List of top Mathematics Questions on Mathematics

The value of

Every continuous real valued function on [a, b] is
(A). Constant.
(B). Bounded above.
(C). Bounded below.
(D). Unbounded.
Choose the correct answer from the options given below:

Let \(<G,*> \) be a group. Then for all a, b, c \(\in\) G
(A). (a*b)*c \(\in\) G
(B). a*b = b*a
(C). a*(b*c) = (a*b)*c
(D). a*b = a*c implies b = c.
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The solution of \(y = xp + \frac{m}{p}\) where \(p = \frac{dy}{dx}\) is

Let \(f\) be a continuous real valued function, defined by, \(f(x) = \sin x\), for all \(x \in [-\frac{\pi}{2}, \frac{\pi}{2}]\). Then which of the following does not hold.

Let an unbiased die be thrown and the random variable X be the number appears on its top. Then the expectation of X is

The integral \( \int_{0}^{\pi/2} \sin^5 x \cos^7 x \,dx = \)

The equation of a straight line passes through the point (4,-5) and is perpendicular to the straight line 3x + 4y + 5 = 0.

Which of the following subsets form subgroups of the group <ℤ, +>?

(A). H₁ = {0}
(B). H₂ = {n+1 : n ∈ ℤ}
(C). H₃ = {2n : n ∈ ℤ}
(D). H₄ = {2n+1 : n ∈ ℤ}

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The series \( \sum_{n=1}^{\infty} \frac{1}{n} \)

If a subset B is a basis of a vector space V, then
(A). B generates V.
(B). B contains zero vector.
(C). B is linearly independent.
(D). B is the only basis of V.
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What is the fundamental assumption behind a Markov model?

What is the key principle behind Monte Carlo simulation?

If \( [x] \) is the greatest integer \( \le x \), then \( \pi^2 \int_{0}^{2} \left( \sin \frac{\pi x}{2} \right) (x - [x])^{[x]} dx \) is equal to :

An angle of intersection of the curves, \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) and \( x^2 + y^2 = ab, a>b \), is :

Let \( f \) be any continuous function on \( [0, 2] \) and twice differentiable on \( (0, 2) \). If \( f(0) = 0, f(1) = 1 \) and \( f(2) = 2 \), then :

If \( y \frac{dy}{dx} = x \left[ \frac{\phi(y^2/x^2)}{\phi'(y^2/x^2)} + \frac{y^2}{x^2} \right], x>0, \phi>0, \) and \( y(1) = -1 \), then \( \phi\left(\frac{y^2}{4}\right) \) is equal to :

If \( \frac{dy}{dx} = \frac{2^x y + 2^y \cdot 2^x}{2^x + 2^{x+y} \log_e 2}, y(0) = 0 \), then for \( y = 1 \), the value of \( x \) lies in the interval :

Let \( f : \mathbb{N} \to \mathbb{N} \) be a function such that \( f(m + n) = f(m) + f(n) \) for every \( m, n \in \mathbb{N} \). If \( f(6) = 18 \), then \( f(2) \cdot f(3) \) is equal to :

Let \( a_1, a_2, a_3, \dots \) be an A.P. If \( \frac{a_1 + a_2 + \dots + a_{10}}{a_1 + a_2 + \dots + a_p} = \frac{100}{p^2}, p \neq 10 \), then \( \frac{a_{11}}{a_{10}} \) is equal to :

The locus of mid-points of the line segments joining \( (-3, -5) \) and the points on the ellipse \( \frac{x^2}{4} + \frac{y^2}{9} = 1 \) is :