GATE IN 2026 Question Paper (07-Feb-2026) (Shift-1)

Exacerbate : Mitigate :: ___________
Choose the option with the correct pair of words to fill the blank.

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high cholesterol and diabetes. Furthermore,

1. the total number of patients with at least one of these conditions is 75,
2. the number of patients with high cholesterol is 10,
3. the number of patients with high BP is 45, and
4. the number of patients with only high BP and no other conditions is 20.

Then the number of patients who have both diabetes and high BP is _______

Four people P, Q, R, and S, of different ages, make the following observations.
P – I am younger than S.
Q – I am neither the youngest nor the oldest.
R – P is older than me.
Based on these observations, the youngest person is ______.

Circles $C_1$, $C_2$, and $C_3$, with centers $O_1$, $O_2$, and $O_3$ , and radii $r_1$ , $r_2$, and $r_3$, respectively, touch each other as shown in the following figure. Given $r_1=2\text{ cm}$, $r_2=1\text{ cm}$ and the angle $\angle O_1{O}_3{O}_2$ is $90^{\circ }$, $r_3=$ _____ cm.