List of practice Questions

If the system of equations $kx + y + 2z = 1$, $3x - y - 2z = 2$, $-2x - 2y - 4z = 3$ has infinitely many solutions, then k is equal to ________
Let A₁, A₂, A₃, … be squares such that for each n ≥ 1, the length of the side of $A_n$ equals the length of diagonal of $A_{n+1}$. If the length of $A_1$ is 12 cm, then the smallest value of n for which area of $A_n$ is less than one, is __________.
The number of points, at which the function f(x) = |2x + 1| - 3|x + 2| + |x² + x - 2|, x ∈ ℝ is not differentiable, is ________
The equation of the line through the point (0, 1, 2) and perpendicular to the line (x-1)/2 = (y+1)/3 = (z-1)/(-2) is:
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 $K_a(\text{HCN}) = 6.2 \times 10^{-10}$]