43030 + Interview Questions in Mathematics Page 35 InterviewSolution

1701.	1. A parabola y=ax2+bx+c crosses the x axis at (p,0) (q,0) both to right of origin. A circle also passes through these two points. The length of tangent from origin to circle is
Answer» 1. A parabola y=ax2+bx+c crosses the x axis at (p,0) (q,0) both to right of origin. A circle also passes through these two points. The length of tangent from origin to circle is

Discussion

1702.	If tan3x+tanx=2tan2x then x is equal to (n∈Z)
Answer» If $tan 3 x + tan x = 2 tan 2 x$ then $x$ is equal to $(n \in Z)$

Discussion

1703.	If a : b = 4 : 5 and b : c = 2 : 3, then a : c = ...........
Answer» If a : b = 4 : 5 and b : c = 2 : 3, then a : c = ...........

Discussion

1704.	Prove the following identities:a+xyzxa+yzxya+z=a2a+x+y+z
Answer» Prove the following identities: $\|\begin{matrix} a + x & y & z \\ x & a + y & z \\ x & y & a + z \end{matrix}\| = a^{2} (a + x + y + z)$

Discussion

1705.	The domain of f(x)=√x−√1−x2 is
Answer» The domain of $f (x) = \sqrt{x - \sqrt{1 - x^{2}}}$ is

Discussion

1706.	Prove the following trigonometric identities.1+cos θ-sin2 θsin θ (1+cos θ)=cot θ
Answer» Prove the following trigonometric identities. $\frac{1 + \cos θ - \sin^{2} θ}{\sin θ (1 + \cos θ)} = \cot θ$

Discussion

1707.	If tanx−tan2x>0 and \|2sinx\|<1 then the range of x for which both conditions hold good is (where n∈Z)
Answer» If $tan x - {tan}^{2} x > 0$ and $\| 2 sin x \| < 1$ then the range of $x$ for which both conditions hold good is (where $n \in Z$ )

Discussion

1708.	Find the differential equation representing the family of curves y=aebx+5, where a and b are arbitrary constants.
Answer» Find the differential equation representing the family of curves $y = a e^{b x + 5}$ , where a and b are arbitrary constants.

Discussion

1709.	The value of limx→06sinx+3sin2x−4sin3xx2sinx is
Answer» The value of $lim x \to 0 \frac{6 sin x + 3 sin 2 x - 4 sin 3 x}{x^{2} sin x}$ is

Discussion

1710.	The angles of a triangle are in the ratio 3 : 5 : 10. Then, the ratio of the smallest side to the greatest side is
Answer» $The angles of a triangle are in the ratio 3 : 5 : 10. Then, the ratio of the smallest side to the greatest side is$

Discussion

1711.	The value of sin50∘−sin70∘+sin10∘ is equal to
Answer» The value of $s i n 50^{\circ} - s i n 70^{\circ} + s i n 10^{\circ}$ is equal to

Discussion

1712.	what is the value of x in given equation ? yAl + xH^+- yAl^{3+}+xH_{}
Answer» what is the value of x in given equation ? yAl + xH^+- yAl^{3+}+xH_{}

Discussion

1713.	Host, his wife and 8 guests are to be seated on a round dining table at random. The probability that the host and his wife sit together is:
Answer» Host, his wife and 8 guests are to be seated on a round dining table at random. The probability that the host and his wife sit together is:

Discussion

1714.	f(x)=ln(x^2-3x+2).find range
Answer» f(x)=ln(x^2-3x+2).find range

Discussion

1715.	f:[2,∞)→(−∞,4],where f(x)=x(4−x)then f−1(x)is
Answer» $f : [2, \infty) \to (- \infty, 4], w h e r e f (x) = x (4 - x) t h e n f^{- 1} (x) i s$

