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If on increasing a, b decreases in such a manner that ab remains _______ and positive, then a and b are said to vary inversely with each other.

Answer: If on increasing a, b decreases in such a manner that ab remains constant and positive, then a and b are said to vary inversely with... View Article

On increasing a, b increases in such a manner that a/b remains ______ and positive, then a and b are said to vary directly with each other

Answer: On increasing a, b increases in such a manner that a/b remains constant and positive, then a and b are said to vary directly with each... View Article

When the speed remains constant, the distance travelled is _____ proportional to the time.

Answer: When the speed remains constant, the distance travelled is directly proportional to the time. By the second equation of motion, s = ut +... View Article

If x varies directly as y, then

Answer: X 12 6 Y 48 — If x and y varies directly, then; x/y = k If x=12 y = 48 Then k = 12/48 =1/4 Now, if x = 6 k = 1/4 Then... View Article

If x varies inversely as y, then

Answer: X — 60 Y 2 10 If x varies inversely as y, then x × y = k If x = 60 y = 10 Then x × y = 60 × 10 = 600 =... View Article

If 12 pumps can empty a reservoir in 20 hours, then time required by 45 such pumps to empty the same reservoir is ______ hours.

Answer: If 12 pumps can empty a reservoir in 20 hours, then the time required by 45 such pumps to empty the same reservoir is 5 hours 20 min... View Article

Fill in the blanks: If x = 5y, then x and y vary ____________with each other.

Answer: If x = 5y, then x and y vary directly with each other. x = 5y Then x/y =5/1 = k(constant) This demonstrates that x and y are directly... View Article

Both x and y vary directly with each other and when x is 10, y is 14, which of the following is not a possible pair of corresponding values of x and y? (a) 25 and 35 (b) 35 and 25 (c) 35 and 49 (d) 15 and 21

Answer: (b) 35 and 25 x and y are directly proportional. x ∝ y If x = 10 and y = 14, then; 10 ∝ 14 or 5 ∝ 7 Now, if we compare,... View Article

If the distance travelled by a rickshaw in one hour is 10 km, then the distance travelled by the same rickshaw with the same speed in one minute is: (a) 250/9 m (b) 500/9 m (c) 1000 m (d) 500/3 m

Answer: (d) 500/3 m Distance travelled = 10km Time taken = 1 hr Distance travelled defines how much path an object has covered to reach its... View Article

If two quantities p and q vary inversely with each other, then: (a) p/q remains constant. (b) p + q remains constant. (c) p × q remains constant. (d) p – q remains constant.

Answer: (c) p × q remains constant. When two quantities p and q change in opposite directions, p×q remains constant. Because a rise... View Article

If two quantities x and y vary directly with each other, then (a) x/y remains constant. (b) x – y remains constant. (c) x + y remains constant. (d) x × y remains constant.

Answer: (a) xy remains constant If two quantities x and y vary directly with each other, then xy = k (constant) Because both x and y increase or... View Article

100 persons had food provision for 24 days. If 20 persons left the place, the provision will last for (a) 30 days (b) 96/5 days (c) 120 days (d) 40 days

Answer: (a) 30 days 100 persons have food provision for = 24 days 1 person will have food provision for = 24 × 100 = 2400 If 20 persons... View Article

Meenakshee cycles to her school at an average speed of 12 km/h and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be (a) 20/3 km/h (b) 16 km/h (c) 20 km/h (d) 15 km/h

Answer: (c) 20 km/h Speed = 12km/h Time taken = 20 minutes Time taken = 20/60 hr = 1/3 hr Distance travelled defines how much path an object... View Article

Both x and y are in direct proportion, then 1/x and 1/y are: (a) in indirect proportion. (b) in inverse proportion. (c) neither in direct nor in inverse proportion. (d) sometimes in direct and sometimes in inverse proportion.

Answer: (b) in inverse proportion. If both x and y are directly proportional, then 1/x and 1/y are in inverse proportion. If a rise in x causes a... View Article

Which of the following vary inversely with each other? (a) speed and distance covered. (b) distance covered and taxi fare. (c) distance travelled and time taken. (d) speed and time taken.

Answer: (d) speed and time taken. By the formula of speed we know; Speed = distance/time As we can see here when the time decreases, the speed... View Article

Which quantities in the question vary inversely with each other? (a) x and y (b) p and q (c) r and s (d) u and v

(a) x 0.5 2 8 32 y 2 8 32 128 (b) p 12 22 32 42 q 13 23 33 43 (c) r 2 5 10 25 50 s 25 10 5 2 0.5 (d) u 2 4 6 9... View Article

In which of the following case, do the quantities vary directly with each other?

(a) x 0.5 2 8 32 y 2 8 32 128 (b) p 12 22 32 42 q 13 23 33 43 (c) r 2 5 10 25 50 s 25 10 5 2 0.5 (d) u 2 4 6 9... View Article

By travelling at a speed of 48 kilometres per hour, a car can finish a certain journey in 10 hours. To cover the same distance in 8 hours, the speed of the car should be (a) 60 km/h (b) 80 km/h (c) 30 km/h (d) 40 km/h

Answer: (a) 60 km/h Speed of car = 48 km/hr Time taken = 10 hr As we know, Distance = speed × time Distance = 48 × 10 Distance =... View Article

A truck needs 54 litres of diesel for covering a distance of 297 km. The diesel required by the truck to cover a distance of 550 km is (a) 100 litres (b) 50 litres (c) 25.16 litres (d) 25 litres

Answer: (a) 100 litres Distance covered by truck using 54 litres diesel = 297 km Distance covered by truck using 1 litre diesel = 297/54 Distance... View Article

The number of teeth and the age of a person vary (a) directly with each other. (b) inversely with each other. (c) neither directly nor inversely with each other. (d) sometimes directly and sometimes inversely with each other

Answer: (d) sometimes directly and sometimes inversely with each other We cannot anticipate the number of teeth with the exact age of a person... View Article