Operations on Rational Numbers

Q.

Find all the zeroes of $2x^4-3x^3-3x^2+6x-2$, if two of its zeroes are $\sqrt{2}$ and $-\sqrt{2}.$

Q. Odd number times an odd number is always an even number.

1. True
2. False

Q. What is the value of ${1.5}^2?$

1. $1.25$
2. $2.15$
3. $2.25$
4. $2.20$

Q. Ross buys a water jug of capacity $3\frac{4}{5}$ litres. If he buys another jug which is $2\frac{2}{3}$ times as large as the smaller jug, how many litres can the larger one hold?

1. $\frac{152}{15}$
2. $10\frac{2}{5}$
3. $\frac{102}{5}$
4. None of the above.

Q. Choose the rational numbers, which lie, between the rational numbers, $\frac{3}{8}$​ and $\frac{7}{12}$​

1. $\frac{48}{96}$
2. $\frac{13}{16}$
3. $\frac{10}{24}$

Q. The product of two rational numbers is $\frac{28}{15}$​. If one of the numbers is $\frac{4}{5}$​ then what will be the value of other number?

1. $\frac{96}{75}$
2. $\frac{7}{3}$
3. $\frac{21}{9}$
4. (b) and (c) above.

Q. Monica spends $\frac{1}{3}$ of her salary on rent, $\frac{2}{5}$ on food and $\frac{1}{10}$ on monthly usuals. What fractional part of salary is left with herself ?

1. $\frac{5}{6}$
2. $\frac{1}{6}$
3. $\mathrm{0.1666....}$
4. (b) and (c) above.

Q.

Simplify $($ $\frac{2}{5}$of $\frac{3}{7}$$)$ $-$$($ $\frac{1}{6}$of $\frac{3}{5}$$)$ $+$$($ $\frac{1}{14}$of $\frac{2}{5}$$)$

Q. In a state, $\frac{17}{20}$ of total number of voters voted for candidate A whereas $\frac{2}{15}$ of voters voted for candidate B. Find the fraction of the voters who voted for candidates other than A and B.

1. $\frac{59}{60}$
2. $\frac{1}{15}$
3. $\frac{1}{60}$
4. $\frac{19}{20}$

Q. If $\frac{3}{4}$ fraction of total number of oranges in a box weighs 3 kg and 225 gm, how much does total number of oranges in the box weigh (in kgs)?

1. $\frac{43}{10}$ kg
2. $\frac{45}{3}$ kg
3. $4.3$ kg
4. (a) and (c) above.

Q.

Compute $4.659\times {10}^4-2.14\times {10}^4$. Round the answer appropriately. Express your answer as an integer using the proper number of significant figures.

Q. Number of digits to the right of the decimal point of $(2.0799{)}^2$ is $4.$

1. True
2. False

Q. Simplify the following:
$(-\frac{8}{25})\times \frac{5}{16}$

1. $0.1$
2. $-\frac{1}{10}$
3. $-0.1$
4. $\frac{1}{10}$

Q. Match the column I with their respective number of digits in the fractional part of that number in column II.

1. $10$
2. $0$
3. $4$
4. $2$

Q. Simplify:
$\frac{2}{3}\times \frac{6}{1}+\frac{3}{5}÷\frac{2}{7}-{\left(\frac{8}{3}\right)}^2\times \frac{3}{4}$

1. $\frac{23}{30}$
2. $\frac{76}{30}$
3. $6\frac{2}{30}$

Q. Find and match the value of the following surds:

1. 9
2. 256
3. 5

Q. Rationalisation of the numbers states that
A) The algebraic identity
$X^2-Y^2=(X+Y)(X-Y)$
which converts two linear expressions into an expression does not have linear terms.

$B)\text{If}X\text{or}Y$ happens to be a square root, the radical will disappear.

1. A is true and B is false
2. Both A and B are true
3. Both A and B are false
4. A is false and B is true

Q.

Simplify:$\frac{\mathrm{a}+1}{2}+\frac{2\mathrm{a}-1}{3}-\frac{3\mathrm{a}+1}{4}$