43030 + Interview Questions in Mathematics

1.	If tanθ=sinα−cosαsinα+cosα, then show that sinα+cosα=√2cosθ.
Answer» If $t a n θ = \frac{s i n α - c o s α}{s i n α + c o s α},$ then show that $s i n α + c o s α = \sqrt{2} c o s θ$ .

Discussion

2.	The minors of - 4 and 9 and the co-factors of - 4 and 9 in determinant ∣∣∣∣−1−23−4−5−6−789∣∣∣∣ are respectively
Answer» The minors of - 4 and 9 and the co-factors of - 4 and 9 in determinant $∣ ∣∣ ∣ \begin{matrix} - 1 & - 2 & 3 - 4 & - 5 & - 6 - 7 & 8 & 9 \end{matrix} ∣ ∣∣ ∣$ are respectively

Discussion

3.	Find the equation of the following line. Each grid = 1 unit.
Answer» Find the equation of the following line. Each grid = 1 unit.

Discussion

4.	The domain of the function f(x)=√log10(2−xx) is
Answer» The domain of the function $f (x) = \sqrt{{log}_{10} (\frac{2 - x}{x})}$ is

Discussion

5.	If l2i+m2i+n2i=1 andlilj+mimj+ninj=0 for i≠j where i,j∈{1,2,3} andA=⎡⎢⎣l1m1n1l2m2n2l3m3n3⎤⎥⎦,then\|A\|=
Answer» If $l_{i}^{2} + m_{i}^{2} + n_{i}^{2} = 1$ and $l_{i} l_{j} + m_{i} m_{j} + n_{i} n_{j} = 0$ for $i \neq j$ where $i, j \in {1, 2, 3}$ and $A = ⎡ ⎢ ⎣ \begin{matrix} l_{1} & m_{1} & n_{1} l_{2} & m_{2} & n_{2} l_{3} & m_{3} & n_{3} \end{matrix} ⎤ ⎥ ⎦, then \| A \| =$

Discussion

6.	Which of the following statements are true?(i) the line x2+y3=0 passes through the point (2, 3).(ii) the line x2+y3=0 passes through the point (4, -6).(iii) the point (8, 7) lies on the line y - 7 = 0(iv) the point (-3, 0) lies on the line x + 3 = 0(v) if the point (2, a) lies on the line 2x - y = 3, then a = 5.
Answer» Which of the following statements are true? (i) the line $\frac{x}{2} + \frac{y}{3} = 0$ passes through the point (2, 3). (ii) the line $\frac{x}{2} + \frac{y}{3} = 0$ passes through the point (4, -6). (iii) the point (8, 7) lies on the line y - 7 = 0 (iv) the point (-3, 0) lies on the line x + 3 = 0 (v) if the point (2, a) lies on the line 2x - y = 3, then a = 5.

6.

Which of the following statements are true?(i) the line x2+y3=0 passes through the point (2, 3).(ii) the line x2+y3=0 passes through the point (4, -6).(iii) the point (8, 7) lies on the line y - 7 = 0(iv) the point (-3, 0) lies on the line x + 3 = 0(v) if the point (2, a) lies on the line 2x - y = 3, then a = 5.

Answer»

Which of the following statements are true?

(i) the line $\frac{x}{2} + \frac{y}{3} = 0$ passes through the point (2, 3).

(ii) the line $\frac{x}{2} + \frac{y}{3} = 0$ passes through the point (4, -6).

(iii) the point (8, 7) lies on the line y - 7 = 0

(iv) the point (-3, 0) lies on the line x + 3 = 0

(v) if the point (2, a) lies on the line 2x - y = 3, then a = 5.

Discussion

7.	The value of limx→0[min(t2+10t+28)⋅tanxx]; x,t∈R is(where [.] denotes greatest integer function )
Answer» The value of $lim x \to 0 [min (t^{2} + 10 t + 28) \cdot \frac{tan x}{x}]; x, t \in R$ is (where $[.]$ denotes greatest integer function )

Discussion

8.	If total cost function of a certain commodity is C(x)=3+2x−14x2, then average variable cost at x=4 is [2 marks]
Answer» If total cost function of a certain commodity is $C (x) = 3 + 2 x - \frac{1}{4} x^{2},$ then average variable cost at $x = 4$ is [2 marks]

Discussion

9.	What are vectors law
Answer» What are vectors law

Discussion

10.	The rate of disintegration of a radioactive substance falls from 800 decay/min to 100 decay/min in 6 hours. Then the half life of the radioactive substance in hours is:
Answer» The rate of disintegration of a radioactive substance falls from $800$ decay/min to $100$ decay/min in 6 hours. Then the half life of the radioactive substance in hours is:

Discussion

11.	The function ‘ t ’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by . Find (i) t (0) (ii) t (28) (iii) t (–10) (iv) The value of C, when t (C) = 212
Answer» The function ‘ t ’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by . Find (i) t (0) (ii) t (28) (iii) t (–10) (iv) The value of C, when t (C) = 212

Discussion

12.	Let →r be a unit vector satisfying →r×→a=→b, where \|→a\|=√3 and \|→b\|=√2. Then which of the following statement is/are true
Answer» Let $\to r$ be a unit vector satisfying $\to r \times \to a = \to b,$ where $\| \to a \| = \sqrt{3}$ and $\| \to b \| = \sqrt{2}$ . Then which of the following statement is/are true

Discussion

13.	Can 3 vectors not lying in a plane never add up to give a null vector? Why?
Answer» Can 3 vectors not lying in a plane never add up to give a null vector? Why?

Discussion

14.	If for x∈(0,π2),log10sinx+log10cosx=−1 and log10(sinx+cosx)=12(log10n−1),n>0then the value of n is equal to:
Answer» If for $x \in (0, \frac{π}{2}), {log}_{10} sin x + {log}_{10} cos x = - 1$ and ${log}_{10} (sin x + cos x) = \frac{1}{2} ({log}_{10} n - 1), n > 0$ then the value of $n$ is equal to:

Discussion

15.	If f(x) = 3x - 7, what is f(-4)?
Answer» If f(x) = 3x - 7, what is f(-4)?

Discussion

16.	Prove that 2nCn=2n×[1.3.5...(2n−1)]n !.
Answer» Prove that $^{2 n} C_{n} = \frac{2^{n} \times [1.3.5... (2 n - 1)]}{n!} .$

Discussion

17.	limx→0ln(cos(x/2))cosx=
Answer» $lim x \to 0 {ln}_{(cos (x / 2))} cos x =$

Discussion

18.	Solution of logx2+6x+8 logx2+2x+3 (x2−2x)=0 is
Answer» Solution of $l o g_{x^{2} + 6 x + 8} l o g_{x^{2} + 2 x + 3} (x^{2} - 2 x) = 0 i s$

Discussion

19.	Determine the contrapositive of each of the following statements : (i) If Mohan is a poet, then he is poor. (ii) Only if max studies will he pass the test. (iii) If she works, she will earn money. (iv) If it snows, then they do not drive the car. (v) It never rains when it is cold. (vi) If Ravish skis, then it snowed. (vii) If x is less than zero, then x is not positive. (viii) If he has courage he will win. (ix) It is necessary to be strong in order to be a sailor. (x) Only if he does not tire will ne win. (xi) If x is an integer and x2 is odd, then x is odd.
Answer» Determine the contrapositive of each of the following statements : (i) If Mohan is a poet, then he is poor. (ii) Only if max studies will he pass the test. (iii) If she works, she will earn money. (iv) If it snows, then they do not drive the car. (v) It never rains when it is cold. (vi) If Ravish skis, then it snowed. (vii) If x is less than zero, then x is not positive. (viii) If he has courage he will win. (ix) It is necessary to be strong in order to be a sailor. (x) Only if he does not tire will ne win. (xi) If x is an integer and $x^{2}$ is odd, then x is odd.

19.

Determine the contrapositive of each of the following statements : (i) If Mohan is a poet, then he is poor. (ii) Only if max studies will he pass the test. (iii) If she works, she will earn money. (iv) If it snows, then they do not drive the car. (v) It never rains when it is cold. (vi) If Ravish skis, then it snowed. (vii) If x is less than zero, then x is not positive. (viii) If he has courage he will win. (ix) It is necessary to be strong in order to be a sailor. (x) Only if he does not tire will ne win. (xi) If x is an integer and x2 is odd, then x is odd.

Answer»

Determine the contrapositive of each of the following statements :

(i) If Mohan is a poet, then he is poor.

(ii) Only if max studies will he pass the test.

(iii) If she works, she will earn money.

(iv) If it snows, then they do not drive the car.

(v) It never rains when it is cold.

(vi) If Ravish skis, then it snowed.

(vii) If x is less than zero, then x is not positive.

(viii) If he has courage he will win.

(ix) It is necessary to be strong in order to be a sailor.

(x) Only if he does not tire will ne win.

(xi) If x is an integer and $x^{2}$ is odd, then x is odd.

Discussion

20.	the general solution of the equation †an^2θ +2\sqrt3 †anθ =1
Answer» the general solution of the equation †an^2θ +2\sqrt3 †anθ =1

Discussion

21.	In a right triangle ABC in which\angle B = 90º, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the †an gent to the circle at P bisect BC.
Answer» In a right triangle ABC in which\angle B = 90º, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the †an gent to the circle at P bisect BC.

Discussion

22.	Not understanding about angle bisectors concept in straight lines
Answer» Not understanding about angle bisectors concept in straight lines

Discussion

23.	Consider the grammar shown below:S→i E t S S'\|αS' → e S \| εE → bIn the predictive parse table M, of this grammar, the entries M[S', e] and M[S', $] respectively are
Answer» Consider the grammar shown below: $\begin{matrix} S \to i E t S S' \| α S' \to e S \| ε E \to b \end{matrix}$ In the predictive parse table M, of this grammar, the entries M[S', e] and M[S', $] respectively are

Discussion

24.	Differentiate thefunction with respect to x.
Answer» Differentiate the function with respect to x.

24.

Differentiate thefunction with respect to x.

Answer»

Differentiate the
function with respect to x.

Discussion

25.	Prove that following identities: tan θ tan (θ+60∘)+tan θ tan(θ−60∘)+tan(θ+60∘) tan(θ−60∘)=−3
Answer» Prove that following identities: $t a n θ t a n (θ + 60^{\circ}) + t a n θ t a n (θ - 60^{\circ}) + t a n (θ + 60^{\circ}) t a n (θ - 60^{\circ}) = - 3$

25.

Prove that following identities: tan θ tan (θ+60∘)+tan θ tan(θ−60∘)+tan(θ+60∘) tan(θ−60∘)=−3

Answer»

Prove that following identities:

$t a n θ t a n (θ + 60^{\circ}) + t a n θ t a n (θ - 60^{\circ}) + t a n (θ + 60^{\circ}) t a n (θ - 60^{\circ}) = - 3$

Discussion

26.	If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?
Answer» If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

Discussion

27.	Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls, and U2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appears then 2 balls are drawn at random from U1 and put into U2. Now 1 ball is drawn at random from U2.
Answer» Let $U_{1}$ and $U_{2}$ be two urns such that $U_{1}$ contains 3 white and 2 red balls, and $U_{2}$ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from $U_{1}$ and put into $U_{2}$ . However, if tail appears then 2 balls are drawn at random from $U_{1}$ and put into $U_{2}$ . Now 1 ball is drawn at random from $U_{2}$ .

