List of top Mathematics Questions

In a triangle \(\triangle ABC\), if \(a, b,\) and \(c\) are in arithmetic progression, then \(\cos A + 2 \cos B + \cos C =\)

If \(I = \int \frac{\sin x + \sin^3 x}{\cos 2x} dx = P \cos x + Q \log \left| \frac{\sqrt{2} \cos x - 1}{\sqrt{2} \cos x + 1} \right|\) (where \(c\) is a constant of integration), then values of \(P\) and \(Q\) are respectively

The equation of the normal to the curve \( y = \log_e x \) at the point \( P(1,0) \) is ____.

If the direction ratios of two lines are given by $ l + m + n = 0 $ and $ mn - 2ln + lm = 0 $, then the angle between the lines is:

Let the function $ f(x) $ be defined as $ f(x) = \frac{x - |x|}{x} $, then:

Gas is being pumped into a spherical balloon at the rate of $ 30 \, \text{ft}^3/\text{min} $. Then the rate at which the radius increases when it reaches the value $ 15 \, \text{ft} $ is:

Let \[ f(x)=\int \frac{\sqrt{x}}{(1+x)^2}\,dx \quad (x\geq 0) \] Then \[ f(3)-f(1) \] is equal to:

Find the local maximum point of the function \[ f(x)=-x^3+3x+1 \]

Let \( R \) be a relation on \( \{1,2,3\} \) defined by \[ R=\{(1,1),(2,2),(3,3),(1,2)\} \] Identify the properties satisfied by \(R\).

For vectors \( \vec{a}=3\hat{i}-\hat{j}+2\hat{k} \) and \( \vec{b}=\hat{i}+2\hat{j}-\hat{k} \), find the scalar projection of \( \vec{a} \) onto \( \vec{b} \).

Find the domain of the function \( f(x)=\sin^{-1(3x-1) \).}

A bag has 4 red and 6 black balls. Two balls are drawn without replacement. What is the probability that the second is red given the first was black?

Maximize \( Z = 5x + 3y \) subject to \( x + y \le 6 \) and \( x, y \ge 0 \). Where does the maximum value occur?

For the linear differential equation \[ \frac{dy}{dx} + \frac{2}{x}y = x^2 \] calculate the integrating factor (I.F.).

Identify the order and degree of the differential equation: \[ \left(\frac{d^3y}{dx^3}\right)^2 + 4\left(\frac{dy}{dx}\right)^4 + y = \sin(x) \]

Analyze the function \( f(x) = |x-1| + |x-2| + |x-3| \). Determine the points where the derivative \( f'(x) \) is undefined.

Let $A$ be a $3 \times 3$ matrix such that $A^2 = I$. If $\det(A) = -1$ and the sum of eigenvalues is $1$, find the set of eigenvalues of $A$.

A shopkeeper earns 20% profit on an article whose cost price is Rs 800. Find the selling price.

Find the simple interest on Rs 5000 at 10% per annum for 2 years.

If \[ A = \begin{bmatrix}2 & 1 \\ 3 & 4\end{bmatrix} \] then find \( |A| \).

Match the following:

Which of the following functions has derivative equal to \( \cos x \)?

If \[ \frac{dy}{dx} = y \] then which of the following is the correct solution?

Find the solution of the differential equation: \[ \frac{dy}{dx} = 3x^2 \]

Find the value of: \[ \int \frac{1}{x} \, dx \]