List of top Mathematics Questions

A courier service agent charged ₹590 to courier a parcel from Nashik to Nagpur. In the tax invoice, the taxable value is ₹500 on which CGST = ₹45 and SGST = ₹45. Find the rate of GST charged for this service.
Write an A.P. whose first term is \(a = 10\) and common difference \(d = 5\).
Form a ‘Road Safety Committee’ of two, from 2 boys (B1, B2) and 2 girls (G1, G2). Complete the activity to write the sample space:
i.Complete the following activity and find the value of \(x\):
\[ \begin{aligned} 5x + 3y &= 9 \quad \text{...(I)} \\ 2x - 3y &= 12 \quad \text{...(II)} \end{aligned} \]
Complete the following activity to determine the nature of the roots of the quadratic equation \(x^2 + 2x - 9 = 0\):
Write the following equation in the form \(ax^2 + bx + c = 0\), then write the values of \(a, b, c\):
\[ 2y = 10 - y^2 \]
On a certain article, if the rate of CGST is 9%, then what is the rate of SGST?
Solve the following simultaneous equations: \[ x + y = 4 \quad \text{and} \quad 2x - y = 2 \]
If one coin is tossed, write the sample space ‘S’.
Find the common difference of the following A.P.: \[ 2, \, 4, \, 6, \, 8, \ldots \]

Complete the following table using the given information:
\[ \begin{array}{|c|c|c|c|} \hline \textbf{Sr. No.} & \textbf{FV (₹)} & \textbf{Share is at} & \textbf{MV (₹)} \\ \hline 1 & 100 & \text{Par} & \boxed{100} \\ \hline 2 & \boxed{75} & \text{Premium ₹500} & 575 \\ \hline 3 & 10 & \boxed{\text{Discount ₹5}} & 5 \\ \hline 4 & 200 & \text{Discount ₹50} & \boxed{150} \\ \hline \end{array} \]

Out of the following equations, which one is not a quadratic equation?
For the given A.P. \(a = 3.5, \, d = 0\), find \(t_n = \, ?\)
If \(n(A) = 2\), \(P(A) = \frac{1}{5}\), then find \(n(S) = ?\)}
Find the value of the following determinant:
\[ \begin{vmatrix} 4 & 3 \\ 2 & 7 \end{vmatrix} \]
To draw the graph of \(4x + 5y = 19\), find \(y\) when \(x = 1\):
If \[ A = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix} \] is a non-singular matrix, then find \( A^{-1} \) by elementary row transformations.

Let the probability mass function (p.m.f.) of a random variable \( X \) be \(P(X = x) = \binom{4}{x} \left( \frac{5}{9} \right)^x \left( \frac{4}{9} \right)^{4-x}\), for \(x = 0, 1, 2, 3, 4\), then \(E(X)\) is equal to 
 

In \( \Delta ABC \), if \( c^2 + a^2 - b^2 = ac \), then \( \angle B = \)
If \( p \land q \) is F, \( p \rightarrow q \) is F, then the truth values of \( p \) and \( q \) are
Prove that: \[ \int_0^a f(x) \, dx = \int_0^a f(x) \, dx + \int_0^a f(2a - x) \, dx \]
Evaluate: \[ \int \frac{2x^2 - 3}{(x^2 - 5)(x^2 + 4)} \, dx \]
Prove that the volume of a tetrahedron with coterminous edges \( \overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c} \) is \[ \text{Volume} = \frac{1}{6} \left| \overrightarrow{a} \cdot (\overrightarrow{b} \times \overrightarrow{c}) \right| \] Hence, find the volume of the tetrahedron whose coterminous edges are \[ \overrightarrow{a} = \hat{i} + 2\hat{j} + 3\hat{k}, \quad \overrightarrow{b} = -\hat{i} + \hat{j} + 2\hat{k}, \quad \overrightarrow{c} = 2\hat{i} + \hat{j} + 4\hat{k}. \]
Verify Lagrange's mean value theorem for the function \( f(x) = \sqrt{x + 4} \) on the interval \([0, 5]\).
Find the length of the perpendicular drawn from the point \( P(3, 2, 1) \) to the line \[ \overrightarrow{r} = (7\hat{i} + 7\hat{j} + 6\hat{k}) + \lambda(-2\hat{i} + 2\hat{j} + 3\hat{k}) \]