List of practice Questions

If \( \alpha, \beta \) are the roots of the equation \( x^2 + bx + c = 0 \) satisfying the conditions \( \alpha+\beta=5 \) and \( \alpha^3+\beta^3=60 \), then \( 3c+2 = \)
What are X and Y respectively in the following set of reactions? X and Y respectively in the following set of reactions
The range of the real valued function \( f(x) = \cos^{-1 \left( \dfrac{3}{\sqrt{9x^2 - 12x + 22}} \right) \) is}
If \( t_n = \dfrac{1}{n(n+2)} \), \( n \in \mathbb{N} \), then which one of the following is true?
Assertion (A): \[ t_1 + t_2 + \cdots + t_{2003} = \dfrac{2003}{3005} \]
Reason (R): \[ t_n = \dfrac{1}{n(n+2)} = \dfrac{1}{2} \left( \dfrac{1}{n} - \dfrac{1}{n+2} \right) \]
The correct statement regarding X and Y in the following set of reactions is
In the given reaction sequence conversion of Y to Z is
reaction sequence conversion of Y to Z is
The preferred reagent for the preparation of pure alkyl chloride from alcohol is
In a colloidal solution, both the dispersed phase and dispersion medium are in liquid phase. What is the type of colloid?
Which of the following is used as froth stabilizer in froth floatation process?
Which method is used to purify liquids having very high boiling points and liquids which decompose at or below their boiling point?
4 mL of 'X volume' \( \text{H}_2\text{O}_2 \) on heating gives 80 mL of oxygen at STP. The value of X is
Consider the following Statement-I : \( \text{Al}_2\text{O}_3 \) is amphoteric in nature. Statement-II : \( \text{Tl}_2\text{O}_3 \) is more basic than \( \text{Ga}_2\text{O}_3 \). The correct answer is
Identify the incorrect order against the stated property.
The correct order of the non-metallic character among the elements B, C, N, F and Si is
How many of the following molecules have two lone pairs of electrons on central atom? SF\(_6\), BF\(_3\), ClF\(_3\), PCl\(_5\), BrF\(_5\), XeF\(_4\), H\(_2\)O, SF\(_4\)
The pair of molecules / ions with the same bond order value is
Consider the following A) 0.0025 B) 500.0 C) 2.0034 Number of significant figures in A, B and C respectively, are
Consider the following reaction A(g) + 3B(g) \( \longrightarrow \) 2C(g); \( \Delta H^\ominus = -24 \) kJ. At \(25 \, ^\circ\text{C}\) if \( \Delta G^\ominus \) of the reaction is -9 kJ, the standard entropy change (in JK\(^{-1}\)) of the same reaction at same temperature is
The ratio of the wavelengths of the first Lyman line and the second Balmer line of hydrogen atom is
Each nuclear fission of \( {}^{235}\text{U} \) releases 200 MeV of energy. If a reactor generates 1 MW power, then the rate of fission in the reactor is
When three NAND logic gates are connected as shown in the figure, then the logic gate equivalent to the circuit is
three NAND logic gates are connected
In a wire of radius 1 mm, a steady current of 2 A uniformly distributed across the cross-section of the wire is flowing. Then the magnetic field at a point 0.25 mm from the centre of the wire is
The magnetic field at the centre of a current carrying circular coil of radius R is \( B_C \) and the magnetic field at a point on its axis at a distance R from its centre is \( B_A \). The value of \( \frac{B_C}{B_A} \) is
A short bar magnet of magnetic moment \( 10^4 \, \text{J T}^{-1} \) is free to rotate in a horizontal plane. The work done in rotating the magnet slowly from the direction parallel to a horizontal magnetic field of \( 4 \times 10^{-5} \, \text{T} \) to a direction \( 60^\circ \) to the direction of the field is
A resistor of \(450 \, \Omega\) and an inductor are connected in series to an ac source of frequency \( \frac{75}{\pi} \, \text{Hz} \). If the power factor of the circuit is 0.6, then the inductance connected in the circuit is