List of top Mathematics Questions

The probability that exactly 3 heads appear in six tosses of an unbiased coin, given that the first three tosses resulted in 2 or more heads, is:
The slope of one of the pair of lines \(2x^2 + hxy + 6y^2 = 0\) is three times the slope of the other line, \(h = ?\)
If the quadratic equation \( 3x^2 + (2k + 1)x - 5k = 0 \) has real and equal roots, then the value of \( k \) such that \( -\frac{1}{2}<k<0 \) is:
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)?
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: