Numerical Ability · General Aptitude · GATE EE

The decimal number system uses the characters 0, 1, 2, ... , 8, 9, and the octal number system uses the characters 0, 1, 2, ... , 6, 7.

For example, the decimal number 12 ( = 1 × 10¹ + 2 × 10⁰) is expressed as 14 ( = 1 × 8¹ + 4 × 8⁰) in the octal number system.

The decimal number 108 in the octal number system is

A shopkeeper buys shirts from a producer and sells them at 20% profit. A customer has to pay ₹3,186.00 including 18% taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer?

If, for non-zero real variables $x$, $y$, and real parameter $a > 1$,

$x : y = (a + 1) : (a - 1)$,

then, the ratio $(x^2 - y^2) : (x^2 + y^2)$ is

Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5', and '6', what is the probability of getting a '1' on the first roll of the dice and a '4' on the second roll?

How many triangles are present in the given figure?

Which of the following options represents the given graph?

the digit in the unit's place of the product $$3^{999}\times7^{1000}$$ is __________.

A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is _________ cm$$^2$$.

In a 500 m race, P and Q have speeds in the ratio of 3 : 4. Q starts the race when P has already covered 140 m. What is the distance between P and Q (in m) when P wins the race?

Three bells P, Q and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes. If all the three bells are rung at 12:00 P.M., when will the three bells ring together again the next time?

The figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of the fixed axes 1-1, 2-2 or 3-3 chosen uniformly at random. What is the probability that the disc DOES NOT retain the same front and rear views after the flipping operation?

In the following figure,

• CD = 5 cm, BE = 10 cm, AE = 12 cm,
• ∠DAB = ∠DCB, and ∠DAE = ∠DBC = 90°

Points AFCD create a rhombus.

The length of BF (in cm) is

The chart below shows the data of the number of cars bought by Millennials and Gen X people in a country from the year 2010 to 2020 as well as the yearly fuel consumption of the country (in Million liters).

Considering the data presented in the chart, which one of the following options is true?

A surveyor has to measure the horizontal distance from her position to a distant reference point C. Using her position as the center, a 200 m horizontal line segment is drawn with the two endpoints A and B. Points A, B, and C are not collinear. Each of the angles ∠CAB and ∠CBA are measured as 87.8°. The distance (in m) of the reference point C from her position is nearest to

There are two identical dice with a single letter on each of the faces. The following six letters : Q, R, S, T, U and V, one on each of the faces. Any of the six outcomes are equally likely.

The two dice are thrown once independently at random.

What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes : Q, U and V?

The price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges Rs.150 for delivery. There are no delivery charges for orders from the store M. A person bought the item from the store S and saved Rs.100. What is the price of the item at the online store S (in Rs.) if there are no other charges than what is described above?

The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.

Consider the following statements :

$$\bullet$$ The line segment joint R and S is longer than the line segment joining P and Q.

$$\bullet$$ The line segment joining R and S is perpendicular to the line segment joining P and Q.

$$\bullet$$ The line segment joining R and U is parallel to the line segment joining T and Q.

Based on the above statements, which one of the following options is CORRECT?

An ant is at the bottom-left corner of a grid (point P) as shown below in the figure. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases. Which one of the following is a part of a possible trajectory of the ant during the movement?