Discussion

1716.	If two non-parallel vectors \overrightarrow a and \overrightarrow b are equal in magnitude, then the vectors (\overrightarrow{ a} - \overrightarrow b) and (\overrightarrow a + \overrightarrow b) will be: (A) parallel to each other (B) perpendicular to each other (C) anti-parallel to each other (D) inclined at an angle less than 90^{
Answer» If two non-parallel vectors \overrightarrow a and \overrightarrow b are equal in magnitude, then the vectors (\overrightarrow{ a} - \overrightarrow b) and (\overrightarrow a + \overrightarrow b) will be: (A) parallel to each other (B) perpendicular to each other (C) anti-parallel to each other (D) inclined at an angle less than 90^{

Discussion

1717.	\sqrt{5\sqrt{5\sqrt{25\sqrt{5\sqrt5}}}}=??
Answer» \sqrt{5\sqrt{5\sqrt{25\sqrt{5\sqrt5}}}}=??

Discussion

1718.	If a4⋅b5=1, then the value of logaa5b4 equals (where a,b∈R+ and a≠1)
Answer» If $a^{4} \cdot b^{5} = 1$ , then the value of ${log}_{a} a^{5} b^{4}$ equals (where $a, b \in R^{+}$ and $a \neq 1$ )

Discussion

1719.	Divide 243 into three parts such that half of the first part, one-third of the second part and one- fourth of the third part are all equal
Answer» Divide 243 into three parts such that half of the first part, one-third of the second part and one- fourth of the third part are all equal

Discussion

1720.	Show thatthe general solution of the differential equation isgiven by (x + y + 1) = A (1 – x –y – 2xy), where A is parameter
Answer» Show that the general solution of the differential equation is given by (x + y + 1) = A (1 – x – y – 2xy), where A is parameter

Discussion

1721.	Let f:(0,infinity) to R defined by f(x)= x + 9(pie)²/2 + cosx then find the range of f(x).
Answer» Let f:(0,infinity) to R defined by f(x)= x + 9(pie)²/2 + cosx then find the range of f(x).

Discussion

1722.	Arun rides his bicycle from house at A to club C via B taking the shortest path. Then the shortest path that he can choose is . Options A)1170 B)630 C)792 D)1200. E)936 I am in need of ur answer and explaination for the soon. Thank you!.
Answer» Arun rides his bicycle from house at A to club C via B taking the shortest path. Then the shortest path that he can choose is . Options A)1170 B)630 C)792 D)1200. E)936 I am in need of ur answer and explaination for the soon. Thank you!.

Discussion

1723.	3. centreand radius2' 412
Answer» 3. centreand radius2' 412

Discussion

1724.	The locus of the centre of circle which touches (y−1)2+x2=1 externally and also touches x-axis, is
Answer» The locus of the centre of circle which touches $(y - 1)^{2} + x^{2} = 1$ externally and also touches x-axis, is

Discussion

1725.	The equation of the plane passing through the points P(1,1,1),Q(3,−1,2),R(−3,5,−4) is
Answer» The equation of the plane passing through the points $P (1, 1, 1), Q (3, - 1, 2), R (- 3, 5, - 4)$ is

Discussion

1726.	Let →a=^i−^j, →b=^j−^k, →c=^k−^i. If →d is a unit vector such that →a⋅→d=0=[→b→c→d], then →d is equal to:
Answer» Let $\to a =^i -^j, \to b =^j -^k, \to c =^k -^i$ . If $\to d$ is a unit vector such that $\to a \cdot \to d = 0 = [\to b \to c \to d]$ , then $\to d$ is equal to:

Discussion

1727.	The maximum of f(x)=logxx2(x>0) occurs, when x is equal to
Answer» The maximum of $f (x) = \frac{log x}{x^{2}} (x > 0)$ occurs, when $x$ is equal to

Discussion

1728.	The circle x^2 + y^2 -4x - 8y - 5=0 intersects the line 3x-4y=m at two distinct points. What is the range of m?
Answer» The circle x^2 + y^2 -4x - 8y - 5=0 intersects the line 3x-4y=m at two distinct points. What is the range of m?

