43030 + Interview Questions in Mathematics Page 150 InterviewSolution

7451.	Reduce the following equations into normal form. Find theirperpendicular distances from the origin and angle betweenperpendicular and the positive x-axis.(i) (ii) y – 2 = 0 (iii) x – y = 4
Answer» Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis. (i) (ii) y – 2 = 0 (iii) x – y = 4

7451.

Reduce the following equations into normal form. Find theirperpendicular distances from the origin and angle betweenperpendicular and the positive x-axis.(i) (ii) y – 2 = 0 (iii) x – y = 4

Answer»

Reduce the following equations into normal form. Find their
perpendicular distances from the origin and angle between
perpendicular and the positive x-axis.

(i)

(ii) y – 2 = 0 (iii) x – y = 4

Discussion

7452.	The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.
Answer» The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

Discussion

7453.	34. If sin+sinα+sinX=4,find sinsinα sinβ sinX
Answer» 34. If sin+sinα+sinX=4,find sinsinα sinβ sinX

Discussion

7454.	If Ar=cosπ3r+isinπ3r, then the value of A1⋅A2⋅A3⋅⋯⋅A∞ is (where i=√−1)
Answer» If $A_{r} = cos \frac{π}{3^{r}} + i sin \frac{π}{3^{r}},$ then the value of $A_{1} \cdot A_{2} \cdot A_{3} \cdot \dots \cdot A_{\infty}$ is (where $i = \sqrt{- 1}$ )

Discussion

7455.	How to represent √41 on a no. Line
Answer» How to represent √41 on a no. Line

Discussion

7456.	22s = -11t + 16 ; 44(t + 2s) = 12 Consider the system of equations above. How many solutions (s, t) does this system have ?
Answer» 22s = -11t + 16 ; 44(t + 2s) = 12 Consider the system of equations above. How many solutions (s, t) does this system have ?

Discussion

7457.	The value of limx→11−√x(cos−1x)2 is
Answer» The value of $lim x \to 1 \frac{1 - \sqrt{x}}{{({cos}^{- 1} x)}^{2}}$ is

Discussion

7458.	The derivative of sec−1(12x2−1),x∈(1√2,1) with respect to √1+3x at x=0 is
Answer» The derivative of ${sec}^{- 1} (\frac{1}{2 x^{2} - 1}), x \in (\frac{1}{\sqrt{2}}, 1)$ with respect to $\sqrt{1 + 3 x}$ at $x = 0$ is

Discussion

7459.	Family of curves which makes an angle π4 whith the family of hyperbola xy = C2 is
Answer» Family of curves which makes an angle $\frac{π}{4}$ whith the family of hyperbola xy = $C^{2}$ is

Discussion

7460.	Evaluate ∫x2+3xx2+5x+6dx(where C is constant of integration)
Answer» Evaluate $\int \frac{x^{2} + 3 x}{x^{2} + 5 x + 6} d x$ (where $C$ is constant of integration)

Discussion

7461.	If in case \|x+2\| =3 , then x+2 = + or - 3 Then why in inequality \|x\| ≥ 4 , + or - x ≥ 4 and why not x≥ + or - 4 ?
Answer» If in case \|x+2\| =3 , then x+2 = + or - 3 Then why in inequality \|x\| ≥ 4 , + or - x ≥ 4 and why not x≥ + or - 4 ?

7461.

If in case |x+2| =3 , then x+2 = + or - 3 Then why in inequality |x| ≥ 4 , + or - x ≥ 4 and why not x≥ + or - 4 ?

Answer»

If in case |x+2| =3 , then x+2 = + or - 3

Then why in inequality |x| ≥ 4 , + or - x ≥ 4 and why not x≥ + or - 4 ?

Discussion

7462.	If tan x + cot x = 4, then tan4x + cot4x = ___________.
Answer» If tan x + cot x = 4, then tan⁴x + cot⁴x = ___________.

Discussion

7463.	limx→1(2x−3)(√x−1)(2x2+x−3) = [IIT 1977]
Answer» $l i m_{x \to 1}$ $\frac{(2 x - 3) (\sqrt{x} - 1)}{({2 x}^{2} + x - 3)}$ = [IIT 1977]

Discussion

7464.	Mark the correct alternative in the following question:If abc=0, then xabcxbca=a 3 b 0 c -1 d 1
Answer» Mark the correct alternative in the following question: $If a b c = 0, then \frac{{\{{(x^{a})}^{b}\}}^{c}}{{\{{(x^{b})}^{c}\}}^{a}} = (a) 3 (b) 0 (c) - 1 (d) 1$

Discussion

7465.	Let A={2, 3, 4, 6} and R={(x,y):y = x2−x; x,y∈A} is a relation on A, then write R as set of ordered pairs ?
Answer» Let $A = {2, 3, 4, 6}$ and $R = {(x, y) : y = x^{2} - x; x, y \in A}$ is a relation on $A$ , then write $R$ as set of ordered pairs ?

