In a true-false test containing 50 questions, a student is to be awarded 2 marks for every correct answer and –2 for every incorrect answer and 0 for not supplying any answer. If Yash secured 94 marks in a test, what are the possibilities of his marking correct or wrong answer?

Water level in a well was 20m below ground level. During rainy season, rain water collected in different water tanks was drained into the well and the water level rises 5 m above the previous level. The wall of the well is 1m 20 cm high and a pulley is fixed at a height of 80 cm. Raghu wants to draw water from the well. The minimum length of the rope that he can use is

Write a negative integer and a positive integer whose difference is – 3.

Write a pair of integers whose product is – 36 and whose difference is 15.

If * is an operation such that for integers a and b we have

a * b = a × b + (a × a + b × b)

then find (i) (– 3) * (– 5)

(ii) ( – 6) * 2

State whether the statements are True or False.

We can write a pair of integers whose sum is not an integer.

Write a negative integer and a positive integer whose sum is – 5.

Evaluate the following, using distributive property.

(i) –39 × 99

(ii) (– 85) × 43 + 43 × (– 15)

(iii) 53 × (– 9) – (– 109) × 53

(iv) 68 × (–17) + ( –68) × 3

Write a positive integer and a negative integer whose sum is a negative integer.

Write a positive integer and a negative integer whose sum is a positive integer.