Numerical Ability · General Aptitude · GATE CSE

Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combinations of elements, they conclude that the spell does not work.

How many attempts does each wizard make before coming to this conclusion, independently?

In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4^th of the number of students who like other branches. The number of students who like both their core and other branches is 500.

The number of students who like their core branches is

For positive non-zero real variables $x$ and $y$, if

$\ln \left( \frac{x + y}{2} \right) = \frac{1}{2} [ \ln (x) + \ln (y) ]$

then, the value of $\frac{x}{y} + \frac{y}{x}$ is

In the sequence 6, 9, 14, $x$, 30, 41, a possible value of $x$ is

Consider the following sample of numbers:

9, 18, 11, 14, 15, 17, 10, 69, 11, 13

The median of the sample is

The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coins is

If two distinct non-zero real variables $x$ and $y$ are such that $(x + y)$ is proportional to $(x - y)$ then the value of $\frac{x}{y}$

For positive non-zero real variables $p$ and $q$, if

$\log \left(p^2 + q^2\right) = \log p + \log q + 2 \log 3$,

then, the value of $\frac{p^4 + q^4}{p^2 q^2}$ is

A series of natural numbers $$F_1,F_2,F_3,F_4,F_5,F_6,F_7,\,.....$$ obeys $$F_{n+1}=F_n+F_{n-1}$$ for all integers $$n\ge2$$.

If $$F_6=37$$, and $$F_7=60$$, then what is $$F_1$$ ?

A function y(x) is defined in the interval [0, 1] on the x-axis as

$$y(x) = \left\{ \matrix{ 2\,if\,0 \le x < {1 \over 3} \hfill \cr 3\,if\,{1 \over 3} \le x < {3 \over 4} \hfill \cr 1\,if\,{3 \over 4} \le x < 1 \hfill \cr} \right.$$

Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?

Let r be a root of the equation x² + 2x + 6 = 0. Then the value of the expression (r + 2) (r + 3) (r + 4) (r + 5) is

Choose the correct expression for $$f(x)$$ given in the graph.

A person sold two different items at the same price. He made 10% profit in one item, and 10% loss in the other item. In selling these two items, the person made a total of

The pie charts depict the shares of various power generation technologies in the total electricity generation of a country for the years 2007 and 2023.

The renewable sources of electricity generation consist of Hydro, Solar and Wind. Assuming that the total electricity generated remains the same from 2007 to 2023, what is the percentage increase in the share of the renewable sources of electricity generation over this period?

A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken.

Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person.

Macronutrient energy contribution

The typical energy density (kcal/g) of these macronutrients is given in the table:

The total fat (all three types), in grams, this person consumes is

A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is

The least number of squares to be added in the figure to make AB a line of symmetry is

Consider two functions of time (t),

$$f(t)=0.01\,t^2$$

$$g(t)=4\,t$$

where $$0 < t < \infty$$.

Now consider the following two statements :

(i) For some $$t > 0,g(t) > f(t)$$.

(ii) There exists a $$T$$, such that $$f(t) > g(t)$$ for all $$t > T$$.

Which one of the following options is TRUE?

$$f(x)$$ and $$g(y)$$ are functions of x and y, respectively, and $$f(x)=g(y)$$ for all real values of x and y. Which one of the following options is necessarily TRUE for al x and y?

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball.

First ball is drawn. What is the probability of getting an orange ball in the next draw?

Which product contributes the greatest fraction to the revenue of the company in that year?

The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking.

What is the average of the marks obtained by the class in the examination?