If \(x \in (a, b)\) satisfies the inequality, \(\frac{x-3}{x^2+3x+2} \ge 1\), then the largest possible value of b - a is

In a class of 65 students 40 like cricket, 25 like football and 20 like hockey, 10 students like both cricket and football, 8 students like football and hockey and 5 students like all three sports. If all the students like at least one sport, then the number of students who like…

If a, b, c are real numbers \(a^2+b^2+c^2=1\), then the set of values \(ab+bc+ca\) can take is:

In a school 70% of the boys like cricket and 50% like football. If x% like both Cricket and Football, then

The inequality…

Placing which of the following two digits at the right end of 4530 makes the resultant six digit number divisible by 6, 7 and 9?

The set of values of x which satisfy the inequality…

The remainder when \((29^{29})^{29}\) is divided by 9 is

A chord is drawn inside a circle, such that the length of the chord is equal to the radius of the circle. Now, two circles are drawn, one on each side of the chord, each touching the chord at its midpoint and the original circle. Let k be the ratio of the areas of the bigger insc…