List of practice Questions

Let $r$ be a root of the equation $x^2 + 2x + 6 = 0$. Then the value of the expression $(r+2)(r+3)(r+4)(r+5)$ is

Given below are four statements.
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.

A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.
\[ \boxed{A} \qquad \boxed{D} \] From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome? The player should use all the five plates exactly once. The plates can be rotated in their plane.

Some people believe that “what gets measured, improves”. Some others believe that “what gets measured, gets gamed”. One possible reason for the difference in the beliefs is the work culture in organizations. In organizations with good work culture, metrics help improve outcomes. However, the same metrics are counterproductive in organizations with poor work culture. Which one of the following is the CORRECT logical inference based on the information in the above passage?

In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates and they accounted for 60% of the qualified candidates.
Which one of the following is the correct logical inference based on the information provided in the above passage?

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball. First ball is drawn. What is the probability of getting an orange ball in the next draw?

The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T, and U, but not necessarily in the same order. Consider the following statements:


The line joining P and R is parallel to the line joining Q and S.
P is placed on the side opposite to the corner T.
S and U cannot be placed on the same side.
Which one of the following statements is correct based on the above information?

A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, R1 and R2, are already present and cannot be moved.
What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.

The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute $10$ minutes later, the rate becomes $2250 $ disintegrations per minute The approximate decay constant is : (Take $\log _{10} 188=0274$ )

Which of the following figure represents the variation of \(ln (\frac{R}{R_0})\) with \(ln\  A\)?
(if \(R\) = radius of a nucleus and \(A\) = its mass number)

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is
(Take log₁₀1.88 = 0.274)

A nucleus of mass M at rest splits into two parts having masses \(\frac{M′}{3}\) and \(\frac{2M′}{3}(M′<M).\)

A radioactive sample decays 7/8 times its original quantity in 15 minutes. The half-life of the sample is

Mass numbers of two nuclei are in the ratio of \(4 : 3\). Their nuclear densities will be in the ratio of

Two lighter nuclei combine to from a comparatively heavier nucleus by the relation given below: \(^2_1X+^2_1X=^4_2Y\). The binding energies per nucleon for, \(^2_1X\) and \(^4_2Y\) are 1.1 MeV and 7.6 MeV respectively. The energy released in the process is ______ MeV.

Two capacitors, each having capacitance $40 \mu F$ are connected in series The space between one of the capacitors is filled with dielectric material of dielectric constant $K$ such that the equivalence capacitance of the system became $24 \mu F$ The value of $K$ will be :

A wire of resistance $R_1$ is drawn out so that its length is increased by twice of its original length The ratio of new resistance to original resistance is:

In a series LR circuit $X_L=R$ and power factor of the circuit is $P _1$ When capacitor with capacitance $C$ such that $X _{ L }= X _{ C }$ is put in series, the power factor becomes $P _2$ The ratio $\frac{ P _1}{ P _2}$ is

The total charge on the system of capacitance $C _1=1\, \mu F , C _2=2 \,\mu F , C _3=4 \,\mu F $ and $C _4=3\, \mu F$ connected in parallel is (Assume a battery of $20 \,V$ is connected to the combination)

A condenser of 2μF capacitance is charged steadily from 0 to 5 C.Which of the following graph represents correctly the variation of potential difference (V) across it’s plates with respect to the charge (Q) on the condenser?

The total charge on the system of capacitors C₁ = 1 μF, C₂ = 2 μF, C₃ = 4 μF and C₄ = 3 μF, connected in parallel is :
(Assume a battery of 20 V is connected to the combination)

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness (t₁ and t₂) as shown in figure. The two different dielectric materials are separated by a conducting foil F. The voltage of the conducting foil is _____V.

A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness (3/4)d, where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be: 

(Given \(C_0\) = capacitance of capacitor with air as medium between plates.)

A capacitor of capacitance \(50pF\) is charged by \(100 V\) source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is _____ nJ.