectively are concurrent. Using vector methods or otherwise, prove that the perpendiculars from P,Q,R to BC,CA,AB respectively are also concurrent.
Answer» Let $A B C$ and $P Q R$ be any two triangles in the same plane. Assume that the perpendiculars from the points $A, B, C$ to the sides $Q R, R P, P Q$ respectively are concurrent. Using vector methods or otherwise, prove that the perpendiculars from $P, Q, R$ to $B C, C A, A B$ respectively are also concurrent.

Discussion

22.	If tan(α−β)=sin 2β3−cos2β,then
Answer» If $t a n (α - β) = \frac{s i n 2 β}{3 - c o s 2 β}$ ,then

Discussion

23.	ABCD is a parallelogram. P, Q and R are the mid-points of AB, AC and BC respectively. If the coordinates of the vertices A, D and C are (l, n) (0, 0) and (m, 0) respectively, then find the sum of the abscissas of points P, Q and R.
Answer» ABCD is a parallelogram. P, Q and R are the mid-points of AB, AC and BC respectively. If the coordinates of the vertices A, D and C are (l, n) (0, 0) and (m, 0) respectively, then find the sum of the abscissas of points P, Q and R.

Discussion

24.	Given a function g continuous on R such that 1∫0g(t)dt=2 and g(1)=5. If f(x)=12x∫0(x−t)2g(t)dt, then the value of (f′′′(1)−f′′(1)) is equal to
Answer» Given a function $g$ continuous on $R$ such that $1 \int 0 g (t) d t = 2$ and $g (1) = 5.$ If $f (x) = \frac{1}{2} x \int 0 (x - t)^{2} g (t) d t,$ then the value of $(f^{'''} (1) - f^{''} (1))$ is equal to

Discussion

25.	Tangents are drawn from the point (4,2) to the curve x2+9y2=9, then the tangent of acute angle between the tangents is
Answer» Tangents are drawn from the point $(4, 2)$ to the curve $x^{2} + 9 y^{2} = 9,$ then the tangent of acute angle between the tangents is

Discussion

26.	TIT, put x=門x2 + x3
Answer» TIT, put x=門x2 + x3

Discussion

27.	Characteristic equation for the matrix A=[1234] is
Answer» Characteristic equation for the matrix $A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$ is

Discussion

28.	Evaluate the given limit limx→3(x+3)
Answer» Evaluate the given limit $lim x \to 3 (x + 3)$

Discussion

29.	An experiment consists of recording boy-girl composition of families with 2 children. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births? (ii) What is the sample space if we are interested in the number of girls in the family?
Answer» An experiment consists of recording boy-girl composition of families with 2 children. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births? (ii) What is the sample space if we are interested in the number of girls in the family?

Discussion

30.	Integrate the rational functions. ∫x(x−1)2(x+2)dx.
Answer» Integrate the rational functions. $\int \frac{x}{(x - 1)^{2} (x + 2)} d x .$

Discussion

31.	The differential equation obtained by eliminating the arbitrary constants a and b in y=a cos(nx+b) is
Answer» The differential equation obtained by eliminating the arbitrary constants a and b in $y = a c o s (n x + b)$ is

Discussion

32.	If K is the coefficient of x4 in the expansion of (1+x+ax2)10, then the absolute value of a for which K is minimum, is
Answer» If $K$ is the coefficient of $x^{4}$ in the expansion of $(1 + x + a x^{2})^{10}$ , then the absolute value of $a$ for which $K$ is minimum, is

Discussion

33.	The area bounded by y=x2, y=[x+1], x≤1 and the y-axis, where [.] represents the greatest integer function, is
Answer» The area bounded by $y = x^{2},$ $y = [x + 1],$ $x \leq 1$ and the $y$ -axis, where $[.]$ represents the greatest integer function, is

Discussion

34.	If ⎡⎢⎣11x1−x1x−1−1⎤⎥⎦ has no inverse, then the real value of \|x\| is
Answer» If $⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & x 1 & - x & 1 x & - 1 & - 1 \end{matrix} ⎤ ⎥ ⎦$ has no inverse, then the real value of $\| x \|$ is

Discussion

35.	The straight lines x+2y-9=0, 3x+5y-5=0 and ax+by-1=0 are concurrent if the straight line 22x-35y-1=0 passes through the point
Answer» The straight lines x+2y-9=0, 3x+5y-5=0 and ax+by-1=0 are concurrent if the straight line 22x-35y-1=0 passes through the point

