List of top Mathematics Questions

The coordinates of the foot of perpendicular from the point \( (2, 3) \) on the line \( y = 3x + 4 \) is given by:
If \( \frac{1}{q + r}, \frac{1}{r + p}, \frac{1}{p + q} \) are in A.P., then:
The coefficient of \( x^{50} \) in \( (1 + x)^{101} (1 - x + x^2)^{100} \) is:
The number of different permutations of all the letters of the word "PERMUTATION" such that any two consecutive letters in the arrangement are neither both vowels nor both identical is:
Negation of the statement \( (p \land r) \rightarrow (r \lor q) \) is:
The equation of a common tangent to the parabolas \( y = x^2 \) and \( y = -(x - 2)^2 \) is:
A and B are independent events of a random experiment if and only if:
The integral \( I = \int_{\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{x + \frac{\pi}{4}}{2 - \cos 2x} \, dx \) is equal to:
The range of \( 2 \left| \sin x + \cos x \right| - \sqrt{2} \) is:
The length of the perpendicular from the point \( (1, -2, 5) \) on the line passing through \( (1, 2, 4) \) and parallel to the line given by \( x + y - z = 0 \) and \( x - 2y + 3z - 5 = 0 \) is:
The probability distribution of a random variable is given below: \[\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline X = x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline P(X = x) & 0 & K & 2K & 2K & 3K & K^2 & 2K^2 & 7K^2 + K \\ \hline \end{array}\]

Find \( P(0<X<5) \).

If the solution of \[ \left( 1 + 2e^\frac{x}{y} \right) dx + 2e^\frac{x}{y} \left( 1 - \frac{x}{y} \right) dy = 0 \] is \[ x + \lambda y e^\frac{x}{y} = c \quad \text{(where \(c\) is an arbitrary constant), then \( \lambda \) is:} \]
The solution of the differential equation: \[ x^4 \frac{dy}{dx} + x^3 y + \csc(xy) = 0 \] is equal to:
Evaluate the integral: $\int_{-\pi}^{\pi} x^2 \sin(x) \, dx$
If  \(f(x) = \frac{\log(\pi + x)}{\log(e + x) }\), then the function is:
If \( f(x) = \ln \left( \frac{x^2 + e}{x^2 + 1} \right) \), then the range of \( f(x) \) is:
If the two lines \( l_1: \frac{x - 2}{3} = \frac{y + 1}{-2} = \frac{z - 2}{0} \) and \( l_2: \frac{x - 1}{1} = \frac{y + 3}{\alpha} = \frac{z + 5}{2} \) are perpendicular, then the angle between the lines \( l_2 \) and \( l_3: \frac{x - 1}{-3} = \frac{y - 2}{-2} = \frac{z - 0}{4} \) is:
Let the vectors \( \overrightarrow{AB} = 2\hat{i} + 2\hat{j} + \hat{k} \) and \( \overrightarrow{AC} = 2\hat{i} + 4\hat{j} + 4\hat{k} \) be two sides of a triangle ABC. If \( G \) is the centroid of \( \triangle ABC \), then \( \frac{22}{7} |\overrightarrow{AG}|^2 + 5 = \): (a) 25
The area bounded by \( y - 1 = |x| \) and \( y + 1 = |x| \) is: (a) \( \frac{1}{2} \)
If \( f(x) \) is continuous and \( \int_0^9 f(x) \, dx = 4 \), then the value of the integral \( \int_0^3 x \cdot f(x^2) \, dx \) is: (a) 2
The maximum area of a right-angled triangle with hypotenuse \( h \) is: (a) \( \frac{h^2}{2\sqrt{2}} \)
The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm/minute. The rate of change of lateral surface when the radius is 7 cm and altitude is 24 cm is:
If \( A \) and \( B \) are the two real values of \( k \) for which the system of equations \( x + 2y + z = 1 \), \( x + 3y + 4z = k \), \( x + 5y + 10z = k^2 \) is consistent, then \( A + B = \): (a) 3
The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrolment in chemistry. How many students take at least one of these two subjects?
The derivative of  \(\sin^2\)\(( \cot^{-1} {\sqrt {( \frac{1 + x}{1 - x}} })\) with respect to \( x \) is equal to: (a) 0