Mathematics — Old Questions (TPSC)
Q51. How many 3 cm long cubes can be cut from a cube whose each edge is 15 cm in length ?
Q52. In a fertilizer which is a mixture of Urea and Potas, the ratio of Urea and Potas is 4:1. If 5 kg of Potas is mixed with 25 kg of that fertilizer, what will be the new ratio of Urea and Potas in that fertilizer ?
Q53. A trader buys some articles at the rate of 5 for a rupee and sells them at the rate of 4 for a rupee. Find his gain per cent.
Q54. Two trains, 132 metre and 108 metre in length are running towards each other on separate parallel lines, one at a speed of 32 km/h and the other at a speed of 40 km/h. In what time will they pass each other from the moment they meet?
Q55. If diagonals of a parallelogram are equal then
Q56. In a Rhombus :
A rhombus is a quadrilateral in which all four sides are equal in length.
However, the angles of a rhombus are not necessarily equal.
So,
Statement (A): All sides are equal ✔️
Statement (B): All sides are not equal ✖️
Correct Option: (A) All sides are equal
📌 Exam tip: Rhombus = equal sides, but angles may differ (except square).
Q57. First Rs. 8,000 of annual income is tax free and income tax is 1 % beyond this. An employee paid Rs. 160 as income tax in a year. His monthly income is :
First Rs. 8,000 of annual income is tax free
Income tax rate beyond Rs. 8,000 = 1%
Given income tax paid in a year = Rs. 160
Let taxable income beyond Rs. 8,000 = x
Then,
1% of x = 160
x = 160 × 100 = 16,000
Total annual income =
Tax free income + Taxable income
= 8,000 + 16,000
= Rs. 24,000
Monthly income =
24,000 ÷ 12 = Rs. 2,000
Answer: The monthly income of the employee is Rs. 2,000.
📌 Exam tip: Always find taxable income first, then add tax-free income.
Q58. Two person start from the same point and walk on a circular path at the same speed but in opposite direction. They will be diametrically opposite to each other when each has covered :
Both persons start from the same point on a circular path
They walk at the same speed but in opposite directions
So, the distance between them increases at double speed
They will be diametrically opposite when the distance between them
equals half of the circumference of the circle
Hence, each person must cover:
Half of circumference ÷ 2 = 1 ÷ 4 of the circular path
Correct Option: (D) 1/4th distance
Exam Tip:
On a circular track, if two persons move at the same speed in opposite directions,
each must cover 1/4th of the track to be diametrically opposite.
Q59. If the radius of a circle is diminished by 10 % , then its area is diminished by :
Area of a circle = πr2
Let original radius = r
Radius is diminished by 10%
New radius = 90% of r = 0.9r
New area = π(0.9r)2
= π × 0.81r2
Original area = πr2
Decrease in area =
(πr2 − 0.81πr2)
= 0.19πr2
Percentage decrease in area = 19%
Answer: The area of the circle is diminished by 19%.
📌 Exam shortcut:
If radius changes by x%,
area changes by (2x − x²/100)%
Here → 2(10) − 1 = 19%
Q60. The value of √156 . 25
Given expression = √156.25
Write 156.25 as a fraction:
156.25 = 15625 ÷ 100
So,
√156.25 = √(15625 ÷ 100)
= √15625 ÷ √100
√15625 = 125
√100 = 10
Therefore,
√156.25 = 125 ÷ 10 = 12.5
Answer: The value of √156.25 is 12.5.
📌 Exam tip:
For square roots of decimals, convert into fractions first—calculation becomes easy and accurate.