List of practice Questions

A projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$ When the acceleration due to gravity is $g$, the range of the projectile is $d$ If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is $g^{\prime}=\frac{g}{081}$, then the new range is $d^{\prime}=n d$ The value of $n$ is ___

If $M=\begin{pmatrix}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{pmatrix}$, then which of the following matrices is equal to $M^{2022}$ ?

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over a frictionless pulley as shown below.
The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of the block is (Given g = 10 ms^–2)

A person moved from A to B on a circular path as shown in figure If the distance travelled by him is 60 m, then the magnitude of displacement would be Given ( Cos 135° = -0.7)

Let $\frac{dy}{dx} = \frac{ax-by+a}{bx+cy+a}$, where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the point (11, 6) from this circle is

A man on diuretics presents with weakness. An ECG was done which showed flat T waves and prominent U waves. What is the most likely diagnosis?

If for p ≠ q ≠ 0, the function
$f(x) = \frac{{^{\sqrt[7]{p(729 + x)-3}}}}{{^{\sqrt[3]{729 + qx} - 9}}}$
is continuous at x = 0, then

The three vertices of a triangle are (0, 0), (3, 1) and (1, 3). If this triangle is inscribed in a circle, then the equation of the circle is

Let
A =$\begin{pmatrix} 4 & -2 \\ \alpha & \beta \\ \end{pmatrix}$
If A² + γA + 18I = 0, then det (A) is equal to ______.

Let $S_1=\left\{z_1 \in C:\left|z_1-3\right|=\frac{1}{2}\right\}$ and $S _2=\left\{ z _2 \in C :\left| z _2-\right| z _2+1||=\left| z _2+\right| z _2-1||\right\}$ Then, for $z_1 \in S_1$ and $z_2 \in S_2$, the least value of $\left|z_2-z_1\right|$ is :

A Carnot engine has efficiency of $50 \%$ .If the temperature of sink is reduced by $40^{\circ} C$, its efficiency increases by $30 \%$ .The temperature of the source will be :

A uniform metal chain of mass m and length ‘$L$’ passes over a massless and frictionless pully. It is released from rest with a part of its length ‘$l$’ is hanging on one side and rest of its length '$L – l$' is hanging on the other side of the pully. At a certain point of time, when $l = L/x$, the acceleration of the chain is $g/2$. The value of $x$ is ______.

If the system of linear equations
2x + 3y – z = –2
x + y + z = 4
x – y + |λ|z = 4λ – 4
where λ ∈ R, has no solution, then

If the initial velocity in horizontal direction of a projectile is unit vector $\hat i$ and the equation of trajectory is $y = 5x(1 – x)$. The y component vector of the initial velocity is ______ $\hat j$.
(Take $g=10\ m/s^2$)

What is the molar mass of solute when 2.3 gram non-volatile solute dissolved in 46 gram benzene at 30°C? (Relative lowering of vapour pressure is 0.06 and molar mass of benzene is 78 gram mol^–1)

If $ \alpha, \beta, \gamma \in [0, \pi] $ and if $ \alpha, \beta, \gamma $ are in AP, then \[ \frac{\sin \alpha - \sin \gamma}{\cos \gamma - \cos \alpha} \] {is equal to:}

When a certain amount of solid A is dissolved in 100 g of water at 25°C to make a dilute solution, the vapour pressure of the solution is reduced to one-half of that of pure water. The vapour pressure of pure water is 23.76 mmHg. The number of moles of solute A added is _________. (Nearest Integer).

Considering the following reaction sequence,