43030 + Interview Questions in Mathematics Page 45 InterviewSolution

2201.	Given A={x,y,z,}B={u,v,w},the function f:A→B defined by f(x)=u,f(y)=v,f(z)=w is
Answer» Given $A = {x, y, z,} B = {u, v, w}, t h e f u n c t i o n f : A \to B d e f i n e d b y f (x) = u, f (y) = v, f (z) = w$ is

Discussion

2202.	If tan 35∘= k, then the value of tan 145∘−tan125∘1+tan145∘tan125∘=
Answer» If tan $35^{\circ}$ = k, then the value of $\frac{t a n 145^{\circ} - t a n 125^{\circ}}{1 + t a n 145^{\circ} t a n 125^{\circ}}$ =

Discussion

2203.	(1+tan α tanβ)+(tan α−tanβ) is equal to
Answer» $(1 + t a n α t a n β) + (t a n α - t a n β)$ is equal to

Discussion

2204.	Kanchan has 10 friends among whom two are married to each other. She wishes to invite five of them for a party. If the married couples refuse to attend separately, then the number of different ways in which she can invite five friends is
Answer» Kanchan has $10$ friends among whom two are married to each other. She wishes to invite five of them for a party. If the married couples refuse to attend separately, then the number of different ways in which she can invite five friends is

Discussion

2205.	Let a1,a2,a3…,a9 be in harmonic progression. If a4=5 and a5=4, then the value of ∣∣∣∣∣1/a11/a21/a31/a41/a51/a61/a71/a81/a9∣∣∣∣∣ is
Answer» Let $a_{1}, a_{2}, a_{3} \dots, a_{9}$ be in harmonic progression. If $a_{4} = 5$ and $a_{5} = 4,$ then the value of $∣ ∣∣∣ ∣ \begin{matrix} 1 / a_{1} & 1 / a_{2} & 1 / a_{3} 1 / a_{4} & 1 / a_{5} & 1 / a_{6} 1 / a_{7} & 1 / a_{8} & 1 / a_{9} \end{matrix} ∣ ∣∣∣ ∣$ is

Discussion

2206.	Let α, β, are roots of (11 – x)3 + (13 – x)3 = (24 – 2x)3 then the value of α + β + is equal to
Answer» Let α, β, are roots of (11 – x)3 + (13 – x)3 = (24 – 2x)3 then the value of α + β + is equal to

Discussion

2207.	This is not a question. I wanted to request you something. Can you send me some very tough iit questions from this and from quadratic equations.
Answer» This is not a question. I wanted to request you something. Can you send me some very tough iit questions from this and from quadratic equations.

2207.

This is not a question. I wanted to request you something. Can you send me some very tough iit questions from this and from quadratic equations.

Answer»

This is not a question.

I wanted to request you something.

Can you send me some very tough iit questions from this and from quadratic equations.

Discussion

2208.	What is cyclicity.
Answer» What is cyclicity.

Discussion

2209.	L1 and L2 are two lines whose vector equations are L1:→r=λ(cosθ+√3)^i+(√2sinθ)^j+(cosθ−√3)^k L2:→r=μ(a^i+b^j+c^k), where λ and μ are scalars and α is the acute angle between L1 and L2. If the angle α is independent of θ, then the value of α is
Answer» $L_{1}$ and $L_{2}$ are two lines whose vector equations are $L_{1} : \to r = λ (cos θ + \sqrt{3})^i + (\sqrt{2} sin θ)^j + (cos θ - \sqrt{3})^k$ $L_{2} : \to r = μ (a^i + b^j + c^k),$ where $λ$ and $μ$ are scalars and $α$ is the acute angle between $L_{1}$ and $L_{2} .$ If the angle $α$ is independent of $θ,$ then the value of $α$ is

Discussion

2210.	Find the real part of ((x+iy)+i(x+iy)+2) Take (\|(x+2)+iy\|) =√1k
Answer» Find the real part of $(\frac{(x + i y) + i}{(x + i y) + 2})$ Take $(\| (x + 2) + i y \|)$ = $\sqrt{\frac{1}{k}}$

Discussion

2211.	A term is selected from the expansion of (x+y+z)10 at random. The probability that two variables out of x, y, z have same power is
Answer» A term is selected from the expansion of $(x + y + z)^{10}$ at random. The probability that two variables out of x, y, z have same power is

