List of practice Questions

A = {1, 2, 3, 4} minimum number of elements added to make an equivalence relation on set A containing (1, 3) & (1, 2) in it.

Area bounded by \(0 ≤ y ≤ \text {min}(x^2+ 2, 2x + 2)\), \(x∈[0, 3]\), then \(12A\) is

The value of \(∫_{\frac \pi6}^{\frac \pi3}\sqrt {1-sin2x\ dx}\) is

IUPAC Name of the compound is

Find the total number of sigma and pi bonds in 2-formyl hex-4-enoic acid.

Match the following: 

	LIST I		LIST II
A	Lyman	I	Near IR
B	Balmer	II	Far IR
C	Paschen	III	Visible
D	p-fund	IV	UV

The major product in the above reaction is

How many of the following compounds have zero dipole moment ?
\(NH_3, H_2O, HF, CO_2, SO_2, BF_3, CH_4\)

Which of the following elements has the highest 1st ionization energy ?

Distance between twice-magnified virtual image of an object placed in front of mirror is 15 cm. Find focal length of spherical mirror in cm.

A particle connected with light thread is performing vertical circular motion. Speed at point B (Lowermost point) is sufficient, so that it is able to complete its circular motion. Ignoring air friction, find the ratio of kinetic energy at A to that at B. (A being top-most point)

Alternating voltage and current in circuit is given as \(V = (100 \;sin \;ωt)\) volt 
\(I = 100\;sin\bigg(ωt+\frac{π}{3}\bigg)mA\)
Find average power dissipated in circuit.

The intensity at each slit is equal for a YDSE and it is maximum \(I_{max}\) at \(7π\) central maxima. If I is intensity for phase difference \(\frac{7π}{2}\) between two waves on screen. Then \(\frac{I}{I_{max}}\) is?

The truth table for the combination of logical gates

A planet at distance r from the sun takes 200 days to complete one revolution around the sun. What will be the time period for a planet at distance \(\frac{r}{4}\) from the sun?

Let \(a_1,a_2,a_3\), ..., an, be in A. P. and \(S_n\) denotes the sum of first \(n\) terms of this A. P. is \(S_{10}\) =\(390, \frac{a_{10}}{a_{50}} =\frac{15}{7}\), then \(S_{15} -S_5 =\) _________.

The ratio of magnitude of potential energy and kinetic energy for \(5^{th}\) excited state of hydrogen atom is

The value of integrate \(∫^1_0 (2x^3 - 3x^2 - x + 1)^\frac{1}{3}dx\) is :

Let the system of equations \(x+2y+3z = 5\), \(2x+3y+z = 9\), \(4x+3y+λz = μ\) have an infinite number of solutions. Then \(λ + 2μ\) is equal to

If the domain of the function \(f(x)\) = \(\frac{\sqrt{x^2-25}}{(4-x^2)}+ \log(x^2+2x-15)\) is \((-∞, α) ∪ (β, ∞)\), then \(α^2+β^2\) is equal to \(b\)

The number of solution of the equation \(4sin^2 x-4cos^3 x+9-4cos x = 0\), \(x ∈ [-2\pi, 2\pi]\)

If the mirror image of the point \(P(3,4,9)\) in the Line 
\(\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}\) is \((α,β,γ)\) then find \(14(a+ẞ+y)\) is:

Let \(α\) and \(β\) the roots of equation \(px^2 + qx - r = 0\), where \(P≠ 0\). If \(p,q,r\) be the consecutive term of non constant G.P and \(\frac{1}{α} + \frac{1}{β} = \frac{3}{4}\) then the value of \((α - β)^2\) is:

Let m and n be the coefficient of \(7^{th}\) and \(13^{th}\) term in expansion of \(\bigg(\frac{1}{3x^{\frac{1}{3}}} +\frac{1}{2x^{\frac{2}{5}}}\bigg)^{18}\), then \(\bigg(\frac{m}{n}\bigg)^{\frac{1}{3}}\) is: