43030 + Interview Questions in Mathematics

1.	If f(x)=⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩sin(a+2)x+sinxx,x<0b ,x=0(x+3x2)1/3−x1/3x4/3,x>0 is continuous at x=0, then the value of a+2b is
Answer» If $f (x) = ⎧ ⎪⎪⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎪⎪ ⎩ \begin{matrix} \frac{sin (a + 2) x + sin x}{x}, & x < 0 b, & x = 0 \frac{(x + 3 x^{2})^{1 / 3} - x^{1 / 3}}{x^{4 / 3}}, & x > 0 \end{matrix}$ is continuous at $x = 0,$ then the value of $a + 2 b$ is

Discussion

2.	If the adjacent sides of a parallelogram are represented by 2x2−5xy+3y2=0 and the equation of one diagonal is x+y−2=0, then the equation of the other diagonal is
Answer» If the adjacent sides of a parallelogram are represented by $2 x^{2} - 5 x y + 3 y^{2} = 0$ and the equation of one diagonal is $x + y - 2 = 0,$ then the equation of the other diagonal is

Discussion

3.	Find the anti-derivative (or integral) of the following by the method of inspection. sin 2x.
Answer» Find the anti-derivative (or integral) of the following by the method of inspection. sin 2x.

Discussion

4.	If x,y,z are real numbers such that x+y+z=4 and x2+y2+z2=6, then the range of x is
Answer» If $x, y, z$ are real numbers such that $x + y + z = 4$ and $x^{2} + y^{2} + z^{2} = 6,$ then the range of $x$ is

Discussion

5.	Find the domain of f(x)=(x^2-\|x\|-2)^1/2+(-x^2+16)^1/2
Answer» Find the domain of f(x)=(x^2-\|x\|-2)^1/2+(-x^2+16)^1/2

Discussion

6.	If 3x=4y=12z ,then prove that (x+y)z=xy.
Answer» If 3^x=4^y=12^z ,then prove that (x+y)z=xy.

Discussion

7.	Find the wrong number in the given series .768,96,16,8,2
Answer» Find the wrong number in the given series . 768,96,16,8,2

Discussion

8.	Find the angle between pair of tangents drawn from point (3,2) to the circle x^2+y^2-6x+4y-2=0
Answer» Find the angle between pair of tangents drawn from point (3,2) to the circle x^2+y^2-6x+4y-2=0

Discussion

9.	Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.
Answer» Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.

Discussion

10.	Prove that the greatest integer function defined by is not differentiable at x = 1 and x = 2.
Answer» Prove that the greatest integer function defined by is not differentiable at x = 1 and x = 2.

Discussion

11.	Length of tangent drawn from any point of circle x2+y2+2gx+2fy+c=0 to the circle x2+y2+2gx+2fy+d=0, (d > c) is
Answer» Length of tangent drawn from any point of circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ to the circle $x^{2} + y^{2} + 2 g x + 2 f y + d = 0$ , (d > c) is

Discussion

12.	what is the Lewis dot structure of P2O5
Answer» what is the Lewis dot structure of P2O5

Discussion

13.	The angle(s) formed by the positive y−axis and the tangent to y=x2+4x−17 at (52,−34) is(are)
Answer» The angle(s) formed by the positive $y -$ axis and the tangent to $y = x^{2} + 4 x - 17$ at $(\frac{5}{2}, \frac{- 3}{4})$ is(are)

Discussion

14.	A descending gradient of 4% meets an ascending grade of 1 in 40 where a valley curve of length 200 m is to be formed.The distance of the lowest point on the valley curve from its first tangent point will be
Answer» A descending gradient of 4% meets an ascending grade of 1 in 40 where a valley curve of length 200 m is to be formed.The distance of the lowest point on the valley curve from its first tangent point will be

Discussion

15.	The domain of the function f(x)=√1−\|x\|\|x\|−2 is
Answer» The domain of the function $f (x) = \sqrt{\frac{1 - \| x \|}{\| x \| - 2}}$ is

Discussion

16.	if f(x)=a^x/a^x+√a then find f(x)+f(1-x)?
Answer» if f(x)=a^x/a^x+√a then find f(x)+f(1-x)?

