List of practice Questions

Let the points \(A(a,-1,2)\), \(B(1,b,-4)\), \(C(-1,1,c)\) and \(D(1,-2,8)\) be the vertices of a parallelogram \(ABCD\). Then its area is equal to:
What is the mirror image of the word \textbf{PRODUCTION along the \(X\!-\!X'\) axis?}
The atomic number of Lanthanum is 57. Its electronic configuration will be ......
If \( \lim_{x \to 0} \frac{3x^3 - (1-x^2)^{3/2}}{x^2\sin x} = p + \log q \) then pq =
Five diagrams \(A, B, C, D,\) and \(E\) are given. Three out of these, when put together, form a square. Identify the correct set of diagrams.
Solve for \( x \) in the equation \( \frac{2x - 3}{4} = 5 \).
An electric dipole with dipole moment \(p = 5 \times 10^{-6}\) Cm is aligned with the direction of a uniform electric field of magnitude \(E = 4 \times 10^5\) N/C. The dipole is then rotated through an angle of \(60^\circ\) with respect to the electric field. The change in the potential energy of the dipole is:
The equation for the RMS velocity is given as \[ v_{\text{rms}} = \sqrt{\frac{3RT}{M_0}} \] where \( R \) is the gas constant, \( T \) is the temperature, and \( M_0 \) is the molecular mass. If the temperature is increased, find the new RMS velocity \( v_{\text{rms}} \) when the temperature is doubled.}
Which of the following states that a specific and definite action is to be taken or not to be taken?
1 mL of "x volume" H\(_2\)O\(_2\) solution on heating gives 20 mL of oxygen gas at STP. The (w/v) % corresponding to "x volume" of H\(_2\)O\(_2\) is
Had he ________ the importance of the meeting, he would have made sure to attend.
What volume of oxygen gas at STP is required to completely burn 12 g of methane (\( \text{CH}_4 \))? (Molar mass of \( \text{CH}_4 = 16 \, \text{g/mol} \), 1 mole of gas at STP occupies \( 22.4 \, \text{L} \)).
The volume of water required to dissolve 0.1 g PbCl\(_2\) to get a saturated solution (in mL) is (Given K\(_{sp}\)(PbCl\(_2\)) = \(3.2 \times 10^{-8}\); Atomic mass of Pb = 207u)
Find the value of \( x \) in the following equation: \[ \frac{2}{x} + \frac{3}{x + 1} = 1 \]
If A = (0,1), B = (1,2), C = (-2,1) then the equation of the locus of a point P such that area of triangle PAB = area of triangle PAC is
If y = 3e2x + 2e3x, then $\frac{d^2y}{dx^2} + 6y$ is equal to
Identify the correct mirror image of the given figure along the \(XY\)-axis.

Calculate the number of moles present in 9.10 × 1016 kg of water.

A projectile is fired with an initial speed of \( 20 \, \text{m/s} \) at an angle of \( 30^\circ \) above the horizontal. Find the maximum height reached by the projectile.
Rearrange the following parts to form a meaningful and grammatically correct sentence: P. to innovate continuously
Q. is what sets
R. a successful company
S. apart from its competitors
Choose the word that best fits the blank in the sentence below: "Despite his remarks, the audience found his ideas intriguing and thought-provoking."
A boy tries to message his friend. Each time, the chance the message is delivered is \( \frac{1}{6} \), and the chance it fails is \( \frac{5}{6} \). He sends 6 messages. Find the probability that exactly 5 messages are delivered.
If the workload of a manager is more than his capacity, which of the following can he use to offload the work?
Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
Which of the following statements are correct about the problems of the Partition of India?