Discussion

36.	{3x^2+7xy+2y^2+5x+5y+2=0} Find equation of the lines
Answer» {3x^2+7xy+2y^2+5x+5y+2=0} Find equation of the lines

Discussion

37.	If e1 is the eccentricity of the conic 9x2+4y2=36 and e2 is the eccentricity of the conic 9x2−4y2=36,then
Answer» $I f e_{1} i s t h e e c c e n t r i c i t y o f t h e c o n i c 9 x^{2} + 4 y^{2} = 36 a n d e^{2} i s t h e e c c e n t r i c i t y o f t h e c o n i c 9 x^{2} - 4 y^{2} = 36, t h e n$

Discussion

38.	If the circle x2+y2−4x−8y+16=0 rolls up (away from x−axis) along the tangent to it at (2+√3,3) by 2 units and its equation in the new position is x2+y2+2ax+2by+c=0, then the value of a2+8b+c is equal to
Answer» If the circle $x^{2} + y^{2} - 4 x - 8 y + 16 = 0$ rolls up (away from $x -$ axis) along the tangent to it at $(2 + \sqrt{3}, 3)$ by $2$ units and its equation in the new position is $x^{2} + y^{2} + 2 a x + 2 b y + c = 0,$ then the value of $a^{2} + 8 b + c$ is equal to

Discussion

39.	The domain for which the functions f(x) = 3x2 −1 and g(x) = 3 + x are equal is __________ .
Answer» The domain for which the functions f(x) = 3x² −1 and g(x) = 3 + x are equal is __________ .

Discussion

40.	If a+b+c is not equal to 0,then prove that a^3+b^{3 }+c^3=3abc,only when a=b=c
Answer» If a+b+c is not equal to 0,then prove that a^3+b^{3 }+c^3=3abc,only when a=b=c

Discussion

41.	The value of the determinant sin Acos Asin A+cos Bsin Bcos Asin B+cos Bsin Ccos Asin C+cos B is ________________.
Answer» The value of the determinant $\|\begin{matrix} \sin A & \cos A & \sin A + \cos B \\ \sin B & \cos A & \sin B + \cos B \\ \sin C & \cos A & \sin C + \cos B \end{matrix}\|$ is ________________.

Discussion

42.	FInd the equation of the tangent to the curve y=√3x−2 which is parallel to the line 4x-2y+5=0
Answer» FInd the equation of the tangent to the curve $y = \sqrt{3 x - 2}$ which is parallel to the line 4x-2y+5=0

Discussion

43.	Draw a venn diagram of A∪B
Answer» Draw a venn diagram of $A \cup B$

Discussion

44.	11-2211.y=cos
Answer» 11-2211.y=cos

Discussion

45.	The centre and radius of the circle 2x2+2y2−x=0 are
Answer» The centre and radius of the circle $2 x^{2} + 2 y^{2} - x = 0$ are

Discussion

46.	If the nth term an of a sequence is given by an=n2−n+1, write down its first five terms.
Answer» If the $n^{t h}$ term $a_{n}$ of a sequence is given by $a_{n} = n^{2} - n + 1$ , write down its first five terms.

Discussion

47.	Let tanA=p(p–1) and tanB=1(2p–1), if A,B∈(0,π/2) then A–B can be
Answer» Let $tan A = \frac{p}{(p - 1)}$ and $tan B = \frac{1}{(2 p - 1)},$ if $A, B \in (0, π / 2)$ then $A - B$ can be

Discussion

48.	limn→∞12+22+....+n2n3
Answer» ${lim}_{n \to \infty} \frac{1^{2} + 2^{2} + . . . . + n^{2}}{n^{3}}$

Discussion

49.	Find the slope, x-intercept & y-intercept of the straight line 2x - 3y + 5 = 0.
Answer» Find the slope, x-intercept & y-intercept of the straight line 2x - 3y + 5 = 0.

Discussion

50.	Evaluate the following integrals:∫1+x2x4dx
Answer» Evaluate the following integrals: $\int \frac{\sqrt{1 + x^{2}}}{x^{4}} d x$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

sinx31. (1+cos x

The number of real solution(s) of the equation ex+x=0 is

Let N=26.55.76.107, then the total number of even factors of N is

find the slope of the tangent to the curve y = 3x^2+2x+1 at x=2

J 04(x e2X)dx

Find the equation of the normal at thepoint (am2, am3) for the curveay2 = x3.

