List of practice Questions

For all real values of \(a_0, a_1, a_2, a_3\) satisfying \(a_{0}+\frac{a_{1}}{2}+\frac{a_{2}}{3}+\frac{a_{3}}{4}=0\), the equation \(a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}=0\) has a real root in the interval

If the four points with position vectors $-2\hat{i}+\hat{j}+k, \hat{i} +\hat{j}+\hat{k}, \hat{j}-\hat{k}, $ and $\lambda\hat{j}+\hat{k}$ are coplanar, then $\lambda=$

The minimum value of $\cos\,\theta + \sin\,\theta+\frac{2}{\sin\,2\theta}$ for $\theta\,\in \left(0, \pi/2\right)$ is

A fair coin is tossed a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is

The area of the region bounded by the curve $y = x^3$, its tangent at $(1, 1)$ and $x-axis$ is

Consider the following salts: $NaCl,\, HgCl_2,\, Hg_2Cl_2,\, CuCl_2,\, CuCl$ and $AgCl$. Identify the correct set of insoluble salts in water

In a mixture, two enantiomers are found to be present in $85\%$ and $15\%$ respectively. The enantiomeric excess $(e, e)$ is

An n-type semiconductor is

In benzene, the triple bond consists of

An electron of mass $9.0 \times 10^{-31} kg$ under the action of a magnetic field moves in a circle of radius $2\, cm$ at a speed of $3 \times 10^6 \, m/s$ . If a proton of mass $1.8 \times 10^{27} \, kg$ was to move in a circle of same radius in the same magnetic field, then its speed will become

If the ionisation energy and electron affinity of an element are $275$ and $86 \,kcal\, mol^{-1}$ respectively, then the electronegativity of the element on the Mulliken scale is

Caffeine has a molecular weight of $194\, u$. If it contains $28.9\%$ by mass of nitrogen, number of atom of nitrogen in one molecule of caffeine is

A current of $2\,A$ is flowing in the sides of an equilateral triangle of side $9\, cm$. The magnetic field at the centroid of the triangle is

A galvanometer with a scale divided into $100$ equal divisions has a current sensitivity of $10$ divisions per milliampere and a voltage sensitivity of $2$ divisions per millivolt. The galvanometer resistance will be

A simple pendulum of length $L$ swings in a vertical plane. The tension of the string when it makes an angle $\theta$ with the vertical and the bob of mass m moves with a speed $v$ is ($g$ is the gravitational acceleration

If $\sin^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\frac{x^{4}}{8}+...\right)-\frac{\pi}{6}$ where $\left|x\right| < 2$ then the value of $x$ is

Match each disease with its correct type of vaccine.

Which of the following diseases is caused by a protozoan?

If $f \left(x\right)=\begin{vmatrix}1&x&x+1\\ 2x&x\left(x-1\right)&\left(x-1\right)x\\ 3x\left(x-1\right)&x\left(x-1\right)\left(x-2\right)&\left(x-1\right)\end{vmatrix}$ Then $f (100)$ is equal to

$X Cl _{2}( excess )+Y Cl _{2} X Cl _{4}+Y \downarrow$ $Y O {->[{\Delta}][{>400^{\circ} C }]} \frac{1}{2} O _{2}+Y$ Ore of Y would be ,

With excess of water, both $P_{2}O_{5}$ and $PCl_{5}$ give

Which one of the following is a case of negative adsorption?

Which of the following reactions is used to prepare isobutane ?

Two points masses, $m$ each carrying charges $-q$ and $+q$ are attached to the ends of a mass less rigid non-conducting wire of length $'L'$. When this arrangement is placed in a uniform electric field, then it deflects through an angle $i$. The minimum time needed by rod to align itself along the field is

Two sources of equal emf are connected to a resistance $R$. The internal resistance of these sources are $r_1$ and $r_2 (r_1 > r_2 )$. If the potential difference across the source having internal resistance $r_2$ is zero, then