Model Question Paper 1

(-10) × 2 + 0 ÷ (-2) is equal to

1. -20

2. 20

3. -22

4. 22

Answer

Using the order of operations (BODMAS), we carry out multiplication and division (from left to right) before addition.

(-10) × 2 + 0 ÷ (-2)

= -20 + 0 ÷ (-2)

= -20 + 0

= -20.

Hence, Option 1 is the correct option.

The sum of a rational number $-\dfrac{1}{2}$ and its multiplicative inverse is

1. 0

2. 1

3. $-2\dfrac{1}{2}$

4. -2

Answer

The multiplicative inverse of $-\dfrac{1}{2}$ is $-\dfrac{2}{1}$ i.e. -2.

$\Rightarrow -\dfrac{1}{2} + (-2)$

$\Rightarrow \dfrac{-1}{2} + \dfrac{-2}{1}$

LCM of 2 and 1 is 2

$\Rightarrow \dfrac{-1 \times 1}{2 \times 1} + \dfrac{-2 \times 2}{1 \times 2}\\[1em] \Rightarrow \dfrac{-1}{2} + \dfrac{-4}{2}\\[1em] \Rightarrow \dfrac{-1 + (-4)}{2}\\[1em] \Rightarrow \dfrac{-5}{2}\\[1em] \Rightarrow -2\dfrac{1}{2}$

Hence, Option 3 is the correct option.

Evaluate: (-36) ÷ ((-14) + 2)

Answer

Solving,

(-36) ÷ ((-14) + 2)

= (-36) ÷ (-12)

= 3

Hence, (-36) ÷ ((-14) + 2) = 3.

If the length of a rectangle is 8.26 cm and its breadth is 5.5 cm, then find the area of the rectangle.

Answer

Length of the rectangle = 8.26 cm

Breadth of the rectangle = 5.5 cm

Area of rectangle = length × breadth

= 8.26 × 5.5

= 45.43 sq. cm

Hence, the area of the rectangle is 45.43 sq. cm.

Reduce the rational number $\dfrac{105}{-168}$ to standard form.

Answer

The denominator of $\dfrac{105}{-168}$ is negative. To make it positive, multiply its numerator and denominator by -1.

$\dfrac{105}{-168} = \dfrac{105 \times (-1)}{(-168) \times (-1)} = \dfrac{-105}{168}$

HCF of 105 and 168 is 21

So, divide its numerator and denominator by 21

$\dfrac{-105 \div 21}{168 \div 21} = \dfrac{-5}{8}$

Hence, the standard form of $\dfrac{105}{-168}$ is $\dfrac{-5}{8}$.

In a competition, the question paper consists of 20 questions. 5 marks are awarded for every correct answer and 2 marks are deducted for every incorrect answer and 0 marks for every question not attempted. Vishal attempted 17 questions and got 11 correct answers. What is his score?

Answer

Number of questions attempted by Vishal = 17

Number of correct answers = 11

Number of incorrect answers = 17 - 11 = 6

Marks awarded for every correct answer = 5

Marks deducted for every incorrect answer = 2

Vishal's score = $(11 \times 5) + (6 \times (-2))$

= 55 + (-12)

= 55 - 12

= 43.

Hence, Vishal's score is 43.

Sara bought $20\dfrac{3}{8}$ kg rice at the rate of ₹$52\dfrac{1}{2}$ per kg. Find the amount spent by Sara.

Answer

Quantity of rice bought by Sara = $20\dfrac{3}{8}$ kg = $\dfrac{163}{8}$ kg

Rate of rice = ₹$52\dfrac{1}{2}$ per kg = ₹$\dfrac{105}{2}$ per kg

$\text{Amount spent by Sara} = \dfrac{163}{8} \times \dfrac{105}{2}\\[1em] = \dfrac{163 \times 105}{8 \times 2}\\[1em] = \dfrac{17115}{16}\\[1em] = 1069\dfrac{11}{16}$

Hence, the amount spent by Sara is ₹$1069\dfrac{11}{16}$.

Which rational number is greater $-5\dfrac{5}{9}$ or $-5\dfrac{7}{12}$?

Answer

The given rational numbers are $-5\dfrac{5}{9}$ and $-5\dfrac{7}{12}$.

$-5\dfrac{5}{9} = -\dfrac{50}{9}$ and

$-5\dfrac{7}{12} = -\dfrac{67}{12}$

LCM of 9 and 12 is 2 × 2 × 3 × 3 = 36

$-\dfrac{50}{9} = -\dfrac{50 \times 4}{9 \times 4} = -\dfrac{200}{36}\\[1em] -\dfrac{67}{12} = -\dfrac{67 \times 3}{12 \times 3} = -\dfrac{201}{36}$

Their numerators are -200 and -201

As -200 > -201, so $-\dfrac{200}{36} \gt -\dfrac{201}{36}$

\Rightarrow -5\dfrac{5}{9} > -5\dfrac{7}{12}

Hence, $-5\dfrac{5}{9}$ is the greater rational number.

Simran walks $1\dfrac{5}{12}$ km from a place A towards north and then from there she walks $2\dfrac{7}{9}$ km towards south. Where will be she now from place A?

Answer

Let us denote the distance walked towards north by positive sign, then the distance walked towards south will be denoted by minus sign.

$\text{Simran's final distance from A} = 1\dfrac{5}{12} + \Big(-2\dfrac{7}{9}\Big)\\[1em] = \dfrac{17}{12} + \Big(-\dfrac{25}{9}\Big)\\[1em] = \dfrac{17}{12} - \dfrac{25}{9}$

LCM of 12 and 9 is 2 × 2 × 3 × 3 = 36

$= \dfrac{17 \times 3}{12 \times 3} - \dfrac{25 \times 4}{9 \times 4}\\[1em] = \dfrac{51}{36} - \dfrac{100}{36}\\[1em] = \dfrac{51 - 100}{36}\\[1em] = \dfrac{-49}{36}\\[1em] = -1\dfrac{13}{36}$

As the final distance is negative, therefore Simran is at a distance of $1\dfrac{13}{36}$ km towards south from place A.

Hence, Simran is at a distance of $1\dfrac{13}{36}$ km towards south from place A.

If the product of two decimal numbers is 17.55 and one of them is 2.7, then find the other number.

Answer

Product of two decimal numbers = 17.55

One of the numbers = 2.7

$\text{Other number} = 17.55 ÷ 2.7\\[1em] = \dfrac{17.55}{2.7}\\[1em] = \dfrac{175.5}{27}\\[1em] = 6.5$

Hence, the other number is 6.5.