43030 + Interview Questions in Mathematics

1.	Evaluate I=∫ex(1+sinx)+e−x(1−sinx)1+cosxdx
Answer» Evaluate $I = \int \frac{e^{x} (1 + sin x) + e^{- x} (1 - sin x)}{1 + cos x} d x$

Discussion

2.	1 – cotxsinxcosx equals
Answer» 1 – cotxsinxcosx equals

Discussion

3.	Let a,b,c (not all equal) be the sides of traingle ABC and if the roots of the equation a(b−c)x2+b(c−a)x+c(a−b)=0 are equal, then sin2A2,sin2B2,sin2C2 are in:
Answer» Let $a, b, c$ (not all equal) be the sides of traingle $A B C$ and if the roots of the equation $a (b - c) x^{2} + b (c - a) x + c (a - b) = 0$ are equal, then ${sin}^{2} \frac{A}{2}, {sin}^{2} \frac{B}{2}, {sin}^{2} \frac{C}{2}$ are in:

Discussion

4.	Insert GM between 0.008 and 0.2
Answer» Insert GM between 0.008 and 0.2

Discussion

5.	−5(x+3)>x+7+6x Which of the following best describe the solutions to the inequality shown above?
Answer» $- 5 (x + 3) > x + 7 + 6 x$ Which of the following best describe the solutions to the inequality shown above?

Discussion

6.	If radius of the circumcircle of the triangle formed by the lines x2−y2=0 and 2x−3y=5 is a units, then value of a2 is
Answer» If radius of the circumcircle of the triangle formed by the lines $x^{2} - y^{2} = 0$ and $2 x - 3 y = 5$ is $a$ units, then value of $a^{2}$ is

Discussion

7.	Prove the following identities (1-16)cosec x-sin x sec x-cos x tan x+cot x=1
Answer» Prove the following identities (1-16) $(cosec x - \sin x) (\sec x - \cos x) (\tan x + \cot x) = 1$

Discussion

8.	Prove that the line x+y=3a touches the curve x+y=3axy and also show that the point of contact is ( 1.5a, 1.5a).
Answer» Prove that the line x+y=3a touches the curve x+y=3axy and also show that the point of contact is ( 1.5a, 1.5a).

Discussion

9.	Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 30∘ with the positive direction of y-axis measured anticlockwise.
Answer» Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of $30^{\circ}$ with the positive direction of y-axis measured anticlockwise.

Discussion

10.	All possible values of θ∈[0,2π] for which sin2θ+tan2θ>0 lie in :
Answer» All possible values of $θ \in [0, 2 π]$ for which $sin 2 θ + tan 2 θ > 0$ lie in :

Discussion

11.	If ∫(2x+3)(x2−3x+1)dx(x4−7x2+1)(1+ln(1+3x+x2))=f(x)+C, where C is constant and f(0)=0, then
Answer» If $\int \frac{(2 x + 3) (x^{2} - 3 x + 1) d x}{(x^{4} - 7 x^{2} + 1) (1 + ln (1 + 3 x + x^{2}))} = f (x) + C,$ where $C$ is constant and $f (0) = 0,$ then

Discussion

12.	3/2∫0\|xcosπx\|dx equals to
Answer» $3 / 2 \int 0 \| x cos π x \| d x$ equals to

Discussion

13.	12.Vertices仕6, 0), foci ± 4,0)
Answer» 12.Vertices仕6, 0), foci ± 4,0)

Discussion

14.	Q117) The set of numerical coefficients that balancesthe equationK2CrO4 + HCl → K2Cr2O7 + kCl + H2O iskerala CEE 2001d) 2, 2, 1, 2, 1
Answer» Q117) The set of numerical coefficients that balances the equation K2CrO4 + HCl → K2Cr2O7 + kCl + H2O is kerala CEE 2001 d) 2, 2, 1, 2, 1

Discussion

15.	The median of the variables x+4,x−72,x−52,x−3,x−2,x+12x−12,x+5(x>0), is
Answer» The median of the variables $x + 4, x - \frac{7}{2}, x - \frac{5}{2}, x - 3, x - 2, x + \frac{1}{2}$ $x - \frac{1}{2}, x + 5 (x > 0)$ , is

