List of practice Questions

Let
$f(x) = 2x^2 - x - 1\ and\ S = \{ n \in \mathbb{Z} : |f(n)| \leq 800 \}$
Then, the value of ∑_n∈S f(n) is equal to ________.

If momentum of a body is increased by 20%, then its kinetic energy increases by

If the system of equations
$ x + y + z = 6 $,
$ 2x + 5y + \alpha z = \beta $,
$ x + 2y + 3z = 14 $
has infinitely many solutions, then $ \alpha + \beta $ is equal to:

For the curve
$\begin{array}{l}C : \left(x^2 + y^2 – 3\right) + \left(x^2 – y^2 – 1\right)^5 = 0, \end{array}$

$\begin{array}{l}\text{the value of}\ 3y’ – y^3y”, \text{at the point}\end{array}$

$(α, α), α > 0$, on C is equal to ________.

In following pairs, the one in which both transition metal ions are colourless is :

Two electric dipoles of dipole moments 1.2 × 10^–30 C-m and 2.4 × 10^–30 C-m are placed in two different uniform electric fields of strength 5 × 10⁴ NC^–1 and 15 × 10⁴NC^–1 respectively. The ratio of maximum torque experienced by the electric dipoles will be 1:x. The value of x is _______

For a cell, $Cu(s)|Cu^{2+}(0.001M)||Ag^+(0.01M)|Ag(s)$
the cell potential is found to be $0.43 V$ at $298 K$. The magnitude of standard electrode potential for $Cu^{2+}/{Cu}$ is ____ $× 10^{–2}$ V.
[Given: $E_{Ag^+/Ag^⊖}=0.80$ V and $\frac {2.303RT}{F}=0.06 V$]

Let
$\begin{array}{l}f\left(x\right) = min \{\left[x – 1\right], \left[x – 2\right], …., \left[x – 10\right]\}\end{array}$
where [t] denotes the greatest integer ≤t. Then
$\begin{array}{l} \displaystyle\int\limits_{0}^{10}f\left(x\right)dx+\displaystyle\int\limits_{0}^{10}\left(f\left(x\right)\right)^2dx+\displaystyle\int\limits_{0}^{10}\left|f\left(x\right)\right|dx\end{array}$
is equal to ________.

Let S be the set containing all 3 × 3 matrices with entries from {-1, 0, 1}. The total number of matrices A ∈ S such that the sum of all the diagonal elements of A^TA is 6 is ________.

The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density 1750 kg m^–3at the rate of 0.35 cms^–1. The coefficient of viscosity of the solution is _______ poise (in nearest integer). (The density of air is negligible).

The torque of a force $5\^{i}+3\^{j}−7\^{k}$ about the origin is τ. If the force acts on a particle whose position vector is$ 2\^{i}+2\^{j}+\^{k}$, then the value of τ will be

If the length of the latus rectum of the ellipse x² + 4y² + 2x + 8y – λ = 0 is 4, and l is the length of its major axis, then λ + l is equal to ________.

A block of mass ‘m’ (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when its speed is halved. The value of spring constant of used spring will be nE Nm^–1 for n = _______.

Which of the following matrices can NOT be obtained from the matrix $\begin{bmatrix} -1 &2 \\ 1 & -1 \end{bmatrix}$ by a single elementary row operation?

$\begin{array}{l}(p \land r )\Leftrightarrow ( p \land (\sim q))\end{array}$is equivalent to (~ p) when r is

The number of stereoisomers formed in a reaction of (±) Ph (C = O) C (OH) (CN) Ph with HCN is_____.
[Where, Ph is – C₆H₅]

Sum of oxidation state (magnitude) and coordination number of cobalt in $Na[Co(bpy)Cl_4]$ is____ .
(Given : bpy =

)

Consider the above reaction sequence, the product ‘C’ is

The number of chlorine atoms in bithionol is ______ .

If $\lim_{{x \to 0}} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}$, where $\alpha, \beta, \gamma \in \mathbb{R}$ then which of the following is NOT correct?

Let the function
$f(x)$=$\begin{cases} \frac{\log_e(1+5x) - \log_e(1+\alpha x)}{x}, & \text{if } x ∈ 0 \\ \space 10 & \text;{if } x = 0 \\ \end{cases}$
be continuous at x = 0. Then α is equal to

A compound ‘X’ is acidic and it is soluble in NaOH solution, but insoluble in NaHCO₃ solution. Compound ‘X’ also gives violet colour with neutral FeCl₃ solution. The compound ‘X’ is :

Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1, 1). If the line AP intersects the line BC at the point Q(k₁, k₂), then k₁ + k₂ is equal to :

Let a line L pass through the point intersection of the lines $bx + 10y – 8 = 0$ and $2x - 3y = 0, \quad b \in \mathbb{R} - \left\{\frac{4}{3}\right\}$. If the line L also passes through the point $(1, 1)$ and touches the circle $17(x^2 + y^2) = 16$, then the eccentricity of the ellipse $\frac{x^2}{5} + \frac{y^2}{5} = 1$ is

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes 5√x s. The value of x will be _____.