Discussion

1729.	The length of the sub-tangent and sub-normal is equal for the curve y=epx+px at the point (0, 1), then the value of p is
Answer» The length of the sub-tangent and sub-normal is equal for the curve $y = e^{px} + px$ at the point (0, 1), then the value of p is

Discussion

1730.	Simplify :4(1 – sin2θ) (1 + tan2θ)
Answer» Simplify : 4(1 – $s i n^{2} θ$ ) (1 + $t a n^{2} θ$ )

Discussion

1731.	19. sin"x
Answer» 19. sin"x

Discussion

1732.	If tan 3x-1tan 3x+1=3, then x = _____________.
Answer» If $\frac{\tan 3 x - 1}{\tan 3 x + 1} = \sqrt{3},$ then x = _____________.

Discussion

1733.	area of a sector of angle p (in degrees) of a circle with radius R is ? explain !
Answer» area of a sector of angle p (in degrees) of a circle with radius R is ? explain !

Discussion

1734.	The line (3x−y+5)+λ(2x−3y−4)=0 will be parallel to y-axis, if λ =
Answer» The line $(3 x - y + 5) + λ (2 x - 3 y - 4) = 0$ will be parallel to y-axis, if $λ$ =

Discussion

1735.	Why is sq. Root sin square x always +ve but square root 25 is +5 or -5?
Answer» Why is sq. Root sin square x always +ve but square root 25 is +5 or -5?

Discussion

1736.	Let P and Q be two points denoting the complex numbers α and β respectively on the complex plane. Which of the following equations can represent the equation of the circle passing through P and Q with least possible area ?
Answer» Let P and Q be two points denoting the complex numbers $α a n d β$ respectively on the complex plane. Which of the following equations can represent the equation of the circle passing through P and Q with least possible area ?

Discussion

1737.	Match the following:Given, U is universal set.A, B are subsets of U.n(U), n(A), n(B) are no. of elements in U, A, B respectively.Number of:(1) Elements neither in A nor in B (A) n(A∪B)(2) Elements only in A (B)n(B)−n(A∩B)(3) Elements only in B (C)n(A)−n(A∪B)(4) Elements either in A (or) in B (D)n(U)−n(A∪B) (E)n(A)−n(A∩B)
Answer» Match the following: Given, U is universal set. A, B are subsets of U. n(U), n(A), n(B) are no. of elements in U, A, B respectively. Number of: (1) Elements neither in A nor in B (A) $n (A \cup B)$ (2) Elements only in A (B) $n (B) - n (A \cap B)$ (3) Elements only in B (C) $n (A) - n (A \cup B)$ (4) Elements either in A (or) in B (D) $n (U) - n (A \cup B)$ (E) $n (A) - n (A \cap B)$

1737.

Match the following:Given, U is universal set.A, B are subsets of U.n(U), n(A), n(B) are no. of elements in U, A, B respectively.Number of:(1) Elements neither in A nor in B (A) n(A∪B)(2) Elements only in A (B)n(B)−n(A∩B)(3) Elements only in B (C)n(A)−n(A∪B)(4) Elements either in A (or) in B (D)n(U)−n(A∪B) (E)n(A)−n(A∩B)

Answer»

Match the following:

Given, U is universal set.

A, B are subsets of U.

n(U), n(A), n(B) are no. of elements in U, A, B respectively.

Number of:

(1) Elements neither in A nor in B (A) $n (A \cup B)$

(2) Elements only in A (B) $n (B) - n (A \cap B)$

(3) Elements only in B (C) $n (A) - n (A \cup B)$

(4) Elements either in A (or) in B (D) $n (U) - n (A \cup B)$

(E) $n (A) - n (A \cap B)$

Discussion

1738.	Ten eggs are drawn succesively with replacement from a lot of 100 eggs containing 10 rotten eggs. Then the probability that there is at least one rotten egg is:
Answer» Ten eggs are drawn succesively with replacement from a lot of $100$ eggs containing $10$ rotten eggs. Then the probability that there is at least one rotten egg is:

