SPSC MATHEMATICS 25 YEARS PAST PAPERS
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چار آپشن میں سے کسی ایک پر کلک کرنے سے جواب سرخ ہو جائے گا۔
- Both u,v are orthogonal and unit vectors
- u,v are orthogonal
- u,v are unit vectors
- None of these
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Explanation
Orthonormal vectors satisfy two conditions: they are orthogonal () and unit vectors ( and .This means they are perpendicular and have a magnitude of 1.
- Normal
- Orthogonal
- Symmetric
- None of these
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Explanation
A matrix is orthogonal if , meaning its transpose is equal to its inverse.This property ensures that the matrix preserves length and angles under transformation.
- Increasing and decreasing both
- Decreasing function
- Increasing function
- None of these
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Explanation
If in an interval, it means the function is increasing in that interval.A positive derivative indicates that the function's slope is positive, meaning it moves upward as increases.
- Associative property
- Transitive property
- Trichotomy property
- None of these
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Explanation
The Trichotomy property states that for any two real numbers and , exactly one of the following holds: , , or .This property ensures a well-defined order among real numbers.
- Poisson
- Binomial
- Normal
- None of these
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Explanation
In a Poisson distribution, the mean and variance are always equal.It is used to model the number of events occurring in a fixed interval of time or space.
- Nonlinear partial differential equations
- System of equations
- Nonlinear equations
- None of these
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Explanation
The Crank-Nicholson method is used for solving time-dependent partial differential equations.It is an implicit finite difference method, ensuring stability and accuracy.
- Abelian group
- Galois group
- Free group
- None of these
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Explanation
Commutative Law: In an Abelian group, for all elements a and b in the group, the operation satisfies a⋅b=b⋅a.
Named after Niels Henrik Abel: The term "Abelian" is derived from the name of the mathematician Niels Henrik Abel.
- The intersection of Df and Dg without the zeros of function g
- The intersection of Df and Dg
- Union of Df and Dg
- None of these
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Explanation
Intersection of Df and Dg: The function gf is defined only where both f and g are defined.
Excluding zeros of g: The function gf is undefined where g(x)=0 because division by zero is not allowed.
- 1/3(2x + 1)^2/3 + C
- 1/3(2x + 1)^3/2 + C
- 3(2x + 1)^3/2 + C
- None of these
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Explanation
To integrate √(2x + 1), we can use the power rule of integration and the chain rule.
Let u = 2x + 1, then du/dx = 2, and du = 2dx.
∫√(2x + 1) dx = (1/2) ∫u^(1/2) du
= (1/2) (2/3) u^(3/2) + C
= (1/3) (2x + 1)^(3/2) + C
- y= -x-13
- y= 2x+2
- y= x^2-1
- None of these
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Explanation
Given:
y=2x^2−13x+5
Differentiate:
dy/dx=4x−13
For slope =−1:
4x−13=−1
x=3
At x=3:
y=2(3)^2−13(3)+5=−16
So the point of contact is (3, −16).
The tangent equation:
y+16=−(x−3)
y=−x−13