If A and B are two events, then the probability of occurrence of A only is _______________.

Who is Jenifer's aunt?

Differentiate sin xx using the first principle.

How to take antilog?

Solve 3-4x≥9 [NCERT EXEMPLAR]

20. If f(x) is thrice differentiable function such that f(k)=-2, f(m)=-2 , f(l)=1,f(n)=3 and f(p)=-2,where k

38. Sin1by2cos inverse x equals 1 find x

If cosec x+cot x=112, then tan x =(a) 2122(b) 1516(c) 44117(d) 11744

The focal distances of points on the parabola y2 = 16x whose ordinate is twice the abscissa, is __________.

If f(9)=9 and f′(9)=4, then limx→9√f(x)−3√x−3=

Y = f( 1 /x) and f'(x) = sin( x ^2) then dy/dx is

The value of 3∫2dxx2−1 is:

Let ABC and PQR be any two triangles in the same plane. Assume that the perpendiculars from the points A,B,C to the sides QR,RP,PQ respectively are concurrent. Using vector methods or otherwise, prove that the perpendiculars from P,Q,R to BC,CA,AB respectively are also concurrent.

If tan(α−β)=sin 2β3−cos2β,then

ABCD is a parallelogram. P, Q and R are the mid-points of AB, AC and BC respectively. If the coordinates of the vertices A, D and C are (l, n) (0, 0) and (m, 0) respectively, then find the sum of the abscissas of points P, Q and R.

Given a function g continuous on R such that 1∫0g(t)dt=2 and g(1)=5. If f(x)=12x∫0(x−t)2g(t)dt, then the value of (f′′′(1)−f′′(1)) is equal to

Tangents are drawn from the point (4,2) to the curve x2+9y2=9, then the tangent of acute angle between the tangents is

TIT, put x=門x2 + x3

Characteristic equation for the matrix A=[1234] is

Evaluate the given limit limx→3(x+3)

An experiment consists of recording boy-girl composition of families with 2 children. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births? (ii) What is the sample space if we are interested in the number of girls in the family?

Integrate the rational functions. ∫x(x−1)2(x+2)dx.

The differential equation obtained by eliminating the arbitrary constants a and b in y=a cos(nx+b) is

If K is the coefficient of x4 in the expansion of (1+x+ax2)10, then the absolute value of a for which K is minimum, is

The area bounded by y=x2, y=[x+1], x≤1 and the y-axis, where [.] represents the greatest integer function, is

If ⎡⎢⎣11x1−x1x−1−1⎤⎥⎦ has no inverse, then the real value of |x| is​​​​​​​

The straight lines x+2y-9=0, 3x+5y-5=0 and ax+by-1=0 are concurrent if the straight line 22x-35y-1=0 passes through the point

{3x^2+7xy+2y^2+5x+5y+2=0} Find equation of the lines

If e1 is the eccentricity of the conic 9x2+4y2=36 and e2 is the eccentricity of the conic 9x2−4y2=36,then

If the circle x2+y2−4x−8y+16=0 rolls up (away from x−axis) along the tangent to it at (2+√3,3) by 2 units and its equation in the new position is x2+y2+2ax+2by+c=0, then the value of a2+8b+c is equal to

The domain for which the functions f(x) = 3x2 −1 and g(x) = 3 + x are equal is __________ .

If a+b+c is not equal to 0,then prove that a^3+b^{3 }+c^3=3abc,only when a=b=c

The value of the determinant sin Acos Asin A+cos Bsin Bcos Asin B+cos Bsin Ccos Asin C+cos B is ________________.

FInd the equation of the tangent to the curve y=√3x−2 which is parallel to the line 4x-2y+5=0

Draw a venn diagram of A∪B

11-2211.y=cos

The centre and radius of the circle 2x2+2y2−x=0 are

If the nth term an of a sequence is given by an=n2−n+1, write down its first five terms.

Let tanA=p(p–1) and tanB=1(2p–1), if A,B∈(0,π/2) then A–B can be

limn→∞12+22+....+n2n3

Find the slope, x-intercept &amp; y-intercept of the straight line 2x - 3y + 5 = 0.

Evaluate the following integrals:∫1+x2x4dx

If ⎡⎢⎣11x1−x1x−1−1⎤⎥⎦ has no inverse, then the real value of |x| is

Find the slope, x-intercept & y-intercept of the straight line 2x - 3y + 5 = 0.