List of top Mathematics Questions

The rank of the matrix\(\begin{bmatrix} 1 & 1 & 1 \\[0.3em] a & a^2 & a^3 \end{bmatrix}\) is ____ .

The mean of the density function is \(f(x) = \lambda e^{-\lambda x}, x > 0\) is ____ .

The values of \( a \) and \( b \) for the function \( f(z) = (x^2 + a y^2 - 2xy) + i (b x^2 - y^2 + 2xy) \) to be analytic are ___ .

For the function \(f(x) = x^2 e^{-x},\) the maximum occurs when \( x \) is equal to ____ .

If \( \alpha, \beta \) (\(\alpha<\beta\)) are the values of \( x \) such that the determinant of the matrix \[ \begin{bmatrix} x - 2 & 0 & 1 \\ 1 & x + 3 & 2 \\ 2 & 0 & 2x - 1 \end{bmatrix} \] is zero (i.e., the matrix is singular), then the value of \( 2\alpha + 3\beta + 4\gamma \) is:
If the mean deviation about the mean is \(m\) and the variance is \(\sigma^2\) for the following data, then \(m + \sigma^2 =\) % Data table \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline f & 4 & 24 & 28 & 16 & 8 \\ \hline \end{array} \]
P is a variable point such that the distance of P from A(4,0) is twice the distance of P from B(-4,0). If the line \( 3y - 3x - 20 = 0 \) intersects the locus of P at the points C and D, then the distance between C and D is:
In \( \triangle ABC \), if \( AB:BC:CA = 6:4.5 \), then \( R : r = \)
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
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 ratio of the sum and product of the roots of the quadratic equation \(7x^2-12x+18=0\) is
△ABC∼△DEF, the area of △ABC=9 cm2 and the area of △DEF = 16 cm2. If BC=2.1 cm, then EF=
In \(△ABC\), \(DE || BC\), \(\frac {AD}{DB}=\frac 35\) and \(AC=5.6\) cm, then \(AE =\)\(?\)
If the slope of the line joining the points (4,2) and (3,-k) is -2, then the value of k is
If tan 48°.tan 23°.tan 42°.tan 67°=tan(A+30°), then the value of A is
If the area of a rectangle is \(112\ m^2\) and its length is \(6\ m\) more than the breadth, then the breadth of the rectangle is