Discussion

28.	49.The solutions of p+cos(px)sin(y)= sin(px)cos(y) ( where p= dy/dx) Options a)y=0 b) cx-y=arcsin(x) c)cx-y= arcsin(c) d)y=(x-1 )-arcsin((x-1)/x)
Answer» 49.The solutions of p+cos(px)sin(y)= sin(px)cos(y) ( where p= dy/dx) Options a)y=0 b) cx-y=arcsin(x) c)cx-y= arcsin(c) d)y=(x-1 )-arcsin((x-1)/x)

Discussion

29.	If coordinates of the centre and one end of a diameter of a circle are (7,3) and (5,−7) respectively, then the coordinates of the other end of the diameter are
Answer» If coordinates of the centre and one end of a diameter of a circle are $(7, 3)$ and $(5, - 7)$ respectively, then the coordinates of the other end of the diameter are

Discussion

30.	Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?
Answer» Axis of a parabola lies along $x$ -axis. If its vertex and focus are at distances $2$ and $4$ respectively from the origin, on the positive $x$ -axis then which of the following points does not lie on it?

Discussion

31.	If f(x)=cos−1[1−(lnx)21+(lnx)2], x≥1, then the value of f′(e) is
Answer» If $f (x) = {cos}^{- 1} [\frac{1 - (ln x)^{2}}{1 + (ln x)^{2}}], x \geq 1,$ then the value of $f^{'} (e)$ is

Discussion

32.	Q) Let f(Q) = sin[arc tan{sinQ/(cos2Q)½}] , where -pie/4 < Q < pie/4 . Then the vapue of d(f(Q))/d(tanQ) is _____.
Answer» Q) Let f(Q) = sin[arc tan{sinQ/(cos2Q)½}] , where -pie/4 < Q < pie/4 . Then the vapue of d(f(Q))/d(tanQ) is _____.

Discussion

33.	The point (-1,2) is on a circle whose centre is (3,-1). Write the standard equation of the circle.
Answer» The point (-1,2) is on a circle whose centre is (3,-1). Write the standard equation of the circle.

Discussion

34.	Obtain all the other zeros of 3x4+6x3−2x2−10x−5.if two of its zeros are √53and−√53.
Answer» Obtain all the other zeros of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5.$ if two of its zeros are $\sqrt{\frac{5}{3}} and - \sqrt{\frac{5}{3}} .$

Discussion

35.	Whichof the given values of xand y makethe following pair of matrices equal(A) (B) Notpossible to find(C) (D)
Answer» Which of the given values of x and y make the following pair of matrices equal (A) (B) Not possible to find (C) (D)

35.

Whichof the given values of xand y makethe following pair of matrices equal(A) (B) Notpossible to find(C) (D)

Answer»

Which
of the given values of x
and y make
the following pair of matrices equal

(A)

(B) Not
possible to find

(C)

(D)

Discussion

36.	The solution set of 1x2−9≥0 is
Answer» The solution set of $\frac{1}{x^{2} - 9} \geq 0$ is

Discussion

37.	If 5(tan2x−cos2x)=2cos2x+9, then the value of cos4x is:
Answer» If $5 ({tan}^{2} x - {cos}^{2} x) = 2 cos 2 x + 9,$ then the value of $cos 4 x$ is:

Discussion

38.	Find acute angle A if Cos3A=Sin(A-26)
Answer» Find acute angle A if Cos3A=Sin(A-26)

Discussion

39.	On the ellipse x28+y24=1, let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x+2y=0. Let S and S′ be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS′, then the value of (5−e2)⋅A is
Answer» On the ellipse $\frac{x^{2}}{8} + \frac{y^{2}}{4} = 1,$ let $P$ be a point in the second quadrant such that the tangent at $P$ to the ellipse is perpendicular to the line $x + 2 y = 0.$ Let $S$ and $S^{'}$ be the foci of the ellipse and $e$ be its eccentricity. If $A$ is the area of the triangle $S P S^{'},$ then the value of $(5 - e^{2}) \cdot A$ is

