List of practice Questions

Let $a, b, c>, a^3, b^3$ and $c^3$ be in AP, and $\log _a b, \log _c a$ and $\log _b c$ be in GP If the sum of first 20 terms of an AP, whose first term is $\frac{a+4 b+c}{3}$ and the common difference is $\frac{a-8 b+c}{10}$ is $-444$, then $a b c$ is equal to:

The number of ways of selecting two numbers $a$ and $b, a \in\{2,4,6, \ldots , 100\}$ and $b \in\{1,3,5, \ldots , 99\}$ such that 2 is the remainder when $a+b$ is divided by 23 is

For $\alpha, \beta \in R$, suppose the system of linear equations $ x-y+z=5 $ $2 x+2 y+\alpha z=8 $ $3 x-y+4 z=\beta$ has infinitely many solutions Then $\alpha$ and $\beta$ are the roots of

The solution of the differential equation $\frac{d y}{d x}=-\left(\frac{x^2+3 y^2}{3 x^2+y^2}\right), y(1)=0$ is

If a plane passes through the points $(-1, k, 0),(2, k,-1),(1,1,2)$ and is parallel to the line $\frac{x-1}{1}=\frac{2 y+1}{2}=\frac{z+1}{-1}$, then the value of $\frac{k^2+1}{(k-1)(k-2)}$ is

The output from a NAND gate having inputs A and B given below will be.

The rms speed of oxygen molecule in a vessel at particular temperature is \((1+\frac{5}{x})^{\frac{1}{2}} v\), where \(v\) is the average speed of the molecule. The value of x will be : (Take \(π = \frac{22}{7}\))

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at A is 1.5 cm², and B is is 25 mm², if the speed of liquid at B is 60 cm/s then \((P_A-P_B)\) is: 
(Given \(P_A\) and \(P_B\) are liquid pressures at A and B points.
density \(ρ = 1000 \space kg \space m^{-3}\)
A and B are on the axis of tube)

A planet having mass \(9M_e\) and radius \(4R_e\), where \(M_e\) and \(R_e\) are mass and radius of earth respectively, has escape velocity in km/s given by: (Given escape velocity on earth \(V_e= 11.2 × 10^3 m/s\))

A bullet of 10 g leaves the barrel of gun with a velocity of 600 m/s. If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be :

$KMnO _4$ oxidises $I ^{-}$in acidic and neutral/faintly alkaline solution, respectively, to

Given below are two statements:
Statement I : During Electrolytic refining, the pure metal is made to act as anode and its impure metallic form is used as cathode
Statement II : During the Hall-Heroult electrolysis process, purified $Al _2 O _3$ is mixed with $Na _3 AlF _6$ to lower the melting point of the mixture
In the light of the above statements, choose the most appropriate answer from the options given below:

Maximum number of electrons that can be accommodated in shell with $n=4$ are:

Given below are two statements:
Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. 
Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.
In the light of above statements, choose the correct answer from the options given below :

3 boys and 5 girls can complete one work in 8 days. 7 boys can complete the work in 4 days. Number of girls required to finish the work in half day is:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason $R$ 
Assertion A : Antihistamines do not affect the secretion of acid in stomach 
Reason R : Antiallergic and antacid drugs work on different receptors 
In the light of the above statements, choose the correct answer from the options given below:

Match List I with List II:

List I (Mixture)		List II (Separation Technique)
A	CHCl3​+C6​H5​NH2​	i	Steam distillation
B	C6​H14​+C5​H12​	ii	Differential extraction
C	C6​H5​NH2​+H2​O	iii	Distillation
D	Organic compound in H2​O	iv	Fractional distillation

The orbital angular momentum of an electron in 3s orbital is  \(\frac{xh}{2π}\) The value of x is___.

Chlorides of which metal are soluble in organic solvents:

Two trains 'A' and 'B' of length \('l'\) and \('4l'\) are travelling into a tunnel of length 'L' in parallel tracks from opposite directions with velocities 108 km/h and 72 km/h, respectively. If train 'A' takes 35s less time than train 'B' to cross the tunnel then. length 'L' of tunnel is:
(Given L = 60 \(l\))

0.400 g of an organic compound (X) gave 0.376 g of AgBr in Carius method for estimation of bromine. % of bromine in the compound (X) is____
(Given: Molar mass AgBr=188g mol^-1)

1g of a carbonate (M₂CO₃) on treatment with excess HCl produces 0.01 mol of CO₂ .The molar mass of M₂CO₃ is g mol^-1. (Nearest integer)

Bond dissociation energy of "E-H" bond of the " $H _2 E$ " hydrides of group $16$ elements (given below), follows order.
A. $O$ B. $S$ C. $Se$ D. $Te$
Choose the correct from the options given below:

The most stable carbocation for the following is:

A stone tied to $180 \,cm$ long string at its end is making $28$ revolutions in horizontal circle in every minute The magnitude of acceleration of stone is $\frac{1936}{x} m s^{-2}$ The value of $x$ _____ ( Take $\pi=\frac{22}{7}$ )