List of top Mathematics Questions

Two trains running in opposite directions pass by a man standing on the platform in 20 seconds and 10 seconds respectively and they completely cross each other in 15 seconds. The ratio of their speeds is:

Find the area of the triangle with vertices A(5,4), B(-2,4) and C(2,14).

In a class of 60 students comprising girls and boys, 30% are boys. On a given day 10% of the class is absent and all the absentees are boys. What is the percentage of girls in this class on that given day?

The average of the first five multiples of 9 is:

If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is:

The straight line $2x + 3y + 4 = 0$ touches the x-axis at:

A box contains 5 pink, 3 green, and 2 yellow balls. Three balls are picked up randomly. What is the probability that none of the balls drawn is green?

What is the sum of the first 10 terms of the sequence 1, 2, 4, 8, 16, ...?

Three taps A, B, and C together can fill an empty cistern in 10 minutes, tap A alone can fill it in 20 minutes and tap B alone in 40 minutes. How long will tap C alone take to fill it?

In a class of 35 students, 24 like to play cricket and 16 like to play football. Also, each student likes to play at least one of the two games. How many students like to play both cricket and football?

If the price of the sugar is raised by 25%, find by how much percent a homemaker should reduce the consumption of sugar so as not to increase his/her expenditure?

How many numbers between 100 and 999 can be formed with the digits 1, 4, 7, 8, and 9 if the digits are not repeated?

What is the chance that a leap year, selected at random, will NOT have 53 Sundays as well as 53 Mondays?

If the lines \( \frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k} \) and \( \frac{x-1}{2k} = \frac{y-3}{2} = \frac{z-5}{1} \) are coplanar, then \( k \) can have

If \[ \begin{vmatrix} a & a^2 & 1+a^3 b & b^2 & 1+b^3 c & c^2 & 1+c^3 \end{vmatrix} = 0 \] and vectors \( (1,a,a^2), (1,b,b^2), (1,c,c^2) \) are non-coplanar, then the product \( abc \) is ___.

If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is \( p \), then \( 96p \) is equal to ___.

A multiple choice examination has 5 questions. Each question has 4 alternatives of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing is

If the foot of the perpendicular drawn from the point \( (0,2,1) \) on a line passing through \( (a,5,1) \) is \( \left(\frac{5}{3}, \frac{7}{3}, \frac{15}{3}\right) \), then \( a \) is equal to ___.

The area of the region described by \( A = \{(x,y) : x^2 + y^2 \le 1 \text{ and } y^2 \le 1 - x \} \) is

The area of the region bounded by the curves \( y = |x - 2| \), \( x = 1 \), \( x = 3 \) and the x-axis is

If \( \int f(x)\,dx = g(x) \), then \( \int x^9 f(x^5)\,dx \) is equal to

For what value of \( \theta \) lying between \(0\) and \( \pi \) which satisfy inequality \( \sin\theta \cos^3\theta>\sin^3\theta \cos\theta \)

Let \( f(x) = \sqrt{1 + x^2} \), then

If \( A \) is an \( n \times n \) non-singular matrix such that \( AA^T = A^{-1}A \) and \( B = A^{-1}A^T \), then \( BB' \) is equal to

If \( A = \{1,2\}, B = \{1,2,3,4\}, C = \{5,6\}, D = \{5,6,7,8\} \), then state which of the following is true?