The inequality \(\log_2\frac{3x-1}{2-x}<1\) holds true for

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:

The set of values of x which satisfy the inequality…

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

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…

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…

Points P, Q, R and S are taken on sides AB, BC, CD and DA of square ABCD respectively, so that AP : PB = BQ : QC = CR : RD = DS : SA = 1 : n. Then the ratio of the area of PQRS to the area of ABCD is

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

On a circular path of radius 6 m a boy starts from a point A on the circumference and walks along a chord AB of length 3 m. He then walks along another chord BC of length 2 m to reach point C. The point B lies on the minor arc AC. The distance between point C and A is