Discussion

1739.	limx→ax5/8−a5/8x1/3−a1/3=
Answer» $lim x \to a \frac{x^{5 / 8} - a^{5 / 8}}{x^{1 / 3} - a^{1 / 3}} =$

Discussion

1740.	The value of x + y + z is 15 if a, x, y, b are in A.P. while the value of 1x+1y+1z is 58 if a, x, y, z b are H.P., then a2+b2=
Answer» The value of x + y + z is 15 if a, x, y, b are in A.P. while the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} i s \frac{5}{8}$ if a, x, y, z b are H.P., then $a^{2} + b^{2} =$

Discussion

1741.	I want the solution for sin9A=sinA.
Answer» I want the solution for sin9A=sinA.

Discussion

1742.	25) If }α and }β are zeros of the polynomial }f(x)=x^2-5x+k , such that }α-β=1. Find }K
Answer» 25) If }α and }β are zeros of the polynomial }f(x)=x^2-5x+k , such that }α-β=1. Find }K

Discussion

1743.	If 2x+y4x5x-74x=77y-13yx+6, then the value of x and y is(a) x = 3, y = 1(b) x = 2, y = 3(c) x = 2, y = 4(d) x = 3, y = 3
Answer» If $[\begin{matrix} 2 x + y & 4 x \\ 5 x - 7 & 4 x \end{matrix}] = [\begin{matrix} 7 & 7 y - 13 \\ y & x + 6 \end{matrix}]$ , then the value of x and y is (a) x = 3, y = 1 (b) x = 2, y = 3 (c) x = 2, y = 4 (d) x = 3, y = 3

Discussion

1744.	The maximum value of the function f(x)=ln(1+x)−x (where x>−1) occurs at x= 0
Answer» The maximum value of the function $f (x) = l n (1 + x) - x$ (where $x > - 1$ ) occurs at $x =$ 0

Discussion

1745.	The derivative of f(x) defined by f(x)=tan−1(√1−cos x1+cos x), −π<x<πis
Answer» The derivative of f(x) defined by $f (x) = {tan}^{- 1} (\sqrt{\frac{1 - cos x}{1 + cos x}}), - π < x < π$ is

Discussion

1746.	An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?
Answer» An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

Discussion

1747.	What are composite number?
Answer» What are composite number?

Discussion

1748.	Find the number of solutions of z2+z2=0
Answer» Find the number of solutions of $z^{2} + {\|z\|}^{2} = 0$

Discussion

1749.	limx→3-x[x]=__________________.
Answer» $\lim_{x \to 3^{-}} \frac{x}{[x]} =__________________.$

Discussion

1750.	If A=538201123. Write the cofactor of the element a32.
Answer» If $A = [\begin{matrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{matrix}]$ . Write the cofactor of the element a₃₂.

Discussion

Explore topic-wise InterviewSolutions in .

1. A parabola y=ax2+bx+c crosses the x axis at (p,0) (q,0) both to right of origin. A circle also passes through these two points. The length of tangent from origin to circle is

If tan3x+tanx=2tan2x then x is equal to (n∈Z)

If a : b = 4 : 5 and b : c = 2 : 3, then a : c = ...........

Prove the following identities:a+xyzxa+yzxya+z=a2a+x+y+z

The domain of f(x)=√x−√1−x2 is

Prove the following trigonometric identities.1+cos θ-sin2 θsin θ (1+cos θ)=cot θ

If tanx−tan2x&gt;0 and |2sinx|&lt;1 then the range of x for which both conditions hold good is (where n∈Z)

Find the differential equation representing the family of curves y=aebx+5, where a and b are arbitrary constants.

