List of top Mathematics Questions

If n is a positive integer and f(n) is the coeffcient of xn in the expansion of (1 + x)(1-x)n, then f(2023) =

In the figure, if AP and AQ are the two tangents to a circle with centre 'O' so that \(∠OQP=15°\), then \(∠QAP=\)
AP and AQ are the two tangents to a circle with centre

The variance of the following grouped data is:

For what value of \( \alpha \), the matrix A is a singular matrix if \(A=\begin{bmatrix} 1 & 3 & \alpha+2 \\[0.3em] 2 & 4 & 8 \\[0.3em] 3 & 5 & 10 \end{bmatrix}\) ?

The eccentricity of \((\frac {x}{25})^2 + (\frac {y}{16})^2 = 1\) is:

Note: Assuming the intended equation is \( \frac{x^2}{25} + \frac{y^2}{16} = 1 \) based on the options. The literal interpretation \( \frac{x^2}{625} + \frac{y^2}{256} = 1 \) yields\(e =\frac {\sqrt{369}}{25}\), which is not among the options.

If \( x^2 + ax + b = 0 \) and \( x^2 + bx + a = 0 \) have exactly one common root, then the value of \( (a + b) \) is:
The sum of the exponents of the prime factors in the prime factorization of 156 is
Which term of the geometric progression \(2,2\sqrt{2},4,…..\)is \(128?\)
If the geometric progressions 162, 54, 18, ..... and \(\frac{2}{81},\frac{2}{27},\frac{2}{9}\),…have their nth term equal, then the value of n is
The points A(-5,0), B(5,0) and C(0,4) are the vertices of which triangle?
The X-axis divides the line joining the points A(2,-3) and B(5,6) in the ratio of
If four vertices of a parallelogram are (-3,-1),(a,b),(3,3) and (4,3) taken in order,then the ratio of a and b is
If the centroid of the triangle formed by the points \((3,-5),(-7,4)\) and \((10,-k )\) is at the point \((k, –1)\), then the value of k is
If AM and PN are the altitudes of two similar triangles \(∆ABC\) and \(∆PQR\) respectively and \((AB)^ 2 : (PQ) ^2 = 4 : 9\), then \(AM : PN =\)
In the given \(∆ABC\), if \(DE || BC, AE = a\) units, \(EC = b\) units, \(DE = x \) units and \(BC = y\) units, then which of the following is true?
if DE || BC, AE = a units, EC = b units, DE = x units
In the given figure, PA is the tangent drawn from an external point P to the circle with center O. If the radius of the circle is 3 cm and PA = 4 cm, then the length of PB is
A is the tangent drawn from an external point P
In two concentric circles, a chord of length 24 cm of larger circle becomes a tangent to the smaller circle whose radius is 5 cm. Then the radius of the larger circle is
two concentric circles
The area of the circle that can be inscribed in a square of side 10 cm is
If the height of a conical tent is 3 m and the radius of its base is 4 m, then the slant height of the tent is
If the radius of the base of a right-circular cylinder is halved, keeping the height same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is
If \(tan\ \theta=\sqrt{3}\), then the value of \(sec\ θ\) is
A chord of a circle of radius 6 cm is making an angle 60º at the centre. Then the length of the chord is
If \(\tan \theta + \cot \theta = 5\),then the value of \(\tan^2 \theta + \cot^2 \theta\) is
\(\cos(36^\circ) \cos(54^\circ) - \sin(36^\circ) \sin(54^\circ)=\)
The angles of elevation and depression of the top and bottom of a lighthouse from the top of a 60 m high building are 30º and 60º respectively. Then the difference between the heights of the lighthouse and building is