List of top Mathematics Questions

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:
An ellipse has \( OB \) as the semi-minor axis, and \( S \), \( S' \) as the foci. If \( \angle SBS' \) is a right angle, then the eccentricity \( e \) of the ellipse is:
A box contains 9 tickets numbered from 1 to 9 inclusive. 3 tickets are drawn from the box one at a time. What is the probability that they are alternatively either (odd, even, odd) or (even, odd, even)?
Smallest angle of a triangle whose sides are \( 6 + \sqrt{12}, \sqrt{48}, \sqrt{54} \) is:
The ratio of areas bounded by curves \( y = \cos x \) and \( y = 0 \) between \( x = 0 \) to \( x = \frac{\pi}{3} \) and \( x = \frac{\pi}{3} \) to \( x = \frac{2\pi}{3} \), with the x-axis is:
Two finite sets have m and n elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are
If A.M. and G.M. of roots of a quadratic equation are 5 and 4 respectively, then the quadratic equation is
The enrolment in a school during six consecutive years was as follows:
1555, 1670, 1750, 2013, 2540, 2820
Find the mean enrolment of the school for this period.
The maximum volume of the right circular cone with slant height 6 units is
Verify the following:
(a) 18 × [ 7 + (–3)] = [18 × 7] + [18 × (–3)]
(b) (–21) × [(– 4) + (– 6)] = [(–21) × (– 4)] + [(–21) × (– 6)]
Let $(gof)(x) = sin x$ and $(fog)(x) = (sin \sqrt x)^2,$ Then

If area of triangle is 35 square units with vertices(2,−6), (5,4),and (k,4).Then k is

Standard deviation of the numbers 31, 32, 33, ... , 46, 47 is
Soln of \(sinx + sin 5x= sin3x\) in \((0,\frac{x}{2})\) are?

\( f(x) = 2x - 3 \quad \text{and} \quad g(x) = x^3 + 5 \), then find \( [f \circ g]^{-1}(-9) = ? \)

Find the approximate value of (25.2)1/2.

Find the differentiation of \(cot^{-1}\frac{3+4tan\,x}{4-3tan\,x}\)
If \(A=\begin{vmatrix}x&1\\1&x\end{vmatrix}\) and \(B=\begin{vmatrix}x &1&1\\1& x&1 \\1&1&x \end{vmatrix}\),then \(\frac{dB}{dx}\) is
Let f : R ⇢ R be defined by $f (x) = x^2 +1$. Then the pre images of 17 and –3 respectively are