SPSC Mathematics 25 years Past Papers

Q131: Let R be an integral domain. Which of the following statement is not true about R?

R is division ring

If R is finite, then it is a field

R has no zero-divisor

None of these

Q132: A consistent system of linear equations has ______?

Maximum two solutions

At least one solution

Minimum two solution

None of these

Q133: A^T= A^-1, where A is a real matrix, then A is?

Normal

Orthogonal

Symmetric

None of these

Explanation

A matrix $A$ is orthogonal if $A^T = A^{-1}$ , meaning its transpose is equal to its inverse.

This property ensures that the matrix preserves length and angles under transformation.

Q134: Crank Nicholson method is a technique to solve numerically which of the following type of equations?

Nonlinear partial differential equations

System of equations

Nonlinear equations

None of these

Q135: Which of the following is not a standard method for finding the solutions for differential equations?

Homogeneous equation

Orthogonal method

Variable separable

None of these

Q136: What is the meaning of the term Topology?

ٹاپولوجی کی اصطلاح کا کیا مطلب ہے؟

It is the of theological salvation

It is the study of places and natural features

It is the study of geometric shapes and features

None of these

Q137: Under Galois theory, the roots of a polynomial is solvable by radicals if and only if the polynomial’s Galois group is?

Solvable

Abelian

Prime

None of these

Q138: The term 'Billion' is an expression of which of the following?

Ten lakhs

Ten millions

Hundred lakhs

Hundred crores

Q139: When each member of a population has an equally/likely chance of being selected, it is?

جب کسی آبادی کے ہر فرد کے پاس یکساں/منتخب ہونے کا امکان ہوتا ہے تو ، ایسا ہوتا ہے؟

A probability selection method

A snowball sample

A quota sample

None of these