Practice IPMAT Indore 2023 Quantitative Ability (MCQ) PYQs

Let \(p\) be a positive integer such that the unit digit of \(p ^ 3\) is \(4\). What are the possible unit digits of \((p + 3) ^ 3\)

Let \([x]\) denote the greatest integer not exceeding \(x\) and {\(x\)} \(= x - [x]\) If \(n\) is a natural number, then the sum of all values of \(x\) satisfying the equation \(2[x] = x + n\){\(x\)} is

The set of all real values of \(x\) satisfying the inequality \(\dfrac{x^2(x+1)}{(x-1)(2x+1)^3} > 0\) is

A goldsmith bought a large solid golden ball at INR 1,000,000 and melted it to make a certain number of solid spherical beads such that the radius of each bead was one-fifth of the radius of the original ball. Assume that the cost of making golden beads is negligible. If the goldsmith sold all the beads at 20% discount on the listed price and made a total profit of 20%, then the listed price of each golden bead, in INR, was

Which of the following straight lines are both tangent to the circle \(x ^ 2 + y ^ 2 - 6x + 4y\) \({}- 12 = 0\)?

If \(A = \begin{bmatrix} 1 & 2 3 & a \end{bmatrix}\) where \(a\) is a real number and det \((A ^ 3 - 3A ^ 2 - 5A) = 0\) then one of the values of \(a\) can be

A helicopter flies along the sides of a square field of side length 100 kms. The first side is covered at a speed of 100 kmph, and for each subsequent side the speed is increased by 100 kmph till it covers all the sides. The average speed of the helicopter is

\(\dfrac{(a + b)}{(b + c)} = \dfrac{(c + d)}{(d + a)} \) which of the following statements is always true?

If the harmonic mean of the roots of the equation \((5 + \sqrt{2}) x ^ 2 - bx + 8\) \({}+ 2\sqrt{5} = 0\) is \(4\) then the value of \(b\) is

In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero points. Which of the following sequences cannot represent the scores of the five players?