Discussion

17.	How many outcomes are there in the sample space of throwing two dice?___
Answer» How many outcomes are there in the sample space of throwing two dice? ___

Discussion

18.	Find the values of p so the line and are at right angles.
Answer» Find the values of p so the line and are at right angles.

Discussion

19.	If the line 3x+4y=7 is a normal at a point P=(x1,y1) of the hyperbola 3x2−4y2=1, then the distance of P from the origin is
Answer» If the line $3 x + 4 y = 7$ is a normal at a point $P = (x_{1}, y_{1})$ of the hyperbola $3 x^{2} - 4 y^{2} = 1,$ then the distance of $P$ from the origin is

Discussion

20.	Which of the following lines have the intercepts of equal lengths made by the circle x2+y2−2x+4y=0 is/are
Answer» Which of the following lines have the intercepts of equal lengths made by the circle $x^{2} + y^{2} - 2 x + 4 y = 0$ is/are

Discussion

21.	Find the equation ofthe plane passing through (a, b, c) and parallelto the plane
Answer» Find the equation of the plane passing through (a, b, c) and parallel to the plane

Discussion

22.	Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX − plane.
Answer» Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX − plane.

Discussion

23.	The domain and range of the function f given by f(x) = 2 − \|x − 5\|, is(a) Domain = R+, Range = (−∞, 1](b) Domain = R, Range = (−∞, 2](c) Domain =R, Range = (−∞, 2)(d) Domain = R+, Range = (−∞, 2]
Answer» The domain and range of the function f given by f(x) = 2 − \|x − 5\|, is (a) Domain = R⁺, Range = (−∞, 1] (b) Domain = R, Range = (−∞, 2] (c) Domain =R, Range = (−∞, 2) (d) Domain = R⁺, Range = (−∞, 2]

Discussion

24.	Determine whether the following relation is reflexive, transitive and symmetric : R = {(x,y) : x and y work at the same place }
Answer» Determine whether the following relation is reflexive, transitive and symmetric : R = {(x,y) : x and y work at the same place }

Discussion

25.	If g(x)=10x−6 is concave upward, then which of the following is true
Answer» If $g (x) = \frac{10}{x - 6}$ is concave upward, then which of the following is true

Discussion

26.	The equation of normal to the curve x3+y3=8xyat the point where it meets the curve y2=4x other than origin is
Answer» The equation of normal to the curve $x^{3} + y^{3} = 8 x y$ at the point where it meets the curve $y^{2} = 4 x$ other than origin is

Discussion

27.	a swimmer crosses a flowing river of width d to and from in time t_{1 }.The time taken to cover the same dis†an ce up and down stream is t_{2.}If t_3is the time the swimmer would take to ewim a dis†an ce 2d in still water. then a.t_2^2=t_1t_3 b.t_3 =t_{1.}\ast t_2 c.t_1=t_2\ast t_3 d.t_3t_1+t_2
Answer» a swimmer crosses a flowing river of width d to and from in time t_{1 }.The time taken to cover the same dis†an ce up and down stream is t_{2.}If t_3is the time the swimmer would take to ewim a dis†an ce 2d in still water. then a.t_2^2=t_1t_3 b.t_3 =t_{1.}\ast t_2 c.t_1=t_2\ast t_3 d.t_3t_1+t_2

Discussion

28.	Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
Answer» Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

Discussion

29.	Product of the roots of the equation x² + 3\|x\| - 28 = 0 is
Answer» Product of the roots of the equation x² + 3\|x\| - 28 = 0 is

Discussion

30.	In the expansion of (1 + a ) m + n , prove that coefficients of a m and a n are equal.
Answer» In the expansion of (1 + a ) m + n , prove that coefficients of a m and a n are equal.

Discussion

31.	Let f:R→R be a function defined by f(x)=max{x, x3}. Then the set of all points where f is not differentiable, is
Answer» Let $f : R \to R$ be a function defined by $f (x) = max {x, x^{3}} .$ Then the set of all points where $f$ is not differentiable, is

Discussion

32.	Question 77Fill in the blanks to make the statements true.A rhombus is a parallelogram in which ___ sides are equal.
Answer» Question 77 Fill in the blanks to make the statements true. A rhombus is a parallelogram in which ___ sides are equal.

