List of top General Aptitude Questions on mathematical reasoning

Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the walkways that join at that junction. The minimum number of guards needed to watch all the walkways is ________.
Consider a five-digit number PQRST that has distinct digits P, Q, R, S, and T, and satisfies the following conditions:
1. \( P<Q \)
2. \( S>P>T \)
3. \( R<T \)
If integers 1 through 5 are used to construct such a number, the value of P is:

For the clock shown in the figure, if
O = O Q S Z P R T, and
X = X Z P W Y O Q,
then which one among the given options is most appropriate for P?


 

A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained:
(i) The sum of Yellow balls and twice the number of Violet balls is 50.
(ii) The sum of Violet and Green balls is 50.
(iii) The sum of Yellow and Red balls is 50.
(iv) The sum of Violet and twice the number of Red balls is 50.
Which one of the following Pie charts correctly represents the balls in the bag?
 

In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled (i), (ii), (iii), and (iv), respectively?


 

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:
The value of the contour integral $\oint \frac{dz}{2z - z^2}$ along the circle $|z| = 1$, oriented in the counterclockwise sense is

In the (4 times 4) array shown below, each cell of the first three rows has either a cross (X) or a number. The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is: 

A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight, and it should not stop till it reaches the other end of the cube. The minimum number of such cuts required 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 \( \frac{x}{y} \) is:

In the given text, the blanks are numbered (i)—(iv). Select the best match for all the blanks. Steve was advised to keep his head ………. (i) before heading ……….. (ii) to bat; for, while he had a head ……….. (iii) batting, he could only do so with a cool head ………. (iv) his shoulders.

The pie chart presents the percentage contribution of different macronutrients to a typical \( 2,000 \, \text{kcal} \) diet of a person. 

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

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

A rectangular paper of \( 20 \, \text{cm} \times 8 \, \text{cm} \) 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: 

The tangent plane to the surface \( x^2 + y^2 + z = 9 \) at the point \( (1, 2, 4) \) is:
The value of the line integral \[ \oint (x^2 \, dx + 2x \, dy) \] along the ellipse \( 4x^2 + y^2 = 4 \), oriented in the counterclockwise sense, is:
The system of linear equations \[ x + 2y + 3z = 4, \quad 2x - y - 2z = a^2, \quad -x - 7y - 11z = a \] has a solution if the values of \( a \) are:
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 rectangular paper sheet of dimensions \( 54 \, \text{cm} \times 4 \, \text{cm} \) 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:
Consider the following sample of numbers: \[ 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 \] The median of the sample is:
If \( \rightarrow \) denotes increasing order of intensity, then the meaning of the words [dry \( \rightarrow \) arid \( \rightarrow \) parched] is analogous to [diet \( \rightarrow \) fast \( \rightarrow \) \(\_\_\_\_\_\_\_\_\)]. Which one of the given options is appropriate to fill the blank?
Ethylene obeys the truncated virial equation-of-state: \[ \frac{PV}{RT} = 1 + \frac{B}{V}, \] where \( P \) is the pressure, \( V \) is the molar volume, \( T \) is the absolute temperature, and \( B \) is the second virial coefficient. The universal gas constant \( R = 83.14 \, \text{bar cm}^3 \text{mol}^{-1}\text{K}^{-1} \). At 340 K, the slope of the compressibility factor vs. pressure curve is \( -3.538 \times 10^{-3} \, \text{bar}^{-1} \). Let \( G^R \) denote the molar residual Gibbs free energy. At these conditions, the value of \( \left( \frac{\partial G^R}{\partial P} \right)_T \), in \( \text{cm}^3 \text{mol}^{-1} \), rounded off to 1 decimal place, is:
Heat is available at a rate of \( 2 \, \text{kW} \) from a thermal reservoir at \( 400 \, \text{K} \). A two-stage process harnesses this heat to produce power. Stages 1 and 2 reject heat at \( 360 \, \text{K} \) and \( 300 \, \text{K} \), respectively. Stage 2 is driven by the heat rejected by Stage 1. If the overall process efficiency is \( 50\% \) of the corresponding Carnot efficiency, the power delivered by the process, in \( \text{kW} \), rounded off to 2 decimal places, is:
For the block diagram shown in the figure, the correct expression for the transfer function \( G_d = \frac{y_2(s){d(s)} \) is:} \includegraphics[width=0.7\linewidth]{q48 CE.PNG}
Consider the line integral \( \int_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r \), with \( \mathbf{F}(\mathbf{r}) = x \mathbf{i} + y \mathbf{j} + z \mathbf{k} \), where \( \mathbf{i}, \mathbf{j}, \mathbf{k} \) are unit vectors in the \( (x, y, z) \) Cartesian coordinate system. The path \( C \) is given by \( \mathbf{r}(t) = \cos(t) \mathbf{i} + \sin(t) \mathbf{j} + t \mathbf{k} \), where \( 0 \leq t \leq \pi \). The value of the integral, rounded off to 2 decimal places, is:}