Discussion

7466.	Let Sk=k∑r=1tan−1(6r22r+1+32r+1), then limk→∞Sk is equal to :
Answer» Let $S_{k} = k \sum r = 1 {tan}^{- 1} (\frac{6^{r}}{2^{2 r + 1} + 3^{2 r + 1}})$ , then $lim k \to \infty S_{k}$ is equal to :

Discussion

7467.	Iflimx→−∞(√x2−x+1−ax−b)=0 then the values of a and b are given by -
Answer» $If l i m x \to - \infty (\sqrt{x^{2} - x + 1} - a x - b) = 0$ then the values of a and b are given by -

Discussion

7468.	14. The value of f(0) so that the function f(x)=log(1+xtanx)/sinx, x not equal to zero, continuous at x=0,is given by
Answer» 14. The value of f(0) so that the function f(x)=log(1+xtanx)/sinx, x not equal to zero, continuous at x=0,is given by

Discussion

7469.	If in a ΔABC, ∠A=45∘, ∠B=60∘, and ∠C=75∘; find the ratio of its sides.
Answer» $If in a Δ A B C, ∠ A = 45^{\circ}, ∠ B = 60^{\circ}, and ∠ C = 75^{\circ}; find the ratio of its sides.$

Discussion

7470.	If x=tan (1a log y), then the value of (1+x2)d2ydx2+(2x−a)dydx is
Answer» $If x = tan (\frac{1}{a} log y), then the value of (1 + x^{2}) \frac{d^{2} y}{{dx}^{2}} + (2 x - a) \frac{dy}{dx} is$

Discussion

7471.	What is the difference between the graph of 4π^2(dr)(psi)^2 and 4πr^2(psi)^2? How to identify whether a graph is that of psi(r) or psi(r^2) (r) or 4π^2(dr)(psi)^2 (r) or 4πr^2(psi)^2 ? Also why does the graph of 4πr^2(dr)(psi)^2 of s and p orbitals start from different points (top or bottom) ?
Answer» What is the difference between the graph of 4π^2(dr)(psi)^2 and 4πr^2(psi)^2? How to identify whether a graph is that of psi(r) or psi(r^2) (r) or 4π^2(dr)(psi)^2 (r) or 4πr^2(psi)^2 ? Also why does the graph of 4πr^2(dr)(psi)^2 of s and p orbitals start from different points (top or bottom) ?

Discussion

7472.	Let A and B are events of an experiment such that P(A)=14,P(A∪B)=12, then the value of P(B/Ac) is
Answer» Let $A$ and $B$ are events of an experiment such that $P (A) = \frac{1}{4}, P (A \cup B) = \frac{1}{2},$ then the value of $P (B / A^{c})$ is

Discussion

7473.	∫tan2(3x+5)dx is equal to (where C is the constant of integration)
Answer» $\int {tan}^{2} (3 x + 5) d x$ is equal to (where $C$ is the constant of integration)

Discussion

7474.	Let y=f(x) be a function satisfying the differential equation xdydx+2y=4x2 and f(1)=1, then f(−3) is equal to
Answer» Let $y = f (x)$ be a function satisfying the differential equation $x \frac{d y}{d x} + 2 y = 4 x^{2}$ and $f (1) = 1$ , then $f (- 3)$ is equal to

Discussion

7475.	Find x from the following equations:(i) cosecπ2+θ+x cos θ cotπ2+θ=sinπ2+θ(ii) x cotπ2+θ+tanπ2+θsin θ+cosecπ2+θ=0
Answer» Find x from the following equations: $(i) cosec (\frac{π}{2} + θ) + x \cos θ \cot (\frac{π}{2} + θ) = \sin (\frac{π}{2} + θ) (ii) x \cot (\frac{π}{2} + θ) + \tan (\frac{π}{2} + θ) \sin θ + cosec (\frac{π}{2} + θ) = 0$

Discussion

7476.	A pariticle is moving along x-axis such that its position varies with time as x=t^2 - 4t + 6. The distance travelled by the particle in 1st 3 second of its motion (x is in meter, t is in time) is___?
Answer» A pariticle is moving along x-axis such that its position varies with time as x=t^2 - 4t + 6. The distance travelled by the particle in 1st 3 second of its motion (x is in meter, t is in time) is___?

Discussion

7477.	Mark the correct alternative in each of the following:If x<7, then(a) -x<-7(b) -x≤-7(c) -x>-7(d) -x≥-7
Answer» Mark the correct alternative in each of the following: If x $<$ 7, then (a) $-$ x $<$ $-$ 7 (b) $-$ x $\leq -$ 7 (c) $-$ x $> -$ 7 (d) $-$ x $\geq -$ 7

Discussion

7478.	Pair the multiplication statements that give the same answer.
Answer» Pair the multiplication statements that give the same answer.

Discussion

7479.	In a library, there are 4 science books, 4 maths books and 3 political science books all of which are on different topics. The number of ways in which at least one book of each subject is selected, is
Answer» In a library, there are $4$ science books, $4$ maths books and $3$ political science books all of which are on different topics. The number of ways in which at least one book of each subject is selected, is

Discussion

7480.	Prove that the function f givenby f(x) = log cos x is strictly decreasing on and strictly increasing on
Answer» Prove that the function f given by f(x) = log cos x is strictly decreasing on and strictly increasing on

Discussion

7481.	Give three examples of sentences which are not statements. Give reasons for the answers.
Answer» Give three examples of sentences which are not statements. Give reasons for the answers.

Discussion

7482.	A point R with x -coordinate 4 lies on the line segment joining the pointsP (2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R. [ Hint suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by
Answer» A point R with x -coordinate 4 lies on the line segment joining the pointsP (2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R. [ Hint suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by

Discussion

7483.	Write the coordinates of the following points: 1. M 2. E 3. G 4. C
Answer» Write the coordinates of the following points: 1. M 2. E 3. G 4. C

7483.

Write the coordinates of the following points: 1. M 2. E 3. G 4. C

Answer»

Write the coordinates of the following points:

1. M 2. E 3. G 4. C

Discussion

7484.	Find the derivative of the following function (it is to be understood that a,is a fixed non-zero constant): f(x)= (x+a)
Answer» Find the derivative of the following function (it is to be understood that a,is a fixed non-zero constant): f(x)= (x+a)

Discussion

7485.	Prove the following trigonometric identities.If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ − 3 cos θ = ± 3.
Answer» Prove the following trigonometric identities. If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ − 3 cos θ = ± 3.

Discussion

7486.	Write the value of 2 (sin6 x + cos6 x) −3 (sin4 x + cos4 x) + 1.
Answer» Write the value of 2 (sin⁶ x + cos⁶ x) −3 (sin⁴ x + cos⁴ x) + 1.

Discussion

7487.	Let f:R→R be a function defined by f(x)={[x], x≤2 0, x>2, where [x] is the greatest integer less than or equal to x. If I=2∫−1xf(x2)2+f(x+1)dx, then the value of (4I–1) is
Answer» Let $f : R \to R$ be a function defined by $f (x) = {\begin{matrix} [x], x \leq 2 0, x > 2 \end{matrix},$ where $[x]$ is the greatest integer less than or equal to $x .$ If $I = 2 \int - 1 \frac{x f (x^{2})}{2 + f (x + 1)} d x,$ then the value of $(4 I - 1)$ is

Discussion

7488.	The sum of all real values of x satisfying the equation (x2−5x+5)(x2+4x−60)=1 is
Answer» The sum of all real values of $x$ satisfying the equation $(x^{2} - 5 x + 5)^{(x^{2} + 4 x - 60)} = 1$ is

Discussion

7489.	Im,n=∫10xm(logx)ndx, then Im,n is equal to
Answer» $I_{m, n} = \int_{0}^{1} x^{m} (log x)^{n} d x$ , then $I_{m, n}$ is equal to

Discussion

7490.	There are ten pairs of shoes in a cup board out of which 4 are picked up at random one after the other. The probability that there is at least one pair is
Answer» There are ten pairs of shoes in a cup board out of which 4 are picked up at random one after the other. The probability that there is at least one pair is

Discussion

7491.	For 0< ϕ < π2, if x=∑∞n=0cos2nϕ, y=∑∞n=0sin2nϕ, z=∑∞n=0cos2n ϕ, then
Answer» For 0< $ϕ$ < $\frac{π}{2}, i f x = \sum_{n = 0}^{\infty} c o s^{2 n} ϕ, y = \sum_{n = 0}^{\infty} s i n^{2 n} ϕ, z = \sum_{n = 0}^{\infty} c o s^{2 n} ϕ, t h e n$

Discussion

7492.	The approximate value of 3√−0.99 is
Answer» The approximate value of $\sqrt[3]{- 0.99}$ is

Discussion

7493.	Question 3 (i)The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC.The median from A meets BC at D. find the coordinates of the point D.
Answer» Question 3 (i) The points $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ are the vertices of $Δ$ ABC. The median from A meets BC at D. find the coordinates of the point D.