Discussion

16.	If the radical axis of the circles x2+y2+2gx+2fy+c=0 and 2x2+2y2+3x+8y+2c=0 touches the circle x2+y2+2x+2y+1=0, then
Answer» If the radical axis of the circles $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ and $2 x^{2} + 2 y^{2} + 3 x + 8 y + 2 c = 0$ touches the circle $x^{2} + y^{2} + 2 x + 2 y + 1 = 0$ , then

Discussion

17.	Evaluate limx→0sin 5xtan 3x
Answer» Evaluate $l i m x \to 0 \frac{s i n 5 x}{t a n 3 x}$

Discussion

18.	21. I if the magnitude of two vectors are 3 and 4 and their scalar product is 6 then find the angle between them
Answer» 21. I if the magnitude of two vectors are 3 and 4 and their scalar product is 6 then find the angle between them

Discussion

19.	Find the number of words formed by permuting all the letters of the following words: (i) INDEPENDENCE (ii) INTERMEDIATE (iii) ARRANGE (iv) INDIA (v) PAKISTAN (vi) RUSSIA (vii) SERIES (viii) EXERCISES (ix) CONSTANTINOPLE
Answer» Find the number of words formed by permuting all the letters of the following words: (i) INDEPENDENCE (ii) INTERMEDIATE (iii) ARRANGE (iv) INDIA (v) PAKISTAN (vi) RUSSIA (vii) SERIES (viii) EXERCISES (ix) CONSTANTINOPLE

Discussion

20.	The area of the triangle whose sides are represented by the graphs of the equations y =x,x = 0 and x + y = 5, is (1) 6 sq. units(2) 6.25 sq. units,(3) 12.5 sq. units(4) 20 sq. units
Answer» The area of the triangle whose sides are represented by the graphs of the equations y =x,x = 0 and x + y = 5, is (1) 6 sq. units(2) 6.25 sq. units,(3) 12.5 sq. units(4) 20 sq. units

Discussion

21.	limx→0{log∈(1+x)x2+x−1x}is equal to
Answer» ${lim}_{x \to 0} {\frac{l o g_{\in} (1 + x)}{x^{2}} + \frac{x - 1}{x}} is equal to$

Discussion

22.	The sum of the intercepts on the axes of the tangent to the curve √x+√y=3 at (4,1) is
Answer» The sum of the intercepts on the axes of the tangent to the curve $\sqrt{x} + \sqrt{y} = 3$ at $(4, 1)$ is

Discussion

23.	The number of real roots of the equation (x²+2x)² - (x-1)² - 55 = 0
Answer» The number of real roots of the equation (x²+2x)² - (x-1)² - 55 = 0

Discussion

24.	In a vaccination drive, there are three types of vaccine A,B,C are available. If 30% population has taken dose of A but not B,35% has taken dose of B but not C,20% has taken dose of C but not A,45% has taken combination of exactly two. Then the percentage of population vaccinated through exactly one type of vaccine is :
Answer» In a vaccination drive, there are three types of vaccine $A, B, C$ are available. If $30 %$ population has taken dose of $A$ but not $B, 35 %$ has taken dose of $B$ but not $C, 20 %$ has taken dose of $C$ but not $A, 45 %$ has taken combination of exactly two. Then the percentage of population vaccinated through exactly one type of vaccine is :

Discussion

25.	The equation of the plane containing the line of intersection of the planes x+y+4z−6=0 and 2x+4y+5=0 and making an angle π4 with the plane x−z+5=0 is
Answer» The equation of the plane containing the line of intersection of the planes $x + y + 4 z - 6 = 0$ and $2 x + 4 y + 5 = 0$ and making an angle $\frac{π}{4}$ with the plane $x - z + 5 = 0$ is

Discussion

26.	Find total no.of 8 digit nos. In which no two consecutive digits are identical.
Answer» Find total no.of 8 digit nos. In which no two consecutive digits are identical.

