A train left point A at 12 noon. Two hours later, another train started from point A in the same direction. It overtook the first train at 8 PM. It is known that the sum of the speeds of the two trains is 140 km/hr. Then, at what time would the second train overtake the first train, if instead the second train had started from point A in the same direction 5 hours after the first train? Assume that both the trains travel at constant speeds.

In a city, 50% of the population can speak in exactly one language among Hindi, English and Tamil, while 40% of the population can speak in at least two of these three languages. Moreover, the number of people who cannot speak in any of these three languages is twice the number o…

The number of 5-digit numbers consisting of distinct digits that can be formed such that only odd digits occur at odd places is

Consider the polynomials \(f(x) = ax^2 + bx + c\), where \(a > 0\), \(b, c\) are real, and \(g(x) = -2x\). If \(f(x)\) cuts the x-axis at \((-2, 0)\) and \(g(x)\) passes through \((a, b)\), then the minimum value of \(f(x) + 9a + 1\) is

There are 10 points in the plane, of which 5 points are collinear and no three among the remaining are collinear. Then the number of distinct straight lines that can be formed out of these 10 points is

The highest possible value of the ratio of a four digit number and the sum of its four digits is:

From the passage: In a football tournament six teams A, B, C, D, E and F participated. E...

Total number of matches ending in draw is

ABCD is a quadrilateral whose diagonals AC and BD intersect at O. If triangles AOB and COD have areas 4 and 9 respectively, then the minimum area that ABCD can have is

The set of all real values of \(p\) for which the equation \(3\sin^2 x + 12\cos x - 3 = p\) has at least one solution is