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'All the mangoes in the basket are good.'If the above statement is false, then which one of the following statements is necessarily true?All the mangoes in the basket are...

What is the next number in the series?$12$ $35$ $81$ $173$ $357$ ____,

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...

A student council of $10$ members consists of two students from engineering school, three students from science school and five students from arts school. The university ...

The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported a...

A firm producing air purifiers sold $200$ units in $2012$. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportati...

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, c...

Two structural members are connected by a hinge and they are externally loaded as shown in the figure below. A and B are roller supports, and C is a pin support. Neglecti...

$\log \tan 1^{\circ} + \log \tan 2^{\circ} + \dots + \log \tan 89^{\circ}$ is$1$$1/\sqrt{2}$$0$$-1$

'The team $\_\_\_\_$ more than $300$ runs in $20$ overs $\_\_\_\_$ rains. However, some players needed to improve their batting skills.'Choose the option with the correct...

The bar chart gives the batting averages of $\mathrm{VK}$ and $\mathrm{RS}$ for $11$ calendar years from $2012$ to $2022$. Considering that $2015$ and $2019$ are world cu...

​​​​​A rigid circular disc of radius $r$ (in $m$ ) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is $\omega...

A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?$B D$$B C$$B A$$A D$

Consider two identical tanks with a bottom hole of diameter $d$. One tank is filled with water and the other tank is filled with engine oil. The height of the fluid colum...

The product of three integers $X$, $Y$ and $Z$ is $192$. $Z$ is equal to $4$ and $P$ is equal to the average of $X$ and $Y$. What is the minimum possible value of $P$?$6$...

If a positive real $x$ satisfies the following equation\[\log _{2} x+\log _{\sqrt{2}} x=48,\]then the value of $x$ is $\_\_\_\_$$2^{16}$$4^{16}$$2^{14}$$4^{14}$

For the matrix $A = \begin{bmatrix} 5 & 3 \\ 1 & 3 \end{bmatrix}$, ONE of the normalized eigen vectors is given as$\begin{pmatrix} \dfrac{1}{2} \\ \dfrac{\sqrt{3}}{2} \en...