List of practice Questions

All possible values of θ ∈ [0, 2π] for which sin 2θ + tan 2θ>0 lie in :
The total number of positive integral solutions (x, y, z) such that xyz=24 is :
Angle of depression from tower top to A is 30°. After 20 seconds at B, it is 45°. Time taken from B to reach the base is :
Let α be the angle between the lines whose direction cosines satisfy the equations l + m - n = 0 and l² + m² - n² = 0. Then the value of sin⁴α + cos⁴α is :
The integer k, for which the inequality x² - 2(3k-1)x + 8k² - 7>0 is valid for every x in ℝ, is :
If Rolle's theorem holds for the function f(x) = x³ - ax² + bx - 4, x ∈ [1, 2] with f'(4/3) = 0, then ordered pair (a, b) is equal to :
The value of the integral ∫ sinθ sin2θ (sin⁶θ + sin⁴θ + sin²θ) / √(2sin⁴θ + 3sin²θ + 6) dθ is: (where c is a constant of integration)
Among the following, the number of halide(s) which is/are inert to hydrolysis is ___________: (A) BF$_3$, (B) SiCl$_4$, (C) PCl$_5$, (D) SF$_6$
Which statement is correct ?
0.4 g mixture of NaOH, Na$_2$CO$_3$ and some inert impurities was first titrated with N/10 HCl using phenolphthalein as an indicator, 17.5 mL of HCl was required at the end point. After this methyl orange was added and titrated. 1.5 mL of same HCl was required for the next end point. The weight percentage of Na$_2$CO$_3$ in the mixture is _________
A car tyre is filled with nitrogen gas at 35 psi at 27$^\circ$C. It will burst if pressure exceeds 40 psi. The temperature in $^\circ$C at which the car tyre will burst is ___________
The major product of the following chemical reaction is : R-CN $\xrightarrow{(1) H_3O^+, \Delta (2) SOCl_2 (3) Pd/BaSO_4, H_2}$ ? (Using $R$ as the alkyl group from the prompt skeleton)
Given below are two statements : Statement I : An allotrope of oxygen is an important intermediate in the formation of reducing smog. Statement II : Gases such as oxides of nitrogen and sulphur present in troposphere contribute to the formation of photochemical smog. In the light of the above statements, choose the correct answer from the options given below :
Complete combustion of 1.80 g of an oxygen containing compound (C$_x$H$_y$O$_z$) gave 2.64 g of CO$_2$ and 1.08 g of H$_2$O. The percentage of oxygen in the organic compound is :
In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption $(x/m)$ is directly proportional to $P^x$. The value of x is :
Ellingham diagram is a graphical representation of :
Which of the following equation depicts the oxidizing nature of $H_2O_2$?
The correct statement about B$_2$H$_6$ is :
Given below are two statements : Statement I : CeO$_2$ can be used for oxidation of aldehydes and ketones. Statement II : Aqueous solution of EuSO$_4$ is a strong reducing agent. In the light of the above statements, choose the correct answer :
In which of the following pairs, the outer most electronic configuration will be the same ?
The solubility of AgCN in a buffer solution of pH=3 is x. The value of x is : [Assume : No cyano complex is formed ; $K_{sp}(\text{AgCN}) = 2.2 \times 10^{-16}$ and $K_a(\text{HCN}) = 6.2 \times 10^{-10}$]
A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R= gas constant) is $\frac{x}{3R}$. Value of x is ________.
A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ________ m/s. (Take g=10 m/s²)
An engine of a train, moving with uniform acceleration, passes the signal-post with velocity $u$ and the last compartment with velocity $v$. The velocity with which middle point of the train passes the signal post is :
Two radioactive substances X and Y originally have $N_1$ and $N_2$ nuclei respectively. Half life of X is half of the half life of Y. After three half lives of Y, number of nuclei of both are equal. The ratio $N_1/N_2$ will be equal to :