Numerical Ability · General Aptitude · GATE ME

Find the odd one out in the set: {19, 37, 21, 17, 23, 29, 31, 11}

In the following series, identify the number that needs to be changed to form the Fibonacci series.

1, 1, 2, 3, 6, 8, 13, 21, …

The real variables $x, y, z$, and the real constants $p, q, r$ satisfy

$\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z}{rp - q^2}$

Given that the denominators are non-zero, the value of $px + qy + rz$ is

Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has 1/4 probability of landing on any of the four rectangular faces. The label on the top face of the dice is the score of the throw.

If thrown together, what is the probability of getting the sum of the two long dice scores greater than 11?

A certain country has 504 universities and 25951 colleges. These are categorised into Grades I, II, and III as shown in the given pie charts.

What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III? 

A person travelled 80 km in 6 hours. If the person travelled the first part with a uniform speed of 10 kmph and the remaining part with a uniform speed of 18 kmph.

What percentage of the total distance is travelled at a uniform speed of 10 kmph?

How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?

Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is

Consider the following inequalities

𝑝² − 4𝑞 < 4

3𝑝 + 2𝑞 < 6

where 𝑝 and 𝑞 are positive integers.

The value of (𝑝 + 𝑞) is _______. 

Fish belonging to species S in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily attack their prey. However, having this extra layer of black pigment results in lower collagen on their skin, making their skin more fragile.

Which one of the following is the CORRECT logical inference based on the information in the above passage?  

For the past m days, the average daily production at a company was 100 units per day.

If today’s production of 180 units changes the average to 110 units per day, what is the value of m?

Consider the following functions for non-zero positive integers, p and q.

$\rm f(p,q)=\frac{p\times p\times p\times.......\times p}{q\ terms}=p^q;\;$; f(p, 1) = p

$g(p,q)=p^{p^{p^{p^{p^{..^{..^{..^{up\ to\ q\ terms}}}}}}}}$; g(p, 1) = p

Which one of the following options is correct based on the above? 

Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.

What is the ratio of the areas of unshaded regions of case M to that of case N?

A rhombus is formed by joining the midpoints of the sides of a unit square.

What is the diameter of the largest circle that can be inscribed within the rhombus?

An equilateral triangle, a square and a circle have equal areas.

What is the ratio of the perimeters of the equilateral triangle to square to circle?