Discussion

7494.	Average daily wage of 50 workers of a factory was Rs 200 with a Standard Deviation of Rs 40. Each worker is given a raise of Rs 20. What is the new average daily wage and Standard Deviation? Have the wages become more or less uniform?
Answer» Average daily wage of 50 workers of a factory was Rs 200 with a Standard Deviation of Rs 40. Each worker is given a raise of Rs 20. What is the new average daily wage and Standard Deviation? Have the wages become more or less uniform?

Discussion

7495.	The locus of a point, which moves such that the sum of squares of its distance from the points (0,0),(1,0),(0,1),(1,1) is 18 units, is a circle of diameter d. Then d2 is equal to
Answer» The locus of a point, which moves such that the sum of squares of its distance from the points $(0, 0), (1, 0), (0, 1), (1, 1)$ is $18$ units, is a circle of diameter $d .$ Then $d^{2}$ is equal to

Discussion

7496.	If f(x)=⎧⎨⎩a+bx, x<1 4 x=1b−ax, x>1 is continuous at x=1 then the value of a,b is
Answer» If $f (x) = ⎧ ⎨ ⎩ \begin{matrix} a + b x, x < 1 4 x = 1 b - a x, x > 1 \end{matrix}$ is continuous at $x = 1$ then the value of $a, b$ is

Discussion

7497.	35 The correct decreasing order of basic strength of species: H2O, NH3,OH-,NH2- is
Answer» 35 The correct decreasing order of basic strength of species: H2O, NH3,OH-,NH2- is

Discussion

7498.	Solve (x2−1)dydx+2xy=1x2−1
Answer» Solve $(x^{2} - 1) \frac{d y}{d x} + 2 x y = \frac{1}{x^{2} - 1}$

Discussion

7499.	The vector equation of the straight line passing through the point with position vector ^i−3^j+^k and parallel to the vector, 2^i+3^j−4^k in standard cartesian form is:
Answer» The vector equation of the straight line passing through the point with position vector $^i - 3^j +^k$ and parallel to the vector, $2^i + 3^j - 4^k$ in standard cartesian form is:

Discussion

7500.	If the ratio of sum of n-terms of two different AP’s is (7n – 4) : (5n + 3), then the ratio of their mth term is equal to
Answer» If the ratio of sum of n-terms of two different AP’s is (7n – 4) : (5n + 3), then the ratio of their mth term is equal to

Discussion

Explore topic-wise InterviewSolutions in .

Reduce the following equations into normal form. Find theirperpendicular distances from the origin and angle betweenperpendicular and the positive x-axis.(i) (ii) y – 2 = 0 (iii) x – y = 4

The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

34. If sin+sinα+sinX=4,find sinsinα sinβ sinX

If Ar=cosπ3r+isinπ3r, then the value of A1⋅A2⋅A3⋅⋯⋅A∞ is (where i=√−1)

How to represent √41 on a no. Line

22s = -11t + 16 ; 44(t + 2s) = 12 Consider the system of equations above. How many solutions (s, t) does this system have ?

The value of limx→11−√x(cos−1x)2 is

The derivative of sec−1(12x2−1),x∈(1√2,1) with respect to √1+3x at x=0 is

Family of curves which makes an angle π4 whith the family of hyperbola xy = C2 is

Evaluate ∫x2+3xx2+5x+6dx(where C is constant of integration)

If in case |x+2| =3 , then x+2 = + or - 3 Then why in inequality |x| ≥ 4 , + or - x ≥ 4 and why not x≥ + or - 4 ?

If tan x + cot x = 4, then tan4x + cot4x = ___________.

limx→1(2x−3)(√x−1)(2x2+x−3) = [IIT 1977]

Mark the correct alternative in the following question:If abc=0, then xabcxbca=a 3 b 0 c -1 d 1

Let A={2, 3, 4, 6} and R={(x,y):y = x2−x; x,y∈A} is a relation on A, then write R as set of ordered pairs ?

Let Sk=k∑r=1tan−1(6r22r+1+32r+1), then limk→∞Sk is equal to :

Iflimx→−∞(√x2−x+1−ax−b)=0 then the values of a and b are given by -

14. The value of f(0) so that the function f(x)=log(1+xtanx)/sinx, x not equal to zero, continuous at x=0,is given by

If in a ΔABC, ∠A=45∘, ∠B=60∘, and ∠C=75∘; find the ratio of its sides.

If x=tan (1a log y), then the value of (1+x2)d2ydx2+(2x−a)dydx is

What is the difference between the graph of 4π^2(dr)(psi)^2 and 4πr^2(psi)^2? How to identify whether a graph is that of psi(r) or psi(r^2) (r) or 4π^2(dr)(psi)^2 (r) or 4πr^2(psi)^2 ? Also why does the graph of 4πr^2(dr)(psi)^2 of s and p orbitals start from different points (top or bottom) ?

Let A and B are events of an experiment such that P(A)=14,P(A∪B)=12, then the value of P(B/Ac) is

∫tan2(3x+5)dx is equal to (where C is the constant of integration)

Let y=f(x) be a function satisfying the differential equation xdydx+2y=4x2 and f(1)=1, then f(−3) is equal to

Find x from the following equations:(i) cosecπ2+θ+x cos θ cotπ2+θ=sinπ2+θ(ii) x cotπ2+θ+tanπ2+θsin θ+cosecπ2+θ=0

A pariticle is moving along x-axis such that its position varies with time as x=t^2 - 4t + 6. The distance travelled by the particle in 1st 3 second of its motion (x is in meter, t is in time) is___?

Mark the correct alternative in each of the following:If x&lt;7, then(a) -x&lt;-7(b) -x≤-7(c) -x&gt;-7(d) -x≥-7

Pair the multiplication statements that give the same answer.

In a library, there are 4 science books, 4 maths books and 3 political science books all of which are on different topics. The number of ways in which at least one book of each subject is selected, is

Prove that the function f givenby f(x) = log cos x is strictly decreasing on and strictly increasing on

Give three examples of sentences which are not statements. Give reasons for the answers.

A point R with x -coordinate 4 lies on the line segment joining the pointsP (2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R. [ Hint suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by

Write the coordinates of the following points: 1. M 2. E 3. G 4. C

Find the derivative of the following function (it is to be understood that a,is a fixed non-zero constant): f(x)= (x+a)

Prove the following trigonometric identities.If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ − 3 cos θ = ± 3.

Write the value of 2 (sin6 x + cos6 x) −3 (sin4 x + cos4 x) + 1.

Let f:R→R be a function defined by f(x)={[x], x≤2 0, x&gt;2, where [x] is the greatest integer less than or equal to x. If I=2∫−1xf(x2)2+f(x+1)dx, then the value of (4I–1) is

The sum of all real values of x satisfying the equation (x2−5x+5)(x2+4x−60)=1 is

Im,n=∫10xm(logx)ndx, then Im,n is equal to

There are ten pairs of shoes in a cup board out of which 4 are picked up at random one after the other. The probability that there is at least one pair is

For 0&lt; ϕ &lt; π2, if x=∑∞n=0cos2nϕ, y=∑∞n=0sin2nϕ, z=∑∞n=0cos2n ϕ, then

The approximate value of 3√−0.99 is

Question 3 (i)The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC.The median from A meets BC at D. find the coordinates of the point D.

Average daily wage of 50 workers of a factory was Rs 200 with a Standard Deviation of Rs 40. Each worker is given a raise of Rs 20. What is the new average daily wage and Standard Deviation? Have the wages become more or less uniform?

The locus of a point, which moves such that the sum of squares of its distance from the points (0,0),(1,0),(0,1),(1,1) is 18 units, is a circle of diameter d. Then d2 is equal to

If f(x)=⎧⎨⎩a+bx, x&lt;1 4 x=1b−ax, x&gt;1 is continuous at x=1 then the value of a,b is

35 The correct decreasing order of basic strength of species: H2O, NH3,OH-,NH2- is

Solve (x2−1)dydx+2xy=1x2−1

The vector equation of the straight line passing through the point with position vector ^i−3^j+^k and parallel to the vector, 2^i+3^j−4^k in standard cartesian form is:

If the ratio of sum of n-terms of two different AP’s is (7n – 4) : (5n + 3), then the ratio of their mth term is equal to

Mark the correct alternative in each of the following:If x<7, then(a) -x<-7(b) -x≤-7(c) -x>-7(d) -x≥-7

Let f:R→R be a function defined by f(x)={[x], x≤2 0, x>2, where [x] is the greatest integer less than or equal to x. If I=2∫−1xf(x2)2+f(x+1)dx, then the value of (4I–1) is

For 0< ϕ < π2, if x=∑∞n=0cos2nϕ, y=∑∞n=0sin2nϕ, z=∑∞n=0cos2n ϕ, then

If f(x)=⎧⎨⎩a+bx, x<1 4 x=1b−ax, x>1 is continuous at x=1 then the value of a,b is