List of top Mathematics Questions

If a square is divided into \( 4 \times 4 \) squares. If two squares are chosen randomly, then the probability that the squares don't share a common side is:
The system of equations: \[ x + y + z = 6, \quad x + 2y + 5z = 9, \quad x + 5y + \lambda z = \mu, \] has no solution if:
Find the length of the chord whose midpoint is \( \left( \frac{3}{2}, 0 \right) \) of the ellipse \[ \frac{x^2}{2} + \frac{y^2}{4} = 1. \]
There are 5 boys and 4 girls. The sum of the number of ways to sit them such that all boys sit together and the number of ways such that no boys sit together is equal to:
Number of terms in an arithmetic progression is \(2n\). Sum of terms occurring at even places is 40 and sum of terms occurring at odd places is 55. If the first term exceeds the last term by 27, then \( n \) equals to:
The system of equations is given as: \[ (\lambda + 1)x + (\lambda + 2)y + (\lambda - 1)z = 0 \] \[ \lambda x + (\lambda - 1)y + (\lambda + 1)z = 0 \] \[ (\lambda - 1)x + (\lambda + 1)y + (\lambda + 2)z = 0 \] If the above system of equations has infinite solutions, then \( \lambda^2 + \lambda \) is:
If \[ (7 + e^{2x}) dy - (1 + 2e^{2x})(y + 3) dx = 0, \quad y(0) = 5, \] then \( y(n2) = \)?
Find the area bounded between two curves: \[ x^2 + y^2 = 25 \quad \text{and} \quad y = |x - 1|. \]
The value of \( a = 3 \), the sum of first 4 terms is equal to the one fifth of the sum of next 4 terms in A.P., then find the sum of the first 20 terms.
Two biased dice are rolled. Out of which one die contains 1, 1, 2, 2, 3, 3, and another die contains 1, 2, 2, 3, 3, 4. Then the probability of getting a sum of 4 or 5 is:
Which of the following does not belong to the same group?
From the English alphabets, 5 letters are chosen and arranged in alphabetical order. The total number of ways in which the middle letter is M is:
Let \( D = \{a, b, c\} \). How many distinct ways can \( D \) be partitioned into non-empty subsets, representing equivalence relations?
If |A| = 2, B = adj(adj(2A)), A is a 3×3 matrix, and tr(A) = 3, what is tr(B) + |B|?
A circle passes through the points \( (1, 1) \) and \( (2, -1) \), and its center lies on the line \( x + y = 4 \). What is the radius of the circle?
A bag contains 4 red balls, 3 blue balls, and 2 green balls. Two balls are picked at random. What is the probability that both balls are of the same color?
What is the solution to the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) with the initial condition \( y(1) = 2 \)?
What is the sum of the infinite series \( S = \sum_{n=0}^{\infty} \frac{1}{3^n} \)?
If the equation of a circle is \( 4x^2 + 4y^2 - 12x + 8y = 0 \), what is the radius of the circle?
Find the value of the integral \( \int_0^{\frac{\pi}{2}} \sin^2(x) \, dx \).
If \( f(x) = \ln \left( \frac{x^2 + e}{x^2 + 1} \right) \), then the range of \( f(x) \) is:
If \( f(x) = \cos^{-1 } \left( \frac{\sqrt{2x^2 + 1}}{x^2 + 1} \right) \), then the range of \( f(x) \) is:
Let
\[ I(R) = \int_0^R e^{-R \sin x} \, dx, \quad R > 0. \]
Which of the following is correct?
A circle passes through the points \( (2, 0) \) and \( (1, 2) \). If the power of the point \( (0, 2) \) with respect to this circle is 4, then the radius of the circle is
The acceleration \( f \) (in ft/sec\(^2\)) of a particle after a time \( t \) seconds starting from rest is given by:
\[ f = 6 - \sqrt{1.2t}. \]
Then the maximum velocity \( v \) and the time \( T \) to attain this velocity are: