List of practice Questions

A message signal of frequency $5 \,kHz$ is used to modulate a carrier signal of frequency $2\, MHz$ The bandwidth for amplitude modulation is:

In chromyl chloride, the number of d-electrons present on chromium is same as in (Given at no. of Ti : 22, V : 23, Cr : 24, Mn : 25, Fe : 26)

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $x$ times its initial resonant frequency $\omega_0$ The value of $x$ is:

The root mean square velocity of molecules of gas is

A parallel plate capacitor has plate area $40\, cm ^2$ and plates separation $2\, mm$ The space between the plates is filled with a dielectric medium of a thickness $1 \,mm$ and dielectric constant $5$ The capacitance of the system is :

Let s₁, s₂, s₃,…..,s₁₀ respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1,2,3, …. ,10 and the common differences are 1, 3, 5, …. , 19 respectively. Then  \(10∑^{10}_{i=1} s_i\) is

Match List-I with List-II :

	List-I		List-II
A	Saccharin	I	High potency sweetener
B	Aspartame	II	First artificial sweetening agent
C	Alitame	III	Stable at cooking temperature
D	Sucralose	IV	Unstable at cooking temperature

Choose the correct answer from the options given below :

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth It is found that when a particle is released in this tunnel, it executes a simple harmonic motion The mass of the particle is $100 \,g$ The time period of the motion of the particle will be (approximately)(Take $g=10 \, m s ^{-2}$, radius of earth $=6400 \,km$ )

$T$ is the time period of simple pendulum on the earth's surface Its time period becomes $x T$ when taken to a height $R$ (equal to earth's radius) above the earth's surface Then, the value of $x$ will be:

A Carnot engine with efficiency $50 \%$ takes heat from a source at $600 \,K$ In order to increase the efficiency to $70 \%$, keeping the temperature of sink same, the new temperature of the source will be :

For the system of linear equations  
2x+4y+2az=b
x+2y+3z=4 
2x-5y+2z=8 
which of the following is NOT correct ?  

An object of mass $8 kg$ is hanging from one end of a uniform rod CD of mass $2 kg$ and length $1 m$ pivoted at its end $C$ on a vertical wall as shown in figure It is supported by a cable $AB$ such that the system is in equilibrium The tension in the cable is : (Take $g =10 m / s ^2$ )

"Konark Samman" is given for the significant contribution in the field of

The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.  
Assertion A: Butan -1- ol has higher boiling point than ethoxyethane.  
Reason R: Extensive hydrogen bonding leads to stronger association of molecules.  
In the light of the above statements, choose the correct answer from the options given below: 

The major product formed in the following reaction is

20 mL of calcium hydroxide was consumed when it was reacted with 10 mL of unknown solution of H₂SO4. Also 20 mL standard solution of 0.5 M HCI containing 2 drops of phenolphthalein was titrated with calcium hydroxide the mixture showed pink colour when burette displayed the value of 35.5 mL whereas the burette showed 25.5 mL initially. The concentration of H₂SO₄ is_____M (Nearest integer)

Choose the halogen which is most reactive towards SN1 reaction in the given compounds (A, B, C & D)

The correct order of spin only magnetic moments for the following complex ions is

An organic compound on combustion gives 0.22 g of CO₂ and 0.126 g of H₂O. If the percentage of C in given organic compound is 40%, the percentage of H will be?

Let \(α=8−14𝑖\), \(𝐴=\{z∈C:\frac {αz−\bar α\bar z}{z^2−(\bar z)^2−112i }=1\}\) and \(𝐵={𝑧∈C:|𝑧+3𝑖|=4}\). Then \(∑_{𝑧∈𝐴∩𝐵 }(\text {𝑅𝑒}\ ⁡𝑧−\text {𝐼𝑚⁡}\ 𝑧)\) is equal to _____ .

Let \(𝑋={11,12,13,…,40,41}\) and \(𝑌={61,62,63,…,90,91}\) be the two sets of observations. If \(\bar 𝑥\) and \(\bar 𝑦\) are their respective means and \(σ^2\) is the variance of all the observations in \(𝑋∪𝑌\), then \(|\bar 𝑥+\bar 𝑦−σ^2|\) is equal to ____ .

Let \({a_k}\) and \({b_k}\), \(𝑘∈N\), be two G.P.s with common ratios \(r_1\) and \(r_2\) respectively such that \(a_1= b_1=4\) and \(r_1<r_2\). Let \(c_k=a_k+b_k\), \(k∈N\). If \(c_2=5\) and \(c_3=\frac {13}{4}\), then \( \displaystyle\sum_{k=1}^{∞ }c_k−(12a_6+8b_4)\) is equal to _____ .