Discussion

2212.	The value of 10∑n=1−2n∫−2n−1sin27x dx+10∑n=12n+1∫2nsin27x dx is equal to
Answer» The value of $10 \sum n = 1 - 2 n \int - 2 n - 1 {sin}^{27} x d x + 10 \sum n = 1 2 n + 1 \int 2 n {sin}^{27} x d x$ is equal to

Discussion

2213.	A cup of coffee cools from 90∘C to 80∘C in t mins, when the room temperature is 20∘C. The time taken by a similar cup of coffee to cool from 80∘C to 60∘C at a room temperature same at 20∘C.
Answer» A cup of coffee cools from $90^{\circ} C$ to $80^{\circ} C$ in $t mins$ , when the room temperature is $20^{\circ} C$ . The time taken by a similar cup of coffee to cool from $80^{\circ} C$ to $60^{\circ} C$ at a room temperature same at $20^{\circ} C$ .

Discussion

2214.	Discuss the continuity of the cosine, cosecant, secant and cotangent functions,
Answer» Discuss the continuity of the cosine, cosecant, secant and cotangent functions,

Discussion

2215.	Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.
Answer» Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.

Discussion

2216.	The equation of the plane which contains the line x4=y2=z1 and is perpendicular to the plane containing the lines x−41=y−54=z−92 and x+84=y+62=z−21
Answer» The equation of the plane which contains the line $\frac{x}{4} = \frac{y}{2} = \frac{z}{1}$ and is perpendicular to the plane containing the lines $\frac{x - 4}{1} = \frac{y - 5}{4} = \frac{z - 9}{2}$ and $\frac{x + 8}{4} = \frac{y + 6}{2} = \frac{z - 2}{1}$

Discussion

2217.	∫dx4+5sin2xdx is equal to.
Answer» $\int \frac{dx}{4 + 5 {sin}^{2} x} dx$ is equal to.

Discussion

2218.	what is mole ? explain in detail.
Answer» what is mole ? explain in detail.

Discussion

2219.	Find the 12thterm of a G.P. whose 8th term is 192 and the common ratiois 2.
Answer» Find the 12^th term of a G.P. whose 8^th term is 192 and the common ratio is 2.

Discussion

2220.	The value of 1.5∫0[x2]dx is
Answer» The value of $1.5 \int 0 [x^{2}] d x$ is

Discussion

2221.	If sinx+siny=3(cosy−cosx), then the value of sin3xsin3y is
Answer» If $sin x + sin y = 3 (cos y - cos x)$ , then the value of $\frac{sin 3 x}{sin 3 y}$ is

Discussion

2222.	Prove that the family of lines represented by x(1+λ)+y(2−λ)+5=0,λ being arbitary, pass through a fixed point .Also,find the fixed point.
Answer» Prove that the family of lines represented by $x (1 + λ) + y (2 - λ) + 5 = 0, λ$ being arbitary, pass through a fixed point .Also,find the fixed point.

Discussion

2223.	Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements,(i) do the words start with P(ii) do all the vowels always occur together(iii) do the vowels never occur together(iv) do the words begin with I and end in P ?
Answer» Find the number of arrangements of the letters of the word $I N D E P E N D E N C E$ . In how many of these arrangements, $(i)$ do the words start with $P$ $(i i)$ do all the vowels always occur together $(i i i)$ do the vowels never occur together $(i v)$ do the words begin with $I$ and end in $P$ ?

Discussion

2224.	If two ordered pairs are related as(a4,a−2b)=(0,6+b), then a+b is
Answer» If two ordered pairs are related as $(\frac{a}{4}, a - 2 b) = (0, 6 + b)$ , then $a + b$ is

Discussion

2225.	Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): x4 (5 sin x – 3 cos x)
Answer» Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): x⁴ (5 sin x – 3 cos x)

Discussion

2226.	The equation of the plane parallel to the plane 2x+3y+4z+5=0 and passing through the point (1,1,1) is:
Answer» The equation of the plane parallel to the plane $2 x + 3 y + 4 z + 5 = 0$ and passing through the point $(1, 1, 1)$ is:

Discussion

2227.	If a,b∈R and limx→1(a[x+1]+b[x−1]) exists, then the value of a+b is(where [.] denotes greatest integer function)
Answer» If $a, b \in R$ and $lim x \to 1 (a [x + 1] + b [x - 1])$ exists, then the value of $a + b$ is $($ where $[.]$ denotes greatest integer function $)$

Discussion

2228.	Given that vectorP+vectorQ=vectorR and that VectorR is perpendicular to vector P.If magnitude of vector P=magnitude of vector R,then what is the angle between P & Q?
Answer» Given that vectorP+vectorQ=vectorR and that VectorR is perpendicular to vector P.If magnitude of vector P=magnitude of vector R,then what is the angle between P & Q?

