List of top Mathematics Questions

Let the vectors \( \overrightarrow{AB} = 2\hat{i} + 2\hat{j} + \hat{k} \) and \( \overrightarrow{AC} = 2\hat{i} + 4\hat{j} + 4\hat{k} \) be two sides of a triangle ABC. If \( G \) is the centroid of \( \triangle ABC \), then \( \frac{22}{7} |\overrightarrow{AG}|^2 + 5 = \): (a) 25

The first term and the 6th term of a G.P. are 2 and \( \frac{64}{243} \) respectively. Then the sum of first 10 terms of the G.P. is:

The area of the shaded region in the given figure is
The area of the shaded region in the given figure is
The end of a latus rectum of the ellipse \(3x^2 + 4y^2 = 12\) is lying in the third quadrant. If the normal drawn at \(L_1\) to this ellipse intersects the ellipse again at the point \(P(a,b)\), then find the value of \(a\):
In a triangle ABC, if \( r_1 = 6 \), \( r_2 = 9 \), \( r_3 = 18 \), then \( \cos A \) is:
The period of the function \( f(x) = \sin\left( \frac{3x}{2} \right) \) is equal to:

The general solution of the differential equation \( \frac{dy}{dx} = xy - 2x - 2y + 4 \) is:

If \( 3^{2n+2} - 8n - 9 \) is divisible by \( 2^p \) \(\forall n \in \mathbb{N}\), then the maximum value of \( p \) is
If \( f(x) \) defined as given below, is continuous on \( R \), then the value of \( a + b \) is equal to: % Function Definition \[f(x) = \begin{cases} \sin x, & x \leq 0 \\ x^2 + a, & 0<x<1 \\ bx + 3, & 1 \leq x \leq 3 \\ -3, & x>3 \end{cases}\]
The locus of the midpoint of the system of parallel chords parallel to the line \( y = 2x \) to the hyperbola \( 9x^2 - 4y^2 = 36 \) is:
The remainder when the square of any prime number greater than 3 is divided by 6 is
If \( \int x^3 \sin 3x \,dx = f(x) \cos 3x + g(x) \sin 3x + c \), then evaluate \( 27(f(x) + xg(x)) \):

The number of all possible combinations of 4 letters which are taken from the letters of the word ACCOMMODATION is

If \( \cos \theta = \frac{2 \cos \alpha + 1}{2 + \cos \alpha} \), then \( \tan^2 \left( \frac{\theta}{2} \right) \) is equal to:
If \( x_1, i=2, 3, \ldots, n \) are \( n \) observations such that \( \sum_{i=1}^{n} x_i^2 = 550 \), mean \( \bar{x} = 5 \) and variance is zero, then the number of observations is equal to:
If the points (1, 2), (-1, k) and (2, 3) are collinear, then the value of k is
The minimum value of \( f(x) = 7x^4 + 28x^3 + 31 \) is:

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with the name of his own wife is ?

If \(\frac{2}{\sqrt{x}} = 2\) and \(\frac{4}{\sqrt{y}} = -1\), then
Evaluate the sum: \[ \sin^2 18^\circ + \sin^2 24^\circ + \sin^2 36^\circ + \sin^2 42^\circ + \sin^2 78^\circ + \sin^2 90^\circ + \sin^2 96^\circ + \sin^2 102^\circ + \sin^2 138^\circ + \sin^2 162^\circ. \]
A circle passing through the points \( (1, 1) \) and \( (2, 0) \) touches the line \( 3x - y - 1 = 0 \). If the equation of this circle is \( x^2 + y^2 + 2gx + 2fy + c = 0 \), then a possible value of \( g \) is
The number of ways in which 15 identical gold coins can be distributed among 3 persons such that each one gets at least 3 gold coins is
The approximate value of \( \sqrt[3]{730} \) obtained by the application of derivatives is:
The general solution of \( 4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0 \) is:
If 1000! = 3n × m, where m is an integer not divisible by 3, then n =?