List of practice Questions

Two circles having radius $r_1$ and $r_2$ touch both the coordinate axes. Line $x+y=2$ makes intercept 2 on both the circles. The value of $r_{1}^{2} + r_{2}^{2} - r_{1}r_{2}$ is:

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is

Assertion A: If $ dQ $ and $ dW $ represent the heat supplied to the system and the work done on the system respectively, then according to the first law of thermodynamics: \[ dQ = dU - dW. \]
Reason R: First law of thermodynamics is based on the law of conservation of energy.
In the light of the above statements, choose the correct answer from the options given below:

The current flowing through a conductor connected across a source is 2A and 1.2 A at 0°C and 100°C respectively. The current flowing through the conductor at 50°C will be ______x10² mA.

Which one amongst the following are good oxidizing agents?
(A) $ \text{Sm}^{\text{2+}}$
(B) $\text{Ce}^{\text{2+}}$
(C)$ \text{Ce}^{\text{4+}}$
(D) $\text{Tb}^{\text{4+}}$
Choose the most appropriate answer from the options given below:

1 L, 0.02 M solution of [Co(NH₃)₅SO₄]Br is mixed with 1 L, 0.02 M solution of [Co(NH₃)₅Br]SO₄. The resulting solution is divided into two equal parts (X) and treated with excess of AgNO₃ solution and BaCl₂ solution respectively as shown below:
1 L Solution (X) + AgNO₃ solution (excess) → Y
1 L Solution (X) + BaCl₂ solution (excess) → Z
The number of moles of Y and Z respectively are

The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

Let $S_1$ and $S_2$ be respectively the sets of all $a \in R -\{0\}$ for which the system of linear equations $ a x+2 a y-3 a z=1$ $ (2 a+1) x+(2 a+3) y+(a+1) z=2$ $(3 a+5) x+(a+5) y+(a+2) z=3$ has unique solution and infinitely many solutions Then

Let $x=2$ be a local minima of the function $f(x)=2 x^4-18 x^2+8 x+12$, $x \in(-4,4)$ If $M$ is local maximum value of the function $f$ in $(-4,4)$, then $M =$

Some amount of dichloromethane $\left( CH _2 Cl _2\right)$ is added to $671.141 \,mL$ of chloroform $\left( CHCl _3\right)$ to prepare $2.6 \times 10^{-3} M$ solution of $CH _2 Cl _2$ (DCM) The concentration of DCM is ______$ppm$ (by mass) Given: atomic mass : $C =12$ $H =1$ $Cl =35.5$ density of $CHCl _3=1.49\, g \,cm ^{-3}$

A parallel plate capacitor with air between the plate has a capacitance of $15\, pF$ The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant $3.5$. Then the capacitance becomes $\frac{x}{4} pF$ The value of $x$ is _______

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$, be in AP and $a_1+a_3=10$ If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to :

Which of the following conformations will be the most stable?

For two different photosensitive materials having work function and 2 respectively, are illuminated with light of sufficient energy to emit electrons. If the graph of stopping potential versus frequency is drawn, for these two different photosensitive materials the ratio of slope of graph for these two materials is

How many statements are correct:

If there is no relation between rate constant and temperature, then activation energy is negative.
If the activation energy is zero, rate constant is temperature independent.
If rate constant increases with increase of temperature, activation energy is positive.
If rate constant decreases with increase in temperature, activation energy is negative.

An electron is moving along positive x direction in xy plane, magnetic field points in negative z direction, then the force due to magnetic field on electron points in the direction

If de-Broglie wavelength is $\lambda$ when energy is E. Find the wavelength at $\frac{E}{4}$ (Kinetic Energy).

$y=f(x)$ is a quadratic function passing through (–1, 0) and tangent to it at (1, 1) is $y=x$. Find x intercept by normal at point (𝛂, 𝛂 + 1), (𝛂 > 0)

$20 \,mL$ of $01 \,M \,NH _4 OH$ is mixed with $40\, mL$ of $005\, M \,HCl$ The $pH$ of the mixture is nearest to: (Given: $K _{ b }\left( NH _4 OH \right)=1 \times 10^{-5}, \log 2=030$, $\log 3=048, \log 5=069, \log 7=084$, $\log 11=104$ )

Let 𝐾 be the sum of the coefficients of the odd powers of 𝑥 in the expansion of $(1+𝑥)^{99}$. Let 𝑎 be the middle term in the expansion of $(2+\frac{1}{\sqrt 2} )^{200}$. If $\frac{⁡^{200}𝐶_{99} 𝐾}{𝑎} =\frac{2^𝑙 𝑚}{𝑛} $, where 𝑚 and 𝑛 are odd numbers, then the ordered pair (𝑙, 𝑛) is equal to

600 mL of 0.04 M HCl is mixed with 400 mL of 0.02 M H₂SO₄. Find out the pH of resulting solution (Nearest integer).

4.5 moles each of hydrogen and iodine is heated in a sealed ten litre vessel. At equilibrium, 3 moles of HI were found. The equilibrium constant for H₂(g) + I₂(g) ⇋ 2HI(g) is _____________ .

During the reaction of permanganate with thiosulphate, the change in oxidation of manganese occurs by value of 3. Identify which of the below medium will favour the reaction

Let the quadratic curve passing through the point $ (-1, 0) $ and touching the line $ y = x $ at $ (1, 1) $ be $ y = f(x) $. Then the x-intercept of the normal to the curve at the point $ (\alpha, \alpha + 1) $ in the first quadrant is:

Let the line $L: \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$ intersect the plane $2 x+y+3 z=16$ at the point $P$ Let the point $Q$ be the foot of perpendicular from the point $R(1,-1,-3)$ on the line $L$ If $\alpha$ is the area of triangle $P Q R$, then $\alpha^2$ is equal to