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پی ڈی ایف میں ڈنلوڈ کرنے کے لیےاس لنک پر کلک کریں۔
Basic Math PDF File
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چار آپشن میں سے کسی ایک پر کلک کرنے سے جواب سرخ ہو جائے گا۔
Scalar quantity
Vector quantity
Both A and B
None of these
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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
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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
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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
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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.
Log-normal distribution
Exponential distribution
Normal
None of these
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Explanation
In an exponential distribution , the mean (μ) and standard deviation (σ) are equal, i.e., μ = σ = 1/λ, where λ is the rate parameter.
Zero
Infinity
15
None of these
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Explanation
Since lim x → 0 x sin ( 15 / a ) lim_{x to 0} x sin(15/a) is of the form x ⋅ constant x cdot text{constant} , and x → 0 x to 0 , the whole expression tends to 0. The sine function remains bounded, so multiplying by x x (which approaches zero) results in zero.
Every Cauchy sequence is convergent
Every convergent sequence is Cauchy
Every bounded sequence is Cauchy
None of these
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Explanation
In any normed space (which is a metric space), every convergent sequence must be Cauchy. This is because, by definition, if a sequence converges to a limit , its terms eventually become arbitrarily close to that limit—and hence to each other.
r(cosθ + isinθ)
r(cosθ - isinθ)
rcosθ + risinθ)
None of these
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Explanation
r(cosθ + isinθ)
This is the polar form of a complex number.
where r is the magnitude (or modulus).
θ is the argument (or angle).
4
5
3
None of these
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Explanation
To find the inverse of 3 in modulo 7, we need to find a number x such that:
3x ≡ 1 (mod 7)
We can try multiplying 3 by each number from 1 to 6:
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9 ≡ 2 (mod 7)
3 × 4 = 12 ≡ 5 (mod 7)
3 × 5 = 15 ≡ 1 (mod 7)
So, the inverse of 3 in modulo 7 is 5.
Connected curve
Multi-connected
Multiple curves
None of these
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Explanation
Simply Connected : A region is simply connected if every closed curve within it can be continuously shrunk to a point without leaving the region.
Multi-Connected : A region is multi-connected if it is not simply connected .
This meaning it has "holes" or other topological features that prevent some closed curves from being shrunk to a point within the region.