List of practice Questions

Given below are two statements:
Statement I: C–Cl bond is stronger in $\mathrm{CH_2 = CH{-}Cl}$ than in $\mathrm{CH_3{-}CH_2{-}Cl}$.
Statement II: The given optically active molecule, on hydrolysis, gives a solution that can rotate the plane polarized light.
In the light of the above statements, choose the correct answer from the options given below:
Given below are two statements :
Statement I : Presence of large number of unpaired electrons in transition metal atoms results in higher enthalpies of their atomisation.
Statement II : $d_{xy} = d_{xz} = d_{yz} < d_{x^2 - y^2} = d_{z^2}$ and $d_{x^2 - y^2} = d_{z^2} = d_{xy} <d_{xz} = d_{yz}$ are the d-orbital splittings in $[Fe(H_2O)_6]^{3+}$ and $[Ni(Cl)_4]^{2-}$ complex ions respectively.
In the light of the above statements, choose the correct answer from the options given below :
If two lines drawn from a point $P(2,3)$ intersect the line $x+y=6$ at a distance $\sqrt{\dfrac{2}{3}}$, then the angle between the lines is
Correct order of acidic strength: (I) Phenol, (II) p-Cresol, (III) m-Nitrophenol, (IV) p-Nitrophenol
$K_2Cr_2O_7 + KI \xrightarrow{H^+} I_2 + Cr^{3+}$
Statement-I : Size of $O^{2-}$ is smaller than $F^-$.
Statement-II: Second ionization energy of $\text{Na}$ is greater than second ionization energy of $\text{Mg}$.
A capacitor of \(10\,\mu F\) is charged to \(50\,V\). Calculate the energy stored in the capacitor.
The sum of the first \(10\) terms of an A.P. is \(150\). If the first term is \(10\), what is the common difference?
Find the distance between the planes \(2x + 3y + 4z = 4\) and \(4x + 6y + 8z = 12\).
In a Young's Double Slit Experiment, if the distance between the slits is halved and the distance to the screen is doubled, what happens to the fringe width?
Five geometric blocks with their dimensions are given below. Calculate the length of the path as shown in the image below, between points A and B.
Ravi has a briefcase with dimensions of two by 1 ½ by 1 ½ feet. He wishes to place several notebooks, each eight by nine by one inch, into the briefcase. What is the largest number of notebooks the briefcase will hold?
Choose the correct synonym for “Diligent.”
Image P shows an object as seen from the top. Which of the objects given below will appear as shown in image P when viewed from the top? Consider all the objects are made with opaque solids.
Several kettles are shown below. What is the total number of usable kettles that are designed to store and pour hot water?
Find the distance of the point \( (1,-2,3) \) from the \(yz\)-plane.
Which one of the following matrices can be obtained by performing elementary row transformations on the \(3\times3\) identity matrix?
The equation \(x^2 - Ky^2 - 4x + 6y - 5 = 0\) represents a pair of straight lines. Find the point of intersection.
If \(A, B, C\) are vertices of a triangle with position vectors \(\vec{a}, \vec{b}, \vec{c}\) respectively, then find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).
In an LCR series circuit, the resonance frequency is \( f \). If the capacitance is made 4 times, what will be the new resonance frequency?
A proton \((q = 1.6 \times 10^{-19}\,C)\) enters a magnetic field of \(2\,T\) with a velocity of \(3 \times 10^6\,\text{m/s}\) perpendicular to the field. Find the magnetic force acting on the proton.
If ‘ORANGE' is coded as ‘PSBOHF', how is ‘GRAPES' coded?
Complete the series: \(285,\,253,\,221,\,189,\, ?\)
Evaluate the integral \[ \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x}\,dx. \]
If \( z = \frac{3i}{2} \), what is the value of \( \arg(z) \)?
Which of the following electrolytes is most effective in the coagulation of a negative sol like \(As_2S_3\)?