SPSC MATHEMATICS 25 YEARS PAST PAPERS
SPSC 5 years Past Papers Click here
چار آپشن میں سے کسی ایک پر کلک کرنے سے جواب سرخ ہو جائے گا۔
- 0
- 1
- 1/2
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
Let the quadratic polynomial be f(x) = ax^2 + bx + c.
Given that f'(1) = 1 and f''(1) = 2.
f'(x) = 2ax + b
f''(x) = 2a
f'(1) = 1 => 2a + b = 1
f''(1) = 2 => 2a = 2 => a = 1
Substituting a = 1 in the first equation, we get:
2 + b = 1 => b = -1
Now, f(x) = x^2 - x + c
f(1) = 1^2 - 1 + c = c
f(0) = 0^2 - 0 + c = c
f(1) - f(0) = c - c = 0
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
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
Probability selection method ensures that every member of the population has an equal chance of being chosen, making the sampling process unbiased.This method includes techniques like simple random sampling and systematic sampling.
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
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
Topology is a branch of mathematics that studies properties of shapes that remain unchanged under continuous transformations.It deals with concepts like connectivity, surfaces, and spaces rather than precise measurements.
- 20
- 13
- 11
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
Given data:
5, 7, 9, 11, 13, 13, 17, 19, 20
Step:
The mode is the number that appears most frequently.
- Secant Method
- Newton-Raphson Method
- Bisection Method
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
The Bisection Method is guaranteed to converge if the function changes signs over the interval.It is a robust and reliable method for root-finding.It ensuring convergence under the condition of a continuous function with opposite signs at the endpoints.
- Simultaneous displacement method
- Gauss-Seidel method
- Newton-Raphson method
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
Jacobi's method involves solving a system of linear equations iteratively, updating all variables simultaneously in each iteration.It is distinct from the Gauss-Seidel method, where variables are updated sequentially.
- Scalar quantity
- Vector quantity
- Both A and B
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
The divergence of a vector field measures the rate at which the field spreads out from a point and results in a scalar quantity.It is given by ∇ • f, producing a single numerical value at each point.
- A(B + C) = AB + AC
- A + (BC) = (A + B)(A + C)
- AB + BC = A(B + C)
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
The distributive law in Boolean algebra states that multiplication distributes over addition: A(B + C) = AB + AC.It ensures logical expressions can be simplified systematically while maintaining equivalence.
- The number of edges incident with the vertex
- Number of edge in a graph
- Number of vertices adjacent to that vertex
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
The degree of a vertex in a graph is the count of edges connected to it.
It represents the number of direct connections the vertex has.
- Laplace's equation
- Euler's equation
- Poisson's equation
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
Explanation
The velocity potential (φ) of an incompressible fluid satisfies Laplace's equation:
∇²φ = 0
This equation represents the conservation of mass for an incompressible fluid.
