Mathematics Test

Question 1
1 / -0

How many words can be formed with the letters of the word VOWELS that begin with O and end with E?

A
24

B
60

C
120

D
720

Question 2

1 / -0

The median for the given frequency distribution is:

x	f
1	8
2	10
3	11
4	16
5	20
6	25
7	15
8	9
9	6

20

5

4

65

Question 3
1 / -0

If at any instant $t$, for a sphere, $r$ denotes the radius, $S$ denotes the surface area and $V$ denotes the volume, then what is $\frac{d V}{d t}$ equal to?

A
$\frac{1}{2} S \frac{d r}{d t}$

B
$\frac{1}{2} r \frac{d S}{d t}$

C
$r \frac{d S}{d t}$

D
$\frac{1}{2} r^2 \frac{d S}{d t}$

Question 4
1 / -0

If $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=3,|\vec{b}|=5$ and $|\vec{c}|=7$, find the angle between $\vec{a}$ and $\vec{b}$.

A
$\frac{\pi}{2}$

B
$\frac{\pi}{3}$

C
$\frac{\pi}{6}$

D
$\frac{\pi}{4}$

Question 5
1 / -0

Find the derivative of $\frac{1}{3 x^{2}}$ with respect to $x$.

A
$-\frac{6}{x^{3}}$

B
$-\frac{1}{x^{3}}$

C
$-\frac{2}{3 x^{3}}$

D
$-\frac{1}{6 x^{3}}$

Question 6
1 / -0

Corner points of the feasible region for an LPP are $(0,2),(3,0),(6,0)$ and $(0,5)$. Let $F=4 x$ $+6 y$ be the objective function. Find the value of the maximum value of $\mathrm{F}$ - minimum value of $\mathrm{F}$.

A
60

B
48

C
42

D
18

Question 7
1 / -0

Let ${f}({x})=2 {x}^{2}+\frac{1}{{x}}$, then ${f'}(1)$ is:

A
1

B
2

C
3

D
4

Question 8
1 / -0

The odds against an event $A$ are $5:3$ and odds in favor of another independent event $B$ and $6:5$. The chances that neither $A$ nor $B$ occurs is:

A
$\frac{52}{88}$

B
$\frac{25}{88}$

C
$\frac{10}{88}$

D
$\frac{12}{88}$

Question 9
1 / -0

A factory owner purchases two types of machines, A and B for his factory. The requirements and the limitations for the machines are as follows:

Machine Area occupied Labour force Daily output (in units)

A $1000 m$^2$$ 12 men 60

B 1200 m$^2$ 8 men 40

He has maximum area of $9000 \mathrm{~m}^{2}$ available, and 72 skilled labourers who can operate both the machines. How many machines of each type should he buy to maximise the daily output?

A
$6$

B
$7$

C
$9$

D
$10$

Question 10
1 / -0

In a class there are $16$ boys and $10$ girls. Three students are randomly selected. What is probability of selecting $1$ boy and $2$ girls?

A
$\frac{21}{73}$

B
$\frac{38}{63}$

C
$\frac{15}{73}$

D
$\frac{18}{65}$

Submit Test

Machine	Area occupied	Labour force	Daily output (in units)
A	$1000 m\(^2\)$	12 men	60
B	1200 m\(^2\)	8 men	40

Mathematics Tes...

Question 1

24

60

120

720

Question 2

20

5

4

65

Question 3

\(\frac{1}{2} S \frac{d r}{d t}\)

\(\frac{1}{2} r \frac{d S}{d t}\)

\(r \frac{d S}{d t}\)

\(\frac{1}{2} r^2 \frac{d S}{d t}\)

Question 4

\(\frac{\pi}{2}\)

\(\frac{\pi}{3}\)

\(\frac{\pi}{6}\)

\(\frac{\pi}{4}\)

Question 5

\(-\frac{6}{x^{3}}\)

\(-\frac{1}{x^{3}}\)

\(-\frac{2}{3 x^{3}}\)

\(-\frac{1}{6 x^{3}}\)

Question 6

60

48

42

18

Question 7

1

2

3

4

Question 8

\(\frac{52}{88}\)

\(\frac{25}{88}\)

\(\frac{10}{88}\)

\(\frac{12}{88}\)

Question 9

\(6\)

\(7\)

\(9\)

\(10\)

Question 10

\(\frac{21}{73}\)

\(\frac{38}{63}\)

\(\frac{15}{73}\)

\(\frac{18}{65}\)

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