Discussion

40.	The line x=y touches a circle at the point (1,1). If the circle also passes through the point (1,−3), then its radius(in units) is
Answer» The line $x = y$ touches a circle at the point $(1, 1) .$ If the circle also passes through the point $(1, - 3),$ then its radius(in units) is

Discussion

41.	Which of the following is the correct notation of a null matrix
Answer» Which of the following is the correct notation of a null matrix

Discussion

42.	If a and b are two consecutive odd positive integers and sum of their squares is 290, then value of a+b is
Answer» If $a$ and $b$ are two consecutive odd positive integers and sum of their squares is $290$ , then value of $a + b$ is

Discussion

43.	Let C1 and C2 be two circles whose equations are given as x2+y2=25 and x2+y2+10x+6y+1=0. C3 is a variable circle which cuts C1 and C2 orthogonally. Tangents are drawn from centre of C3 to C1. If the locus of mid-point of chord of contact of tangents is αx+3y+13β(x2+y2)=0, then the value of βα is
Answer» Let $C_{1}$ and $C_{2}$ be two circles whose equations are given as $x^{2} + y^{2} = 25$ and $x^{2} + y^{2} + 10 x + 6 y + 1 = 0.$ $C_{3}$ is a variable circle which cuts $C_{1}$ and $C_{2}$ orthogonally. Tangents are drawn from centre of $C_{3}$ to $C_{1}$ . If the locus of mid-point of chord of contact of tangents is $α x + 3 y + \frac{13}{β} (x^{2} + y^{2}) = 0$ , then the value of $\frac{β}{α}$ is

Discussion

44.	Evaluate: cossin-135+sin-1513
Answer» Evaluate: $\cos (\sin^{- 1} \frac{3}{5} + \sin^{- 1} \frac{5}{13})$

Discussion

45.	A group of 123 workers went to a canteen for cold drinks, ice-cream and tea. 42 workers took ice-cream, 36 took tea and 30 took cold drinks. 15 workers purchased ice-cream and tea, 10 purchased ice-cream and cold drinks, and 4 purchased cold drinks and tea but not ice-cream. Then the number of workers who did not purchase anything is
Answer» A group of $123$ workers went to a canteen for cold drinks, ice-cream and tea. $42$ workers took ice-cream, $36$ took tea and $30$ took cold drinks. $15$ workers purchased ice-cream and tea, $10$ purchased ice-cream and cold drinks, and $4$ purchased cold drinks and tea but not ice-cream. Then the number of workers who did not purchase anything is

Discussion

46.	Question 2 (v)Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows.(v) a=−1.25,d=−0.25
Answer» Question 2 (v) Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows. (v) $a = - 1.25, d = - 0.25$

Discussion

47.	The number of real roots of the equation 2x4−4x3−4x+2=0 is
Answer» The number of real roots of the equation $2 x^{4} - 4 x^{3} - 4 x + 2 = 0$ is

Discussion

48.	Let →a=2→i+3→j+4→k and →b=3i+4j+5k. Find the angle between them.
Answer» Let $\to a = 2 \to i + 3 \to j + 4 \to k$ and $\to b = 3 i + 4 j + 5 k$ . Find the angle between them.

Discussion

49.	A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, then the probability that the missing card is black, is:
Answer» A pack of playing cards was found to contain only $51$ cards. If the first $13$ cards which are examined are all red, then the probability that the missing card is black, is:

Discussion

50.	Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = – 8x
Answer» Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = – 8x

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If tanθ=sinα−cosαsinα+cosα, then show that sinα+cosα=√2cosθ.

The minors of - 4 and 9 and the co-factors of - 4 and 9 in determinant ∣∣∣∣−1−23−4−5−6−789∣∣∣∣ are respectively

Find the equation of the following line. Each grid = 1 unit.