Discussion

33.	If →a=(^i+^j+^k)→a.→b=1and →a×→b=^j−^kThen \|→b\| = __
Answer» If $\to a = (^i +^j +^k)$ $\to a . \to b = 1$ and $\to a \times \to b =^j -^k$ Then $\| \to b \|$ = __

Discussion

34.	If α and β are the roots of the equation x2+3x+1=0, then the value of (α1+β)2+(βα+1)2 is equal to
Answer» If $α$ and $β$ are the roots of the equation $x^{2} + 3 x + 1 = 0$ , then the value of ${(\frac{α}{1 + β})}^{2} + {(\frac{β}{α + 1})}^{2}$ is equal to

Discussion

35.	Why can't we have negative bases in logarithm? We can for an equation (-3)^3=-27 therefore log(-27) with base -3 is 3. That way log of some negative numbers can be defined
Answer» Why can't we have negative bases in logarithm? We can for an equation (-3)^3=-27 therefore log(-27) with base -3 is 3. That way log of some negative numbers can be defined

Discussion

36.	\log_3x^3/3-2\log_33x^3=a-b\log_3x, then find the value of a+b
Answer» \log_3x^3/3-2\log_33x^3=a-b\log_3x, then find the value of a+b

Discussion

37.	A circle with centre at the origin and radius equal to a meets the axis of x and A and B. P(α) and Q(β) are two points on this circle so that α−β=2γ, where γ is a constant. The locus of the point of intersection of AP and BQ is
Answer» A circle with centre at the origin and radius equal to a meets the axis of x and A and B. $P (α)$ and $Q (β)$ are two points on this circle so that $α - β = 2 γ$ , where $γ$ is a constant. The locus of the point of intersection of AP and BQ is

Discussion

38.	Find the standard deviation for the following data : (i)x:38131823f:71015106 (ii)x:234567f:491614116
Answer» Find the standard deviation for the following data : (i) $\begin{matrix} x : & 3 & 8 & 13 & 18 & 23 f : & 7 & 10 & 15 & 10 & 6 \end{matrix}$ (ii) $\begin{matrix} x : & 2 & 3 & 4 & 5 & 6 & 7 f : & 4 & 9 & 16 & 14 & 11 & 6 \end{matrix}$

38.

Find the standard deviation for the following data : (i)x:38131823f:71015106 (ii)x:234567f:491614116

Answer»

Find the standard deviation for the following data :

(i) $\begin{matrix} x : & 3 & 8 & 13 & 18 & 23 f : & 7 & 10 & 15 & 10 & 6 \end{matrix}$

(ii) $\begin{matrix} x : & 2 & 3 & 4 & 5 & 6 & 7 f : & 4 & 9 & 16 & 14 & 11 & 6 \end{matrix}$

Discussion

39.	If sin3θ+sin3(θ+2π3)+sin3(θ+4π3)=asinbθ, then the value of ∣∣∣ba∣∣∣ is
Answer» If ${sin}^{3} θ + {sin}^{3} (θ + \frac{2 π}{3}) + {sin}^{3} (θ + \frac{4 π}{3}) = a sin b θ,$ then the value of $∣ ∣ ∣ \frac{b}{a} ∣ ∣ ∣$ is

Discussion

40.	The number of polynomial functions f of degree ≥ 1 satisfying f(x2) = (f (x)) 2 = f (f(x)) is
Answer» The number of polynomial functions f of degree ≥ 1 satisfying f(x²) = (f (x))² = f (f(x)) is

Discussion

41.	Let R be a relation from N to N defined by R = {( a , b ): a , b ∈ N and a = b 2 }. Are the following true? (i) ( a , a ) ∈ R, for all a ∈ N (ii) ( a , b ) ∈ R, implies ( b , a ) ∈ R (iii) ( a , b ) ∈ R, ( b , c ) ∈ R implies ( a , c ) ∈ R. Justify your answer in each case.
Answer» Let R be a relation from N to N defined by R = {( a , b ): a , b ∈ N and a = b 2 }. Are the following true? (i) ( a , a ) ∈ R, for all a ∈ N (ii) ( a , b ) ∈ R, implies ( b , a ) ∈ R (iii) ( a , b ) ∈ R, ( b , c ) ∈ R implies ( a , c ) ∈ R. Justify your answer in each case.