The value of limx→06sinx+3sin2x−4sin3xx2sinx is

The angles of a triangle are in the ratio 3 : 5 : 10. Then, the ratio of the smallest side to the greatest side is

The value of sin50∘−sin70∘+sin10∘ is equal to

what is the value of x in given equation ? yAl + xH^+- yAl^{3+}+xH_{}

Host, his wife and 8 guests are to be seated on a round dining table at random. The probability that the host and his wife sit together is:

f(x)=ln(x^2-3x+2).find range

f:[2,∞)→(−∞,4],where f(x)=x(4−x)then f−1(x)is

\sqrt{5\sqrt{5\sqrt{25\sqrt{5\sqrt5}}}}=??

If a4⋅b5=1, then the value of logaa5b4 equals (where a,b∈R+ and a≠1)

Divide 243 into three parts such that half of the first part, one-third of the second part and one- fourth of the third part are all equal

Show thatthe general solution of the differential equation isgiven by (x + y + 1) = A (1 – x –y – 2xy), where A is parameter

Let f:(0,infinity) to R defined by f(x)= x + 9(pie)²/2 + cosx then find the range of f(x).

Arun rides his bicycle from house at A to club C via B taking the shortest path. Then the shortest path that he can choose is . Options A)1170 B)630 C)792 D)1200. E)936 I am in need of ur answer and explaination for the soon. Thank you!.

3. centreand radius2' 412

The locus of the centre of circle which touches (y−1)2+x2=1 externally and also touches x-axis, is

The equation of the plane passing through the points P(1,1,1),Q(3,−1,2),R(−3,5,−4) is

Let →a=^i−^j, →b=^j−^k, →c=^k−^i. If →d is a unit vector such that →a⋅→d=0=[→b→c→d], then →d is equal to:

The maximum of f(x)=logxx2(x&gt;0) occurs, when x is equal to

The circle x^2 + y^2 -4x - 8y - 5=0 intersects the line 3x-4y=m at two distinct points. What is the range of m?

The length of the sub-tangent and sub-normal is equal for the curve y=epx+px at the point (0, 1), then the value of p is

Simplify :4(1 – sin2θ) (1 + tan2θ)

19. sin"x

If tan 3x-1tan 3x+1=3, then x = _____________.

area of a sector of angle p (in degrees) of a circle with radius R is ? explain !

The line (3x−y+5)+λ(2x−3y−4)=0 will be parallel to y-axis, if λ =

Why is sq. Root sin square x always +ve but square root 25 is +5 or -5?

Let P and Q be two points denoting the complex numbers α and β respectively on the complex plane. Which of the following equations can represent the equation of the circle passing through P and Q with least possible area ?

Ten eggs are drawn succesively with replacement from a lot of 100 eggs containing 10 rotten eggs. Then the probability that there is at least one rotten egg is:

limx→ax5/8−a5/8x1/3−a1/3=

The value of x + y + z is 15 if a, x, y, b are in A.P. while the value of 1x+1y+1z is 58 if a, x, y, z b are H.P., then a2+b2=

I want the solution for sin9A=sinA.

25) If }α and }β are zeros of the polynomial }f(x)=x^2-5x+k , such that }α-β=1. Find }K

If 2x+y4x5x-74x=77y-13yx+6, then the value of x and y is(a) x = 3, y = 1(b) x = 2, y = 3(c) x = 2, y = 4(d) x = 3, y = 3

The maximum value of the function f(x)=ln(1+x)−x (where x&gt;−1) occurs at x= 0

The derivative of f(x) defined by f(x)=tan−1(√1−cos x1+cos x), −π&lt;x&lt;πis

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

What are composite number?

Find the number of solutions of z2+z2=0

limx→3-x[x]=__________________.

If A=538201123. Write the cofactor of the element a32.

If tanx−tan2x>0 and |2sinx|<1 then the range of x for which both conditions hold good is (where n∈Z)

The maximum of f(x)=logxx2(x>0) occurs, when x is equal to

The maximum value of the function f(x)=ln(1+x)−x (where x>−1) occurs at x= 0

The derivative of f(x) defined by f(x)=tan−1(√1−cos x1+cos x), −π<x<πis