List of top Mathematics Questions

Write all the factors of the following numbers:

1. 24
2. 15
3. 21
4. 27
5. 12
6. 20
7. 18
8. 23
9. 36

The value of \[ \int_1^4 \log(\lfloor x \rfloor) \, dx \] where \( \lfloor x \rfloor \) is the greatest integer less than or equal to \( x \), is:

Some pictures (a) to (c) are given below. Tell which of them show:
\((a)\)

\((b)\)

\((c)\)

(i) 3 × \(\frac{1}{5}\) =\(\frac{3}{5}\)
(ii) 2 × \(\frac{1}{3}\) =\(\frac{2}{3}\)
(iii) 3 × \(\frac{3}{4}\) = \(\frac{21}{4}\)

Solve and check result: \(8x + 4 = 3(x - 1) + 7\)

If y=2x^3x,then \(\frac{dy}{dx}\) at x=1 is

Solve the equation: \[ x + \log_{15}(5 + 3x) = x \log_{15} 5 + \log_{15} 24 \]

If the angle \( \theta \) between the line \[ \frac{2t + 1}{1} = \frac{y - 1}{2} = \frac{z}{2} \] and the plane \( 2x - y\sqrt{7} + z + 4 = 0 \) is such that \( \sin \theta = \frac{8}{\sqrt{3}} \), then the value of the expression is:

If \( y = y(x) \) satisfies \[ \left( \frac{2 + \sin x}{1 + y} \right) \frac{dy}{dx} = -\cos x, \] such that \( y(0) = 2 \), then the value of \( y\left( \frac{\pi}{2} \right) \) is:

Evaluate the integral: \[ \int_{-1}^{1} \log\left(\frac{2 - x}{2 + x}\right) dx \]

(i) For any integer a, what is (–1) × a equal to?
(ii) Determine the integer whose product with (–1) is
(a) –22
(b) 37
(c) 0

If \[ f(x) = 2 \left( \cos x + i \sin x \right) \left( \cos 3x + i \sin 3x \right) \cdots \left( \cos (2n-1)x + i \sin (2n-1)x \right) \] where \( n \in \mathbb{N} \), then what is the value of \( f''(x) \) ?

Find the area bounded between the parabola \( y^2 = 4x \) and the line \( y = 2x - 3 \).

The value of \[ \int_1^4 \log(\lfloor x \rfloor) \, dx \] where \( \lfloor x \rfloor \) is the greatest integer less than or equal to \( x \), is equal to:

Let \[ f(x) = (\cos x + \sin x) \cdot \cos(3x + i \sin x) \cdot \left[ (2n - 1)x + i \sin((2n - 1)x) \right], \] where \( n \in \mathbb{N} \), and \( i = \sqrt{-1} \). Then: \[ f''(x) = \, ? \]

A population \( P(t) \) of 1000 bacteria introduced to a nutrient medium grows according to the relation \[ P(t) = \frac{1000t + 1000t}{100 + t^2} \] The maximum size of this bacterial population is:

If \[ [2\vec{p} - 3\vec{q} \ \vec{q} \ \vec{s}] + [3\vec{p} + 2\vec{q} \ \vec{r} \ \vec{s}] = m[\vec{p} \ \vec{r} \ \vec{s}] + n[\vec{q} \ \vec{r} \ \vec{s}] + l[\vec{p} \ \vec{q} \ \vec{s}], \] then the values of \( m, n, l \) respectively are:

In a triangle \( ABC \), with usual notation, if \[ \frac{b + c}{11} = \frac{c + a}{12} = \frac{a + b}{13} \] then the ratio \( \cos A : \cos B : \cos C \) is:

A plane passes through the point \( (1, -2, 1) \) and is perpendicular to both the planes \[ 2x - 2y - 2z = 5 \quad \text{and} \quad x - y + 2z = 24 \] Then, the distance of the point \( (1, 2, 2) \) from this plane is:

Smallest angle of a triangle whose sides are \( 6 + \sqrt{12}, \sqrt{48}, \sqrt{54} \) is: