List of top Mathematics Questions

The position vector of the point of intersection of the line joining the points \( \mathbf{i} - \mathbf{j} + \mathbf{k} \) and the line joining the points \( 2\mathbf{i} + \mathbf{j} - 6\mathbf{k} \), \( 3\mathbf{i} - \mathbf{j} - 7\mathbf{k} \) is:
P and Q are the points of trisection of the line segment AB. If the position vectors of A and B are \( 2\hat{i} - 5\hat{j} + 3\hat{k} \) and \( 4\hat{i} + \hat{j} - 6\hat{k} \) respectively, then the position vector of the point that divides PQ in the ratio 2:3 is:
The equation of the pair of transverse common tangents drawn to the circles \( x^2 + y^2 + 2x + 2y + 1 = 0 \) and \( x^2 + y^2 - 2x - 2y + 1 = 0 \) is:
Evaluate the integral: \[ \int (\log x)^3 \, dx \]
The coordinates of the point P which is equidistant from the three vertices of the △AOB as shown in the figure is
The coordinates of the point P which is equidistant from the three vertices of the △AOB
If the mode and mean of a data are 24 and 60 respectively, then the median of the data is
A tree is broken by wind, its upper part touches the ground at a point 10 metre from the foot of the tree and makes an angle of 45° with the ground. Then what is the entire height of the tree?
If two towers of heights h1, and h2 subtend angles of 30° and 60° respectively at the midpoint of the line joining their feet, then the ratio of h1: h2 is
The HCF of 306 and 657 is
If the centroid of a triangle formed by the points \((a,b), (b, c)\) and \((c,a)\) is at the origin, then \(a^3+b^3+c^3 =\)
The remainder when the square of any prime number greater than 3 is divided by 6 is
A plane \( \pi_1 \) passing through the point \( 3\hat{i} - 7\hat{j} + 5\hat{k} \) is perpendicular to the vector \( \hat{i} + 2\hat{j} - 2\hat{k} \) and another plane \( \pi_2 \) passing through the point \( 2\hat{i} + 7\hat{j} - 8\hat{k} \) is perpendicular to the vector \( 3\hat{i} + 2\hat{j} + 6\hat{k} \). If \( p_1 \) and \( p_2 \) are the perpendicular distances from the origin to the planes \( \pi_1 \) and \( \pi_2 \) respectively, then \( p_1 - p_2 \) is:
In the given figure, PA and PB are the tangents to the circle with centre at O. If ∠APB = 36°, then ∠AOB =
In the given figure, PA and PB are the tangents to the circle with centre at O
The value of \(log_2 32\) is
The average of the observations 10, 20, 65, 102, 108, 115 is
In what ratio, Y-axis divides the line segment joining the points P(-4, 2) and Q(8, 3)?
If the volume of a cylinder is 500 m3 and the area of its base is 25 m2, then its height (in m) is
The variance of the first 10 natural numbers which are multiples of 3 is:
The ratio of the sum and product of the roots of the quadratic equation \(7x^2-12x+18=0\) is
Evaluate the integral: \[ \int \frac{2\cos 3x - 3\sin 3x}{\cos 3x + 2\sin 3x} dx. \]
A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then the semi-vertical angle of the cone is:
If \( \theta \) is the acute angle between the curves \( y^2 = x \) and \( x^2 + y^2 = 2 \), then \( \tan \theta \) is:
The number of normals that can be drawn through the point \((9,6)\) to the parabola \(y^2 = 4x\) is:
△ABC∼△DEF, the area of △ABC=9 cm2 and the area of △DEF = 16 cm2. If BC=2.1 cm, then EF=
If \( \alpha,\,\beta,\,\gamma \) are the roots of the equation \[ \begin{vmatrix} x & 2 & 2\\ 2 & x & 2\\ 2 & 2 & x \end{vmatrix} = 0 \]