Changing Scale (Including Flags)

Q.

$\frac{d}{dx}\left[\log \left(x+\frac{1}{x}\right)\right]=$

1. $x+\frac{1}{x}$

2. $\frac{(1+{\displaystyle \frac{1}{x^2}})}{(x+\frac{1}{x})}$

3. $\frac{(1-{\displaystyle \frac{1}{x^2}})}{(x+\frac{1}{x})}$

4. $1+\frac{1}{x}$

Q.

In a triangle $ABC$, if vector $BC=8$, $CA=7$, $AB=10$, then the projection of the vector $\overrightarrow{AB}$ on $\overrightarrow{AC}$ is equal to:

1. $\frac{25}{4}$

2. $\frac{85}{14}$

3. $\frac{127}{20}$

4. $\frac{115}{16}$

Q.

Prove that, $(100-100)$ Divided by $(100-100)$ is equal to $2$.

Q.

Let $f\left(x\right)=\left|x-2\right|$ and $g\left(x\right)=f\left(f\right(x\left)\right),x\in \left[0,4\right]$.Then ${\int }_0^3\left(g\right(x)-f(x\left)\right)dx$ is equal to:

1. $\frac{1}{2}$

2. $0$

3. $1$

4. $\frac{3}{2}$

Q.

$\text{Re}\frac{{\left(1-i\right)}^2}{\left(3-i\right)}$ is equal to

1. $-\frac{1}{5}$

2. $\frac{1}{5}$

3. $\frac{1}{10}$

4. $-\frac{1}{10}$

Q.

A picnic is being planned in a school for Class $VII$. Girls are $60\%$ of the total number of students and are$18$ in number. The picnic site is $55km$from the school and the transport company is charging the rate of $Rs12perkm$. The total cost of refreshments will be $Rs4280.$ Find the ratio of the number of girls to the number of boys in the class?

Q.

If ${\log }_{0.3}(x-1)<{\log }_{0.09}(x-1)$, then $x$ lies in the interval:

1. $\left(2,\infty \right)$

2. $\left(1,2\right)$

3. $\left(-2,-1\right)$

4. None of these

Q.

The maximum value of $\frac{\log x}{x}$ in $\left(2,\infty \right)$ is

1. $1$

2. $\frac{2}{e}$

3. $e$

4. $\frac{1}{e}$

Q.

Find the range of the following data: 26, 21, 33, 17, 14, 15, 27.

1. 13

2. 15

3. 17

4. 19

Q.

If ${\log }_3\left({\log }_4\right({\log }_{2}x\left)\right)=0$, then the value of $x$ is

1. $16$

2. $8$

3. $32$

4. $2$

Q.

Question 88

Length and breadth of the floor of a room are 5 m and 3 m respectively. Forty tiles, each with area $\frac{1}{16}{m}^2$ are used to cover the floor partially. Find the ratio of the tiled to the non-tiled portion of the floor.

Q.

$\int \left\{e^x\left[\frac{\left(x^2+1\right)}{{\left(x+1\right)}^2}\right]\right\}dx=$

1. $\left[\frac{-e^x}{\left(x+1\right)}\right]+c$

2. $\left[\frac{e^x}{\left(x+1\right)}\right]+c$

3. $\left[\frac{x{e}^x}{\left(x+1\right)}\right]+c$

4. $\left\{e^x\left[\frac{\left(x-1\right)}{\left(x+1\right)}\right]\right\}+c$

Q.

Write the simplest form of the ratio $16:12$

Q. Two numbers are in the ratio of 15:11. If their H.C.F is 13, the numbers will be:

1. 195 and 143
2. 190 and 140
3. 185 and 163
4. 185 and 143

Q.

If $a^x=b^y=c^z=d^w$ then the value of $x\left[\right(1/y)+(1/z)+(1/w\left)\right]$is

Q.

Question 3 (vi)

Find the product:
$\frac{3}{-5}\times \frac{-5}{3}$

Q.

A car covers a distance of 600 m in 2 minutes whereas a train covers a distance of 75 km in 50 minutes. Find the ratio of their speed.

1. 1:5

2. 1:1

3. 1:2

4. 2:9

Q.

If $[\frac{(1-i)}{(1+i)}{]}^{100}=a+ib,$ then values of $a,b$

Q.

If $x,24,30$ and $16$ are in proportion, then $x=\_\_\_\_$ $\left[x=20/x=45\right]$

Q.

State whether the given statement is true (T) or false (F).

The ratio of $1hour$ to one day is $1:12$.

1. True
2. False

Q.

Which of the following statements is incorrect?

1. $xsgnx=\left|x\right|$

2. $\left|x\right|sgnx=x$

3. $x(sgnx)(sgnx)=x$

4. $\left|x\right|{(sgnx)}^3=\left|x\right|$

Q.

Find the ratio of:-

$3years$to $8months$

Q.

Ravi and Rani started a business and invested money in the ratio 2 : 3. After one year the total profit was Rs 40, 000. The shares of Ravi in the profit is Rs.24000.

1. True
2. False

Q.

If Rs. 60 is divided into two parts in the ratio 1:3, then find the difference between those two parts.

1. Rs. 40

2. Rs. 30

3. Rs. 50

4. Rs. 60

Q.

Determine $n,\mathrm{if}{}^{2\mathrm{n}}\mathrm{C}_2:{}^{\mathrm{n}}\mathrm{C}_2::9:2$.

1. $5$

2. $4$

3. $3$

4. $2$

Q.

Dividing 90 in the ratio 1:2 gives ___ and 60

Q.

There are $102$ teachers in a school of $3300$ students. Find the ratio of the number of teachers to the number of students.

Q. Ratio of two numbers is 2 : 3 and their LCM is 36. Find the two numbers.

1. 12, 18
2. 8 , 12
3. 18, 24
4. 16, 24

Q.

$76ladies$complete a job in $33days$. Due to some reason, some ladies did not join the work and therefore it was completed in $44days$. The number of ladies who did not report for the work is

1. $17$

2. $18$

3. $19$

4. $20$

Q.

The value of ${\int }_2^4\frac{\log \left(t\right)}{t}dt$ is

1. $\frac{1}{2}\log {\left(2\right)}^2$

2. $\frac{5}{2}\log {\left(2\right)}^2$

3. $\frac{3}{2}\log {\left(2\right)}^2$

4. $\log {\left(2\right)}^2$