The domain of the function f(x)=√log10(2−xx) is

If l2i+m2i+n2i=1 andlilj+mimj+ninj=0 for i≠j where i,j∈{1,2,3} andA=⎡⎢⎣l1m1n1l2m2n2l3m3n3⎤⎥⎦,then|A|=

The value of limx→0[min(t2+10t+28)⋅tanxx]; x,t∈R is(where [.] denotes greatest integer function )

If total cost function of a certain commodity is C(x)=3+2x−14x2, then average variable cost at x=4 is [2 marks]

What are vectors law

The rate of disintegration of a radioactive substance falls from 800 decay/min to 100 decay/min in 6 hours. Then the half life of the radioactive substance in hours is:

The function ‘ t ’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by . Find (i) t (0) (ii) t (28) (iii) t (–10) (iv) The value of C, when t (C) = 212

Let →r be a unit vector satisfying →r×→a=→b, where |→a|=√3 and |→b|=√2. Then which of the following statement is/are true

Can 3 vectors not lying in a plane never add up to give a null vector? Why?

If for x∈(0,π2),log10sinx+log10cosx=−1 and log10(sinx+cosx)=12(log10n−1),n&gt;0then the value of n is equal to:

If f(x) = 3x - 7, what is f(-4)?

Prove that 2nCn=2n×[1.3.5...(2n−1)]n !.

limx→0ln(cos(x/2))cosx=

Solution of logx2+6x+8 logx2+2x+3 (x2−2x)=0 is

the general solution of the equation †an^2θ +2\sqrt3 †anθ =1

In a right triangle ABC in which\angle B = 90º, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the †an gent to the circle at P bisect BC.

Not understanding about angle bisectors concept in straight lines

Consider the grammar shown below:S→i E t S S'|αS' → e S | εE → bIn the predictive parse table M, of this grammar, the entries M[S', e] and M[S', $] respectively are

Differentiate thefunction with respect to x.

Prove that following identities: tan θ tan (θ+60∘)+tan θ tan(θ−60∘)+tan(θ+60∘) tan(θ−60∘)=−3

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

49.The solutions of p+cos(px)sin(y)= sin(px)cos(y) ( where p= dy/dx) Options a)y=0 b) cx-y=arcsin(x) c)cx-y= arcsin(c) d)y=(x-1 )-arcsin((x-1)/x)

If coordinates of the centre and one end of a diameter of a circle are (7,3) and (5,−7) respectively, then the coordinates of the other end of the diameter are

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

If f(x)=cos−1[1−(lnx)21+(lnx)2], x≥1, then the value of f′(e) is

Q) Let f(Q) = sin[arc tan{sinQ/(cos2Q)½}] , where -pie/4 < Q < pie/4 . Then the vapue of d(f(Q))/d(tanQ) is _____.

The point (-1,2) is on a circle whose centre is (3,-1). Write the standard equation of the circle.

Obtain all the other zeros of 3x4+6x3−2x2−10x−5.if two of its zeros are √53and−√53.

Whichof the given values of xand y makethe following pair of matrices equal(A) (B) Notpossible to find(C) (D)

The solution set of 1x2−9≥0 is

If 5(tan2x−cos2x)=2cos2x+9, then the value of cos4x is:

Find acute angle A if Cos3A=Sin(A-26)

On the ellipse x28+y24=1, let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x+2y=0. Let S and S′ be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS′, then the value of (5−e2)⋅A is

The line x=y touches a circle at the point (1,1). If the circle also passes through the point (1,−3), then its radius(in units) is

Which of the following is the correct notation of a null matrix

If a and b are two consecutive odd positive integers and sum of their squares is 290, then value of a+b is

Evaluate: cossin-135+sin-1513

Question 2 (v)Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows.(v) a=−1.25,d=−0.25

The number of real roots of the equation 2x4−4x3−4x+2=0 is

Let →a=2→i+3→j+4→k and →b=3i+4j+5k. Find the angle between them.

A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, then the probability that the missing card is black, is:

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = – 8x

If for x∈(0,π2),log10sinx+log10cosx=−1 and log10(sinx+cosx)=12(log10n−1),n>0then the value of n is equal to: