Quantitative Ap...

Find the remainder of 25! when divided by 29.

α and β are distinct roots of a quadratic equation where α² + 1 = 3α and β² = 3β - 1. Find the equation whose roots are [(1/α) + 2] and [(1/β) + 2].

In the Year 2024, Abhijeet spent 60% of what he earned. His income increased by 100rs. every month as compared to the preceding month. if he saved 48000rs. in that year, find his income in the second last month.

Two positive integers p and q are in the ratio 7:13. If 14 and 26 are subtracted respectively from p and q, the ratio of the resulting numbers, which are positive, taken in the same order, is again 7:13. what is the second least value of (p+q).

Roger and Misha attempted to solve a quadratic equation. Roger made a mistake in writing down the constant term. He ended up with the roots (7, 3). Misha made a mistake in writing down the coefficient of x. She got the roots as (3, 3). Find the exact roots of the original quadratic equation.

In how many ways can eight letters be selected from the word CONTINUATION such that at least five distinct letters are included in it?

The ratio of men and women in shift I workers is 1 : 3 and ratio between the women and men in shift II workers is 2 : 3. When both shift workers are present then ratio between the men and women is 23 : 27. Find the ratio between the men of shift II and shift I.

The number x is a five-digit number with no Os and the last 3 digits of x form a perfect cube divisible by 8. When the digits of x are considered in the reverse order, the resulting
number also shows the same property. How many such numbers are possible?

If the vertices of an octagon are used to form a triangle, what is the probability that the triangle doesn't have any side common with the octagon?

A trader under weighs rice and gets a profit of 40%. Had he used the correct weight he would have still got a profit of 19%. What weight does he use for 1 kg?