Discussion

27.	Let A=[3725] and B=[6879] verify that (AB)−1=B−1A−1
Answer» Let $A = [\begin{matrix} 3 & 7 2 & 5 \end{matrix}]$ and $B = [\begin{matrix} 6 & 8 7 & 9 \end{matrix}]$ verify that $(A B)^{- 1} = B^{- 1} A - 1$

Discussion

28.	If root over x+1 + root over x-1=2. Then the value of x is
Answer» If root over x+1 + root over x-1=2. Then the value of x is

Discussion

29.	The value of cot(19∑n=1cot−1(1+n∑p=12p)) is :
Answer» The value of $cot (19 \sum n = 1 {cot}^{- 1} (1 + n \sum p = 1 2 p))$ is :

Discussion

30.	Let A(z1) be the point of intersection of curves arg(z−2+i)=3π4 and arg(z+√3i)=π3. B(z2) is the point on arg(z+√3i)=π3 such that \|z2−5\| is minimum, and C(z3) is the centre of circle \|z−5\|=3. If the area of triangle ABC is √k sq. units, then the value of k is
Answer» Let $A (z_{1})$ be the point of intersection of curves $arg (z - 2 + i) = \frac{3 π}{4}$ and $arg (z + \sqrt{3} i) = \frac{π}{3} .$ $B (z_{2})$ is the point on $arg (z + \sqrt{3} i) = \frac{π}{3}$ such that $\| z_{2} - 5 \|$ is minimum, and $C (z_{3})$ is the centre of circle $\| z - 5 \| = 3.$ If the area of triangle $A B C$ is $\sqrt{k}$ sq. units, then the value of $k$ is

Discussion

31.	The value of 0.2log√5(14+18+116+...) is
Answer» The value of $0.2 \sqrt[l o g]{5} (\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + . . .)$ is

Discussion

32.	Question 12Prove that 1+sec θ−tan θ1+sec θ+tan θ=1−sin θcos θ
Answer» Question 12 Prove that $\frac{1 + s e c θ - t a n θ}{1 + s e c θ + t a n θ} = \frac{1 - s i n θ}{c o s θ}$

Discussion

33.	The minimum value of function (sin(sin−1x))2−6sin(sin−1x)+10(3(sin4x+cos4x)−2(sin6x+cos6x)),x∈[−1,1] is
Answer» The minimum value of function $(sin ({sin}^{- 1} x))^{2} - 6 sin ({sin}^{- 1} x) + 10 (3 ({sin}^{4} x + {cos}^{4} x) - 2 ({sin}^{6} x + {cos}^{6} x)), x \in [- 1, 1]$ is

Discussion

34.	Which of the following should be the LAST sentence after rearrangement?
Answer» Which of the following should be the LAST sentence after rearrangement?

Discussion

35.	Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?
Answer» Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?

Discussion

36.	Find the equations of transverse common tangents for two circlesx2 + y2 + 6x − 2y + 1 =0 , x2 + y2 − 2x − 6y + 9 = 0
Answer» Find the equations of transverse common tangents for two circles $x^{2} + y^{2} + 6 x - 2 y + 1 = 0, x^{2} + y^{2} - 2 x - 6 y + 9 = 0$

36.

Find the equations of transverse common tangents for two circlesx2 + y2 + 6x − 2y + 1 =0 , x2 + y2 − 2x − 6y + 9 = 0

Answer»

Find the equations of transverse common tangents for two circles

$x^{2} + y^{2} + 6 x - 2 y + 1 = 0, x^{2} + y^{2} - 2 x - 6 y + 9 = 0$

Discussion

37.	Given P(A) = and P(B) = . Find P(A or B), if A and B are mutually exclusive events.
Answer» Given P(A) = and P(B) = . Find P(A or B), if A and B are mutually exclusive events.

Discussion

38.	Three positive numbers form an increasing G.P. If the middle term in this G.P is doubled, then new numbers are in A.P. Then, the common ratio of the G.P. is
Answer» Three positive numbers form an increasing G.P. If the middle term in this G.P is doubled, then new numbers are in A.P. Then, the common ratio of the G.P. is

Discussion

39.	The set of values of a for which the function f(x)=ax33+(a+2)x2+(a−1)x+2 possesses a negative point of inflection is
Answer» The set of values of $a$ for which the function $f (x) = \frac{a x^{3}}{3} + (a + 2) x^{2} + (a - 1) x + 2$ possesses a negative point of inflection is

Discussion

40.	Three normals are drawn from the point (7,14) to the parabola x2−8x−16y=0. Then the coordinates of the foot of the normal is/are
Answer» Three normals are drawn from the point $(7, 14)$ to the parabola $x^{2} - 8 x - 16 y = 0$ . Then the coordinates of the foot of the normal is/are

Discussion

41.	4centreattheorigin:focionthexaxis
Answer» 4centreattheorigin:focionthexaxis

Discussion

42.	Find the derivative of sin(log x) using first principle method
Answer» Find the derivative of sin(log x) using first principle method

Discussion

43.	4 sinx +cosxJ0 9+16 sin 2xdx
Answer» 4 sinx +cosxJ0 9+16 sin 2xdx

Discussion

44.	If sinx+siny=√3(cosy−cosx), then sin3x+sin3y=
Answer» If $s i n x + s i n y = \sqrt{3} (c o s y - c o s x)$ , then $s i n 3 x + s i n 3 y =$

Discussion

45.	I1=π2∫0sinx−cosx1+sinxcosxdx, I2=2π∫0cos6xdx,I3=π2∫−π2sin3xdx, I4=1∫0ln(1x−1)dx, then
Answer» $I_{1} = \frac{π}{2} \int 0 \frac{sin x - cos x}{1 + sin x cos x} d x, I_{2} = 2 π \int 0 {cos}^{6} x d x$ , $I_{3} = \frac{π}{2} \int - \frac{π}{2} {sin}^{3} x d x, I_{4} = 1 \int 0 ln (\frac{1}{x} - 1) d x$ , then

Discussion

46.	Mark the correct alternative in each of the following:If f(x) = x sinx, then f'π2= (a) 0 (b) 1 (c) −1 (d) 12
Answer» Mark the correct alternative in each of the following: If f(x) = x sinx, then $f' (\frac{π}{2}) =$ (a) 0 (b) 1 (c) −1 (d) $\frac{1}{2}$

Discussion

47.	14.(xdx +ydy)÷ (xdy+ydx)=root((a square - xsquare - ysquare)÷ (x square + ysquare))
Answer» 14.(xdx +ydy)÷ (xdy+ydx)=root((a square - xsquare - ysquare)÷ (x square + ysquare))

Discussion

48.	Let f be a function whose domain is all real numbers. If f(x)+2f(x+2001x−1)=4013−x for all x not equal to 1, then the value of f(2003) is
Answer» Let $f$ be a function whose domain is all real numbers. If $f (x) + 2 f (\frac{x + 2001}{x - 1}) = 4013 - x$ for all $x$ not equal to $1,$ then the value of $f (2003)$ is

Discussion

49.	The value of (√2+1)6 + (√2−1)6 will be
Answer» The value of ${(\sqrt{2} + 1)}^{6}$ + ${(\sqrt{2} - 1)}^{6}$ will be

Discussion

50.	If r is the radius of the void and R is the radius of the sphere, what is AC in the following diagram?
Answer» If r is the radius of the void and R is the radius of the sphere, what is AC in the following diagram?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Evaluate I=∫ex(1+sinx)+e−x(1−sinx)1+cosxdx

1 – cotxsinxcosx equals

Let a,b,c (not all equal) be the sides of traingle ABC and if the roots of the equation a(b−c)x2+b(c−a)x+c(a−b)=0 are equal, then sin2A2,sin2B2,sin2C2 are in:

Insert GM between 0.008 and 0.2

−5(x+3)&gt;x+7+6x Which of the following best describe the solutions to the inequality shown above?

If radius of the circumcircle of the triangle formed by the lines x2−y2=0 and 2x−3y=5 is a units, then value of a2 is

Prove the following identities (1-16)cosec x-sin x sec x-cos x tan x+cot x=1

Prove that the line x+y=3a touches the curve x+y=3axy and also show that the point of contact is ( 1.5a, 1.5a).

Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 30∘ with the positive direction of y-axis measured anticlockwise.

