SPSC Mathematics 25 years Past Papers

Q31: Samad purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?

6.5

3.5

5.6

None of these

Q32: If a, b are positive integers, where in the (modulo 7) with the multiplication operation, then inverse of 3 in the group is?

4

5

3

None of these

Q33: Y = 5x and dx/dt = 2 the day/dt will be _____?

12

11

10

None of these

Q34: 2 (x^2 + y^2 + xy) = _____?

x^2 + y^2 + 2xy

2xy + 2y^2

2x^2 + 2y^2 + 2xy

None of these

Explanation

Distribute the 2 across the terms inside the parentheses:

$2 (x^{2} + y^{2} + x y) = 2 x^{2} + 2 y^{2} + 2 x y$

Q35: Average rate of change of function f(x)=x ^3 +1 over the interval [2,3] will be?

21

20

19

None of these

Q36: Two non-coplanar straight lines neither intersect nor they are parallel. Such straight lines are called?

Perpendicular lines

Skew lines

Symmetric lines

None of these

Q37: Which of the following property doesn't satisfied by the matrices?

مندرجہ ذیل میں سے کون سی پراپرٹی میٹرکس سے مطمئن نہیں ہے؟

Matrix multiplication is associate

Matrix addition is associated

Matrix multiplication is commutative

Matrix addition is commutative

Q38: a, b and c are real numbers then either a < b, a > b or a = b. This property of real numbers is called?

Associative property

Transitive property

Trichotomy property

None of these

Explanation

The Trichotomy property states that for any two real numbers $a$ and $b$ , exactly one of the following holds: $a < b$ , $a > b$ , or $a = b$ .

This property ensures a well-defined order among real numbers.

Q39: If every element of a group G is its own inverse then G is called?

Cyclic

Abelian

Finite

None of these

Explanation

If every element of a group $G$ is its own inverse, then $g^2 = e$ for all $g in G$ , meaning all elements are of order 2.

Such a group is Abelian because the group operation commutes: $(gh)^2 = e$ implies $g$ and $h$ must commute.

Q40: Find the missing number: 102, 109, 116, 123, 130, _____?

135

137

141

None of these