Discussion

42.	If the range of x2+x+dx2+2x+d is [56,32] for all real x, then the value of d is
Answer» If the range of $\frac{x^{2} + x + d}{x^{2} + 2 x + d}$ is $[\frac{5}{6}, \frac{3}{2}]$ for all real $x$ , then the value of $d$ is

Discussion

43.	how to find domain of sinx / 1+sinx
Answer» how to find domain of sinx / 1+sinx

Discussion

44.	The differential equation whose general solution is given by, y = (c1 cos(x+c2))−(c3e−x+c4)+(c5 sin x), where c1,c2,c3,c4,c5 are arbitrary constants, is
Answer» The differential equation whose general solution is given by, y = $(c_{1} c o s (x + c_{2})) - (c_{3} e^{- x + c_{4}}) + (c_{5} s i n x)$ , where $c_{1}, c_{2}, c_{3}, c_{4}, c_{5}$ are arbitrary constants, is

Discussion

45.	Find the domain of the given function f(x)=√a^2-x^2 ,a>0
Answer» Find the domain of the given function f(x)=√a^2-x^2 ,a>0

Discussion

46.	Prove that the function f(x) = log (2x-1) notderivable at x=0.
Answer» Prove that the function f(x) = log (2x-1) notderivable at x=0.

Discussion

47.	How many trivial relations can be formed on a set which has 64 elements? __
Answer» How many trivial relations can be formed on a set which has 64 elements? __

Discussion

48.	limx→∞sin(2+√3)nπ(2−√3)n(nϵN)=
Answer» $l i m x \to \infty \frac{s i n (2 + \sqrt{3})^{n} π}{(2 - \sqrt{3})^{n}} (n ϵ N) =$

Discussion

49.	19. Point of contact of line y x+4\sqrt2 to the circle x^2+y^2=16 i
Answer» 19. Point of contact of line y x+4\sqrt2 to the circle x^2+y^2=16 i

Discussion

50.	If x=3cosθ−cos3θ and y=3sinθ−sin3θ, then dydx is
Answer» If $x = 3 cos θ - cos 3 θ$ and $y = 3 sin θ - sin 3 θ,$ then $\frac{d y}{d x}$ is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If f(x)=⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩sin(a+2)x+sinxx,x&lt;0b ,x=0(x+3x2)1/3−x1/3x4/3,x&gt;0 is continuous at x=0, then the value of a+2b is

If the adjacent sides of a parallelogram are represented by 2x2−5xy+3y2=0 and the equation of one diagonal is x+y−2=0, then the equation of the other diagonal is

Find the anti-derivative (or integral) of the following by the method of inspection. sin 2x.

If x,y,z are real numbers such that x+y+z=4 and x2+y2+z2=6, then the range of x is

Find the domain of f(x)=(x^2-|x|-2)^1/2+(-x^2+16)^1/2

If 3x=4y=12z ,then prove that (x+y)z=xy.

Find the wrong number in the given series .768,96,16,8,2

Find the angle between pair of tangents drawn from point (3,2) to the circle x^2+y^2-6x+4y-2=0

Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.

Prove that the greatest integer function defined by is not differentiable at x = 1 and x = 2.

Length of tangent drawn from any point of circle x2+y2+2gx+2fy+c=0 to the circle x2+y2+2gx+2fy+d=0, (d &gt; c) is

what is the Lewis dot structure of P2O5

The angle(s) formed by the positive y−axis and the tangent to y=x2+4x−17 at (52,−34) is(are)

A descending gradient of 4% meets an ascending grade of 1 in 40 where a valley curve of length 200 m is to be formed.The distance of the lowest point on the valley curve from its first tangent point will be

The domain of the function f(x)=√1−|x||x|−2 is

if f(x)=a^x/a^x+√a then find f(x)+f(1-x)?

How many outcomes are there in the sample space of throwing two dice?___

Find the values of p so the line and are at right angles.