All possible values of θ∈[0,2π] for which sin2θ+tan2θ&gt;0 lie in :

If ∫(2x+3)(x2−3x+1)dx(x4−7x2+1)(1+ln(1+3x+x2))=f(x)+C, where C is constant and f(0)=0, then

3/2∫0|xcosπx|dx equals to

12.Vertices仕6, 0), foci ± 4,0)

Q117) The set of numerical coefficients that balancesthe equationK2CrO4 + HCl → K2Cr2O7 + kCl + H2O iskerala CEE 2001d) 2, 2, 1, 2, 1

The median of the variables x+4,x−72,x−52,x−3,x−2,x+12x−12,x+5(x&gt;0), is

If the radical axis of the circles x2+y2+2gx+2fy+c=0 and 2x2+2y2+3x+8y+2c=0 touches the circle x2+y2+2x+2y+1=0, then

Evaluate limx→0sin 5xtan 3x

21. I if the magnitude of two vectors are 3 and 4 and their scalar product is 6 then find the angle between them

Find the number of words formed by permuting all the letters of the following words: (i) INDEPENDENCE (ii) INTERMEDIATE (iii) ARRANGE (iv) INDIA (v) PAKISTAN (vi) RUSSIA (vii) SERIES (viii) EXERCISES (ix) CONSTANTINOPLE

The area of the triangle whose sides are represented by the graphs of the equations y =x,x = 0 and x + y = 5, is (1) 6 sq. units(2) 6.25 sq. units,(3) 12.5 sq. units(4) 20 sq. units

limx→0{log∈(1+x)x2+x−1x}is equal to

The sum of the intercepts on the axes of the tangent to the curve √x+√y=3 at (4,1) is

The number of real roots of the equation (x²+2x)² - (x-1)² - 55 = 0

The equation of the plane containing the line of intersection of the planes x+y+4z−6=0 and 2x+4y+5=0 and making an angle π4 with the plane x−z+5=0 is

Find total no.of 8 digit nos. In which no two consecutive digits are identical.

Let A=[3725] and B=[6879] verify that (AB)−1=B−1A−1

If root over x+1 + root over x-1=2. Then the value of x is

The value of cot(19∑n=1cot−1(1+n∑p=12p)) is :

Let A(z1) be the point of intersection of curves arg(z−2+i)=3π4 and arg(z+√3i)=π3. B(z2) is the point on arg(z+√3i)=π3 such that |z2−5| is minimum, and C(z3) is the centre of circle |z−5|=3. If the area of triangle ABC is √k sq. units, then the value of k is

The value of 0.2log√5(14+18+116+...) is

Question 12Prove that 1+sec θ−tan θ1+sec θ+tan θ=1−sin θcos θ

The minimum value of function (sin(sin−1x))2−6sin(sin−1x)+10(3(sin4x+cos4x)−2(sin6x+cos6x)),x∈[−1,1] is

Which of the following should be the LAST sentence after rearrangement?

Find the equations of transverse common tangents for two circlesx2 + y2 + 6x − 2y + 1 =0 , x2 + y2 − 2x − 6y + 9 = 0

Given P(A) = and P(B) = . Find P(A or B), if A and B are mutually exclusive events.

Three positive numbers form an increasing G.P. If the middle term in this G.P is doubled, then new numbers are in A.P. Then, the common ratio of the G.P. is

The set of values of a for which the function f(x)=ax33+(a+2)x2+(a−1)x+2 possesses a negative point of inflection is

Three normals are drawn from the point (7,14) to the parabola x2−8x−16y=0. Then the coordinates of the foot of the normal is/are

4centreattheorigin:focionthexaxis

Find the derivative of sin(log x) using first principle method

4 sinx +cosxJ0 9+16 sin 2xdx

If sinx+siny=√3(cosy−cosx), then sin3x+sin3y=

I1=π2∫0sinx−cosx1+sinxcosxdx, I2=2π∫0cos6xdx,I3=π2∫−π2sin3xdx, I4=1∫0ln(1x−1)dx, then

Mark the correct alternative in each of the following:If f(x) = x sinx, then f'π2= (a) 0 (b) 1 (c) −1 (d) 12

14.(xdx +ydy)÷ (xdy+ydx)=root((a square - xsquare - ysquare)÷ (x square + ysquare))

Let f be a function whose domain is all real numbers. If f(x)+2f(x+2001x−1)=4013−x for all x not equal to 1, then the value of f(2003) is

The value of (√2+1)6 + (√2−1)6 will be

If r is the radius of the void and R is the radius of the sphere, what is AC in the following diagram?

−5(x+3)>x+7+6x Which of the following best describe the solutions to the inequality shown above?

All possible values of θ∈[0,2π] for which sin2θ+tan2θ>0 lie in :

The median of the variables x+4,x−72,x−52,x−3,x−2,x+12x−12,x+5(x>0), is