SPSC MATHEMATICS 25 YEARS PAST PAPERS
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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
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.
u = 0
u ∧ n = 0, where n is the unit normal to the boundary
u . n = 0, where n is the null normal to the boundary
None of these
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Explanation
u . n = 0, where n is the unit normal to the boundary
This is the impermeability condition, which states that the fluid cannot flow through the fixed boundary.
x > 4
x ≥ -2
x > - 2
None of these
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Explanation
Since ln(x + 3) ≥ 0, we have:
x + 3 ≥ 1 (since ln(u) ≥ 0 when u ≥ 1)
x ≥ -2
2π/3
π/3
π/3
None of these
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Explanation
The standard period of cos(x) is 2π. For cos(3x + 5), the period is given by:
Period = 2π / |coefficient of x|
= 2π / 3
-1
2
5
None of these
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Explanation
Using Vieta's formulas, we know that α + β = 4/2 = 2 and αβ = 5/2.
Now, α^2β + αβ^2 = αβ(α + β) = (5/2)(2) = 5.
