List of practice Questions

The expression \((6 + 5\sqrt{3}) - (4 - 3\sqrt{3})\) is:
If \( \times \) means \( \div \), \( \div \) means \( + \), \( + \) means \( - \), and \( - \) means \( \times \), then calculate: \[ 2 \, \, 50 \, \, 40 \, \, 10 \, \, 96 \, ? \, - \, + \, \times \, \div \]
At 290 K, a vessel (I) contains equal moles of three liquids (A, B, C). The boiling points of A, B, and C are 348 K, 378 K, and 368 K respectively. Vessel (I) is heated to 300 K and vapors were collected into vessel (II). Identify the correct statements. (Assume vessel (I) contains liquids and vapors and vessel (II) contains only vapors.)
Statements:
I.Vessel – I is rich in liquid
II.Vessel – II is rich in vapors of C.
III. The vapor pressures of A, B, and C in Vessel (I) at 300 K follows the order \( C>A>B \).
An 18-year-old male accused of rape claims he is 16 years old. Which joint X-ray should be done?
Let f(z) be an analytic function, where z = x + iy. If the real part of f(z) is cosh x cos y, and the imaginary part of f(z) is zero for y = 0, then f(z) is
For n ≥ 3, let a regular n-sided polygon Pn be circumscribed by a circle of radius Rn and let rn be the radius of the circle inscribed in Pn. Then
\(\lim\limits_{n \rightarrow \infin}(\frac{R_n}{r_n})^{n^2}\)
equals
Assertion (A): An electron and a proton enter with the same momentum \( \vec{p} \) in a magnetic field \( \vec{B} \) such that \( \vec{p} \perp \vec{B} \). Then both describe a circular path of the same radius.
Reason (R): The radius of the circular path described by the charged particle (charge \( q \), mass \( m \)) moving in the magnetic field \( \vec{B} \) is given by \( r = \frac{mv}{qB} \).
In the Wurtz-Fitting reaction, a compound \(X\) reacts with an alkyl halide. What is \(X\)?

For a hypothetical economy, assume the government increased infrastructural investment by ₹10,000 crore. 80% of additional income is consumed in the economy. Estimate the increase in income and the corresponding increase in consumption expenditure in the economy.

What is the chemical name of Vitamin B6?
The divergence of a 3-dimensional vector \(\frac{𝑟̂}{𝑟^3}\) (𝑟̂ is the unit radial vector) is:
The speed distribution for a sample of \(N\) gas particles is shown below. \(P(v) = 0\) for \(v > 2v_0\). How many particles have speeds between \(1.2v_0\) and \(1.8v_0\)?
Ques Fig
In a 600 m race, the ratio of the speeds of two participants A and B is 4:5. If A has a head start of 200 m, then the distance by which A wins is:
Two heaters A and B have power rating of 1 kW and 2 kW, respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is :

A patient presents with no pulse, and the ECG shows the following rhythm. What is the next appropriate step? 

Three capacitors of capacitances 10 \(\mu\)F, 5 \(\mu\)F and 20 \(\mu\)F are connected in series with a 14 V dc supply. The charge on 5 \(\mu\)F capacitor is
If \( \tan A = -\frac{60}{11} \) and A does not lie in the 4th quadrant. \( \sec B = \frac{41}{9} \) and B does not lie in the 1st quadrant. If \( \csc A + \cot B = K \), then \( 24K = \):
A point source \(S\) emits unpolarized light uniformly in all directions. At two points A and B, the ratio \(r = I_A/I_B\) of the intensities of light is \(2\). If a set of two polaroids having 45° angle between their pass-axes is placed just before point B, then the new value of r will be ____

How many sisters does Sunny have?
(I) Sunny is the only son of his parents.
(II) Sunny’s parents have three children.

The covering of an omphalocele is derived from which layer?
Let \( \Delta = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) be a square matrix such that \( \text{adj} A = A \). Then, \( (a + b + c + d) \) is equal to:
Consider two Ordinary Differential Equations (ODEs) :
\(P:\frac{dy}{dx}=\frac{x^4+3x^2y^2+2y^4}{x^3y}\)
\(Q:\frac{dy}{dx}=\frac{-y^2}{x^2}\)
Which one of the following options is CORRECT ?
(b) Analyse the role of scholars in the task of preparing the critical edition of the Mahabharata.
A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds and him in 8 seconds. The length of the train is:
Assertion (A): For the matrix \[ A = \begin{bmatrix} 1 & \cos \theta & 1 \\ -\cos \theta & 1 & \cos \theta \\ -1 & -\cos \theta & 1 \end{bmatrix}, \quad \text{where } \theta \in [0, 2\pi], \] \(|A| \in [2, 4]\).
Reason (R): \(\cos \theta \in [-1, 1], \ \forall \ \theta \in [0, 2\pi].\)