Discussion

2229.	Find the equation of the hyperbola satisfying the give conditions: Vertices (±7, 0),
Answer» Find the equation of the hyperbola satisfying the give conditions: Vertices (±7, 0),

Discussion

2230.	If log xb−c=log yc−a=log za−b, then which of the following is true
Answer» If $\frac{l o g x}{b - c} = \frac{l o g y}{c - a} = \frac{l o g z}{a - b}$ , then which of the following is true

Discussion

2231.	The area bounded by the curve y=sin2x, x=0, x=π and X-axis is
Answer» The area bounded by the curve $y = sin 2 x, x = 0, x = π$ and X-axis is

Discussion

2232.	The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, then the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is:
Answer» The product of three consecutive terms of a $G.P.$ is $512.$ If $4$ is added to each of the first and the second of these terms, then the three terms now form an $A.P.$ Then the sum of the original three terms of the given $G.P.$ is:

Discussion

2233.	Check the injectivity and surjectivity of the following functions: (i) f : N → N given by f ( x ) = x 2 (ii) f : Z → Z given by f ( x ) = x 2 (iii) f : R → R given by f ( x ) = x 2 (iv) f : N → N given by f ( x ) = x 3 (v) f : Z → Z given by f ( x ) = x 3
Answer» Check the injectivity and surjectivity of the following functions: (i) f : N → N given by f ( x ) = x 2 (ii) f : Z → Z given by f ( x ) = x 2 (iii) f : R → R given by f ( x ) = x 2 (iv) f : N → N given by f ( x ) = x 3 (v) f : Z → Z given by f ( x ) = x 3

Discussion

2234.	Equation of the ellipse with foci (±5,0) and length of major axis 26 is
Answer» Equation of the ellipse with foci ( $\pm$ 5,0) and length of major axis 26 is

Discussion

2235.	If y=f(x) is quadratic polynomial having vertex at (6,8), as shown in the figure below, then f(x) is
Answer» If $y = f (x)$ is quadratic polynomial having vertex at $(6, 8),$ as shown in the figure below, then $f (x)$ is

Discussion

2236.	If √x+1 + √x-1 = 2 , then the value of x is
Answer» If √x+1 + √x-1 = 2 , then the value of x is

Discussion

2237.	The probability that A speaks truth is 45, while this probability for B is 34. The probability that they contradict each other when asked to speak on a fact is
Answer» The probability that A speaks truth is $\frac{4}{5}$ , while this probability for B is $\frac{3}{4}$ . The probability that they contradict each other when asked to speak on a fact is

Discussion

2238.	The value of limx→0cos2x−1cosx−1 is
Answer» The value of $lim x \to 0 \frac{cos 2 x - 1}{cos x - 1}$ is

Discussion

2239.	If x2+y2=4, then ydydx+x+2 is equal to
Answer» If $x^{2} + y^{2} = 4,$ then $y \frac{d y}{d x} + x + 2$ is equal to

Discussion

2240.	Show that the relation R defined in the set A of all polygons as R = {(P1,P2):P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?
Answer» Show that the relation R defined in the set A of all polygons as R = { $(P_{1}, P_{2}) : P_{1}$ and $P_{2}$ have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?

