List of top Mathematics Questions

Find the sum of the products of the corresponding terms of the sequences 2, 4, 8,16, 32 and 128, 32, 8, 2, \(\frac{1}{2}\).

Evaluate the Given limit: lim \(\lim_{x\rightarrow 3}\)x+3

Find the distance of the line \(4x + 7y + 5 = 0\)  from the point (1, 2) along the line  \(2x - y = 0\)

Evaluate the Given limit: \(\lim_{x\rightarrow \pi}\)(x - \(\frac{22}7{}\))

Evaluate the Given limit: \(\lim_{x\rightarrow 1}\pi r^2\)

Evaluate the Given limit: \(\lim_{x\rightarrow 1}4\) \(\frac{4x-3}{x-2}\)

Evaluate the Given limit: \(\lim_{x\rightarrow -1}\) \(\frac{x^{10}+x^5+1}{x-1}\)

Find the shortest distance between the following pairs of lines: \( \vec{r} = \hat{i} - 4\hat{j} + 5\hat{k} + \mu(5\hat{i} + 9\hat{j} + \hat{k}) \) and \( \vec{r} = 2\hat{i} + 8\hat{j} - 6\hat{k} + \lambda(3\hat{i} - 2\hat{j} + \hat{k}) \).

Adjacent sides of a parallelogram are given by \( 6\hat{i} - \hat{j} + 5\hat{k} \) and \( \hat{i} + 5\hat{j} - 2\hat{k} \). Find the area of parallelogram.

If \( A = \begin{bmatrix} 3 & 2 \\ 4 & 7 \end{bmatrix} \) and \( f(x) = x^2 - 10x + 13 \), then show that \( f(A) = O \) and using this result find \( A^{-1} \).

Express \( \begin{bmatrix} 5 & 1 \\ 3 & 7 \end{bmatrix} \) as the sum of a symmetric matrix and a skew-symmetric matrix.

Ajay, Sameer and Meenal have Rs. 20/- each and some footballs, basketballs and volleyballs in their shops. In a week, Ajay sold 3 footballs and a volleyball but he bought 2 basketballs for his shop and he has Rs. 35/- now. In same duration, Sameer sold 2 basketballs and 2 volleyballs but he bought a football for his shop and he has Rs. 95/- now. Similarly, Meenal sold 2 footballs and a basketball but she bought 3 volleyballs for her shop and she has Rs. 15/- now. Find the cost of a football, a basketball and a volleyball by the help of matrices.

If \( X = \begin{bmatrix} 3 & 1 \\ 2 & -1 \end{bmatrix} \) and \( 2X - Y = \begin{bmatrix} 5 & 10 \\ 3 & -5 \end{bmatrix} \), then find the matrix \( Y \).

Using determinants, find the value of \( k \) if the area of the triangle formed by the points \( (-3, 6), (-4, 4) \) and \( (k, -2) \) is 12 sq. units.

If \( A = \begin{bmatrix} 2 & 1 & 3 \\ 4 & 1 & 0 \end{bmatrix} \), \( B = \begin{bmatrix} 1 & -1 \\ 0 & 2 \\ 5 & 0 \end{bmatrix} \) then verify that \( (AB)' = B'A' \)

Find the angle between the lines \( \vec{r} = 3\hat{i} + 8\hat{j} + 3\hat{k} + \mu(\hat{i} + 2\hat{j} - \hat{k}) \) and \( \vec{r} = -3\hat{i} + 9\hat{j} - \hat{k} + \lambda(5\hat{i} + 3\hat{j} + 4\hat{k}) \).

Evaluate \( \int \frac{x^2}{x^4+1} dx \).

Find the height of the right circular cone of maximum volume, which is inscribed in a sphere of radius 12cm.

Solve the following linear programming problem graphically: Maximize and minimize \( Z = 4x + 2y - 7 \) subject to the constraints \( x + 3y \le 60, x + y \ge 10, x - y \le 0, x \ge 0, y \ge 0 \).
Correct Answer: Max Value \( Z = 73 \) at \( (15, 15) \); Min Value \( Z = 13 \) at \( (5, 5) \). (Based on standard corner point analysis)

Evaluate \( \int \frac{3x+2}{(x^2+1)(x-2)}dx \).

Solve: \( x \log x \frac{dy}{dx} + y = \frac{2}{x} \log x \).

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact present. However, the test also yields a false positive result for 0.5% of the healthy person tested. If 0.1% of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?