Most Expected IPMAT 2026 Quant Questions PDF with Solutions

Let $$\alpha$$, $$\beta$$ be the roots of $$x^{2} - x + p = 0$$ and $$\gamma$$, $$\delta$$ be the roots of $$x^{2}- 4x + q = 0$$ where p and q are integers. If $$\alpha, \beta, \gamma, \delta$$ are in geometric progression then p + q is

Let $$f(x) = a^2x^2 + 2bx + c$$ where, $$a \neq 0, b, c$$ are real numbers and x is a real variable then

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

If the polynomial $$ax^2 + bx + 5$$ leaves a remainder 3 when divided by $$x - 1$$, and a remainder 2 when divided by $$x + 1$$, then $$2b - 4a$$ equals

Let $$\alpha$$, $$\beta$$ be the roots of $$x^{2} - x + p = 0$$ and $$\gamma$$, $$\delta$$ be the roots of $$x^{2}- 4x + q = 0$$ where p and q are integers. If $$\alpha, \beta, \gamma, \delta$$ are in geometric progression then p + q is

Let $$f(x) = a^2x^2 + 2bx + c$$ where, $$a \neq 0, b, c$$ are real numbers and x is a real variable then

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

If the polynomial $$ax^2 + bx + 5$$ leaves a remainder 3 when divided by $$x - 1$$, and a remainder 2 when divided by $$x + 1$$, then $$2b - 4a$$ equals

Amisha can complete a particular task in twenty days. After working for four days she fell sick for four days and resumed the work on the ninth day but with half of her original work rate. She completed the task in another twelve days with the help of a co-worker who joined her from the ninth day. The number of days required for the co-worker to complete the task alone would be ______.

Fruits were purchased for Rs 350. 9 boys ate $$\dfrac{3}{5}th$$ of them in 2 hours. 6 boys feel their stomach as full so do not eat further. In how many hours the remaining fruits will get finished by remaining boys?

Work done by P in one day is double the work done by Q in one day and work done by Q in one day is thrice the work done by R in one day. If P, Q and R together can complete the work in 30 days then in how many days P alone can do the work?

Three workers working together need 1 hour to construct a wall. The first worker, working alone, can construct the wall twice as fast as the third worker, and can complete the task an hour sooner than the second worker. Then, the average time in hours taken by the three workers, when working alone, to construct the wall is

Train A takes 45 minutes more than train B to travel 450 km. Due to engine trouble, speed of train B falls by a quarter. So it takes 30 minutes more than Train A to complete the same journey. Find the speed of Train A.

Guru and Chela walk around a circular path of 115 km in circumference, they start together from the same point. If they walk at speed of 4 and 5 kmph respectively, also they walk in the same direction, when will they meet?

Two small insects, which are x metres apart, take u minutes to pass each other when they are flying towards each other, and v minutes to meet each other when they are flying in the same direction. Then, the ratio of the speed of the slower insect to that of the faster insect is

In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?

The value of $$\cos^{2}\dfrac{\pi}{8} + \cos^{2}\dfrac{3\pi}{8} + \cos^{2}\dfrac{5\pi}{8} + \cos^{2}\dfrac{7\pi}{8}$$ is

If $$\cos \alpha + \cos \beta = 1$$ ,then the maximum value of $$\sin \alpha − \sin \beta$$ is

If $$\sin \alpha + \sin \beta = \frac{\sqrt{2}}{\sqrt{3}}$$ and $$\cos \alpha + \cos \beta = \frac{1}{\sqrt{3}}$$, then the value of $$(20 \cos (\frac{\alpha - \beta}{2}))^{2}$$ 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

For $$0 < \theta < \dfrac{\pi}{4}$$, let
$$a = ((\sin \theta)^{\sin \theta}) (\log_{2} \cos \theta)$$, $$b = ((\cos \theta)^{\sin \theta}) (\log_{2} \sin \theta)$$
$$c = ((\sin \theta)^{\cos \theta}) (\log_{2} \cos \theta)$$ and $$d = ((\sin \theta)^{\sin \theta}) (\log_{2} \sin \theta)$$
Then, the median value in the sequence a, b, c, d is

Ayesha is standing atop a vertical tower 200m high and observes a car moving away from the tower on a straight, horizontal road from the foot of the tower. At 11:00 AM, she observes the angle of depression of the car to be $$45^{\circ}$$. At 11:02 AM, she observes the angle of depression of the car to be $$30^{\circ}$$. The speed at which the car is moving is approximately

If $$\log_{cos  x} (\sin  x) + \log_{\sin  x}(cos  x) = 2$$, then the value of x is

If $$\sin \theta + \cos \theta = m$$, then $$\sin^{6} \theta + \cos^{6}\theta$$ equals

The number of pairs (x, y) satisfying the equation $$\sin x + \sin y = \sin(x + y)$$ and $$|x| + |y| = 1$$ is