Discussion

2241.	If a line y=mx+c is a tangent to the circle (x−3)2+y2=1 and it is perpendicular to a line L1, where L1 is the tangent to the circle x2+y2=1 at the point (1√2,1√2); then:
Answer» If a line $y = m x + c$ is a tangent to the circle $(x - 3)^{2} + y^{2} = 1$ and it is perpendicular to a line $L_{1}$ , where $L_{1}$ is the tangent to the circle $x^{2} + y^{2} = 1$ at the point $(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})$ ; then:

Discussion

2242.	Evaluate the Given limit:
Answer» Evaluate the Given limit:

Discussion

2243.	Find the value of λ if the point (3, 5) lies inside the circle x2+y2+6x+λy+5=0
Answer» Find the value of λ if the point (3, 5) lies inside the circle $x^{2} + y^{2} + 6 x + λ y + 5 = 0$

Discussion

2244.	Let ∫ex2⋅ex(2x2+x+1) dx=ex2f(x)+c, where c is constant of integration. If the minimum value of f(x) is m, then the value of [−1m] is (where [.] represents grestest integer function)
Answer» Let $\int e^{x^{2}} \cdot e^{x} (2 x^{2} + x + 1) d x = e^{x^{2}} f (x) + c$ , where $c$ is constant of integration. If the minimum value of $f (x)$ is $m$ , then the value of $[- \frac{1}{m}]$ is (where [.] represents grestest integer function)

Discussion

2245.	Solution of the differential equation (x3−3xy2)dx=(y3−3x2y)dy is:(where C is integration constant)
Answer» Solution of the differential equation $(x^{3} - 3 x y^{2}) d x = (y^{3} - 3 x^{2} y) d y$ is: (where $C$ is integration constant)

Discussion

2246.	Let h(x)=f(x)−a(f(x))2+a(f(x))3 for every real number x. If f(x) is strictly increasing function, then h(x) is non-monotonic function given
Answer» Let $h (x) = f (x) - a (f (x))^{2} + a (f (x))^{3}$ for every real number $x$ . If $f (x)$ is strictly increasing function, then $h (x)$ is non-monotonic function given

Discussion

2247.	The value of k for which the planes 3x - 6y - 2z = 7 and 2x + y - kz = 5 are perpendicular to each other, is [MP PET 1992]
Answer» The value of k for which the planes 3x - 6y - 2z = 7 and 2x + y - kz = 5 are perpendicular to each other, is [MP PET 1992]

2247.

The value of k for which the planes 3x - 6y - 2z = 7 and 2x + y - kz = 5 are perpendicular to each other, is [MP PET 1992]

Answer»

The value of k for which the planes 3x - 6y - 2z = 7 and 2x + y - kz = 5 are perpendicular to each other, is
[MP PET 1992]

Discussion

2248.	If 4x≥7, then the range of x is
Answer» If $\frac{4}{x} \geq 7$ , then the range of $x$ is

Discussion

2249.	If l, m, n are the direction cosines of the normal to the plane and p be the perpendicular distance of the plane from the origin, then the equation of the plane is:
Answer» If l, m, n are the direction cosines of the normal to the plane and p be the perpendicular distance of the plane from the origin, then the equation of the plane is:

Discussion

2250.	A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 ½ m apart, what is the length of the wood reqired for the rungs?
Answer» A ladder has rungs $25 c m$ apart. The rungs decrease uniformly in length from $45 c m$ at the bottom to $25 c m$ at the top. If the top and bottom rungs are 2 ½ m apart, what is the length of the wood reqired for the rungs?

Discussion

Explore topic-wise InterviewSolutions in .

Given A={x,y,z,}B={u,v,w},the function f:A→B defined by f(x)=u,f(y)=v,f(z)=w is

If tan 35∘= k, then the value of tan 145∘−tan125∘1+tan145∘tan125∘=

(1+tan α tanβ)+(tan α−tanβ) is equal to

Kanchan has 10 friends among whom two are married to each other. She wishes to invite five of them for a party. If the married couples refuse to attend separately, then the number of different ways in which she can invite five friends is

Let a1,a2,a3…,a9 be in harmonic progression. If a4=5 and a5=4, then the value of ∣∣∣∣∣1/a11/a21/a31/a41/a51/a61/a71/a81/a9∣∣∣∣∣ is

Let α, β, are roots of (11 – x)3 + (13 – x)3 = (24 – 2x)3 then the value of α + β + is equal to

This is not a question. I wanted to request you something. Can you send me some very tough iit questions from this and from quadratic equations.

What is cyclicity.