If the line 3x+4y=7 is a normal at a point P=(x1,y1) of the hyperbola 3x2−4y2=1, then the distance of P from the origin is

Which of the following lines have the intercepts of equal lengths made by the circle x2+y2−2x+4y=0 is/are

Find the equation ofthe plane passing through (a, b, c) and parallelto the plane

Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX − plane.

The domain and range of the function f given by f(x) = 2 − |x − 5|, is(a) Domain = R+, Range = (−∞, 1](b) Domain = R, Range = (−∞, 2](c) Domain =R, Range = (−∞, 2)(d) Domain = R+, Range = (−∞, 2]

Determine whether the following relation is reflexive, transitive and symmetric : R = {(x,y) : x and y work at the same place }

If g(x)=10x−6 is concave upward, then which of the following is true

The equation of normal to the curve x3+y3=8xyat the point where it meets the curve y2=4x other than origin is

a swimmer crosses a flowing river of width d to and from in time t_{1 }.The time taken to cover the same dis†an ce up and down stream is t_{2.}If t_3is the time the swimmer would take to ewim a dis†an ce 2d in still water. then a.t_2^2=t_1t_3 b.t_3 =t_{1.}\ast t_2 c.t_1=t_2\ast t_3 d.t_3t_1+t_2

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

Product of the roots of the equation x² + 3|x| - 28 = 0 is

In the expansion of (1 + a ) m + n , prove that coefficients of a m and a n are equal.

Let f:R→R be a function defined by f(x)=max{x, x3}. Then the set of all points where f is not differentiable, is

Question 77Fill in the blanks to make the statements true.A rhombus is a parallelogram in which ___ sides are equal.

If →a=(^i+^j+^k)→a.→b=1and →a×→b=^j−^kThen |→b| = __

If α and β are the roots of the equation x2+3x+1=0, then the value of (α1+β)2+(βα+1)2 is equal to

Why can't we have negative bases in logarithm? We can for an equation (-3)^3=-27 therefore log(-27) with base -3 is 3. That way log of some negative numbers can be defined

\log_3x^3/3-2\log_33x^3=a-b\log_3x, then find the value of a+b

A circle with centre at the origin and radius equal to a meets the axis of x and A and B. P(α) and Q(β) are two points on this circle so that α−β=2γ, where γ is a constant. The locus of the point of intersection of AP and BQ is

Find the standard deviation for the following data : (i)x:38131823f:71015106 (ii)x:234567f:491614116

If sin3θ+sin3(θ+2π3)+sin3(θ+4π3)=asinbθ, then the value of ∣∣∣ba∣∣∣ is

The number of polynomial functions f of degree ≥ 1 satisfying f(x2) = (f (x)) 2 = f (f(x)) is

Let R be a relation from N to N defined by R = {( a , b ): a , b ∈ N and a = b 2 }. Are the following true? (i) ( a , a ) ∈ R, for all a ∈ N (ii) ( a , b ) ∈ R, implies ( b , a ) ∈ R (iii) ( a , b ) ∈ R, ( b , c ) ∈ R implies ( a , c ) ∈ R. Justify your answer in each case.

If the range of x2+x+dx2+2x+d is [56,32] for all real x, then the value of d is

how to find domain of sinx / 1+sinx

The differential equation whose general solution is given by, y = (c1 cos(x+c2))−(c3e−x+c4)+(c5 sin x), where c1,c2,c3,c4,c5 are arbitrary constants, is

Find the domain of the given function f(x)=√a^2-x^2 ,a>0

Prove that the function f(x) = log (2x-1) notderivable at x=0.

How many trivial relations can be formed on a set which has 64 elements? __

limx→∞sin(2+√3)nπ(2−√3)n(nϵN)=

19. Point of contact of line y x+4\sqrt2 to the circle x^2+y^2=16 i

If x=3cosθ−cos3θ and y=3sinθ−sin3θ, then dydx is

If f(x)=⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩sin(a+2)x+sinxx,x<0b ,x=0(x+3x2)1/3−x1/3x4/3,x>0 is continuous at x=0, then the value of a+2b is

Length of tangent drawn from any point of circle x2+y2+2gx+2fy+c=0 to the circle x2+y2+2gx+2fy+d=0, (d > c) is