L1 and L2 are two lines whose vector equations are L1:→r=λ(cosθ+√3)^i+(√2sinθ)^j+(cosθ−√3)^k L2:→r=μ(a^i+b^j+c^k), where λ and μ are scalars and α is the acute angle between L1 and L2. If the angle α is independent of θ, then the value of α is

Find the real part of ((x+iy)+i(x+iy)+2) Take (|(x+2)+iy|) =√1k

A term is selected from the expansion of (x+y+z)10 at random. The probability that two variables out of x, y, z have same power is

The value of 10∑n=1−2n∫−2n−1sin27x dx+10∑n=12n+1∫2nsin27x dx is equal to

A cup of coffee cools from 90∘C to 80∘C in t mins, when the room temperature is 20∘C. The time taken by a similar cup of coffee to cool from 80∘C to 60∘C at a room temperature same at 20∘C.

Discuss the continuity of the cosine, cosecant, secant and cotangent functions,

Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.

The equation of the plane which contains the line x4=y2=z1 and is perpendicular to the plane containing the lines x−41=y−54=z−92 and x+84=y+62=z−21

∫dx4+5sin2xdx is equal to.

what is mole ? explain in detail.

Find the 12thterm of a G.P. whose 8th term is 192 and the common ratiois 2.

The value of 1.5∫0[x2]dx is

If sinx+siny=3(cosy−cosx), then the value of sin3xsin3y is

Prove that the family of lines represented by x(1+λ)+y(2−λ)+5=0,λ being arbitary, pass through a fixed point .Also,find the fixed point.

Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements,(i) do the words start with P(ii) do all the vowels always occur together(iii) do the vowels never occur together(iv) do the words begin with I and end in P ?

If two ordered pairs are related as(a4,a−2b)=(0,6+b), then a+b is

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): x4 (5 sin x – 3 cos x)

The equation of the plane parallel to the plane 2x+3y+4z+5=0 and passing through the point (1,1,1) is:

If a,b∈R and limx→1(a[x+1]+b[x−1]) exists, then the value of a+b is(where [.] denotes greatest integer function)

Given that vectorP+vectorQ=vectorR and that VectorR is perpendicular to vector P.If magnitude of vector P=magnitude of vector R,then what is the angle between P & Q?

Find the equation of the hyperbola satisfying the give conditions: Vertices (±7, 0),

If log xb−c=log yc−a=log za−b, then which of the following is true

The area bounded by the curve y=sin2x, x=0, x=π and X-axis is

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, then the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is:

Check the injectivity and surjectivity of the following functions: (i) f : N → N given by f ( x ) = x 2 (ii) f : Z → Z given by f ( x ) = x 2 (iii) f : R → R given by f ( x ) = x 2 (iv) f : N → N given by f ( x ) = x 3 (v) f : Z → Z given by f ( x ) = x 3

Equation of the ellipse with foci (±5,0) and length of major axis 26 is

If y=f(x) is quadratic polynomial having vertex at (6,8), as shown in the figure below, then f(x) is

If √x+1 + √x-1 = 2 , then the value of x is

The probability that A speaks truth is 45, while this probability for B is 34. The probability that they contradict each other when asked to speak on a fact is

The value of limx→0cos2x−1cosx−1 is

If x2+y2=4, then ydydx+x+2 is equal to

Show that the relation R defined in the set A of all polygons as R = {(P1,P2):P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?

If a line y=mx+c is a tangent to the circle (x−3)2+y2=1 and it is perpendicular to a line L1, where L1 is the tangent to the circle x2+y2=1 at the point (1√2,1√2); then:

Evaluate the Given limit:

Find the value of λ if the point (3, 5) lies inside the circle x2+y2+6x+λy+5=0

Let ∫ex2⋅ex(2x2+x+1) dx=ex2f(x)+c, where c is constant of integration. If the minimum value of f(x) is m, then the value of [−1m] is (where [.] represents grestest integer function)

Solution of the differential equation (x3−3xy2)dx=(y3−3x2y)dy is:(where C is integration constant)

Let h(x)=f(x)−a(f(x))2+a(f(x))3 for every real number x. If f(x) is strictly increasing function, then h(x) is non-monotonic function given

The value of k for which the planes 3x - 6y - 2z = 7 and 2x + y - kz = 5 are perpendicular to each other, is [MP PET 1992]

If 4x≥7, then the range of x is

If l, m, n are the direction cosines of the normal to the plane and p be the perpendicular distance of the plane from the origin, then the equation of the plane is:

A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 ½ m apart, what is the length of the wood reqired for the rungs?