List of practice Questions

\(∫^{\frac{π}{3}} _0\) \(cos^4x\) \(dx\) is equal to a \(\pi + b\sqrt3\), then \(a^2 + b\) is equal to:
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:
The minimum value of \(| z+ \frac{3+4i}{2}|, |z| \leq 1\) is,
Let vertex \(A(2, 3, 1), B(3, 2, -1), C(-2, 1, 3)\). If \(AD\) is angle bisector of angle \(A\), then projection of \(\overrightarrow{AD}\) on \(\overrightarrow{AC}\) is equal to:
Find out charge (in C) required for electrolysis of \(1\) mole of \(H_2O\) to produce \(O_2\) on one of the electrodes. \((F = 96500 \;C)\)
Ethylene glycol of \(x\) \(kg\) is mixed with \(18.6\) \(kg\) of solvent, \(24 °C\) depression in freezing point takes place. Calculate value of \(x\). (Given: \(K_1\) = \(1.6 °C/molal\) M.W. of ethylene glycol = \(62\) \(g/mol\))
Consider the following two statements 
Statement I: In \(p\) and \(d\) block both metals and non - metals are present 
Statement II: Electronegativity and ionisation enthalpy of metals is greater than non - metals
Consider the following two statements Statement I: \(SiO_2\) and GeO₂\(GeO_2\) are acidic, \(SnO\) and \(PbO\) are amphoteric Statement II: Allotropes of carbon are formed due to catenation and \(dπ - ρπ\) bond
Consider the following two statements Statement I: \(π\) \(2p\) bonding molecular orbital has low electron density above & below internuclear axis Statement II: \(π\times2p\) antibonding molecular orbital has only one nodal plane
Which is following compound is easily attacked by electrophile?
Complementary stand of DNA ATGCTTCA is:
Which of the following is correct for adiabatic free expansion against vacuum?
We are given with three NaCl samples and their Van't Hoff factors. Which is correct option ?
SampleVan't Haff Factor 
Sample - 1 (0.1 M)\(i_1\)
Sample - 2 (0.01 M)\(i_2\)
Sample - 3 (0.001 M)\(i_2\)
Which of the following have a trigonal bipyramidal shape?
\(PF_5, PBr_5, [PtCl_4], SF_6, BF_3, BrF_5, PCl_5, [Fe(CO)_5]\)
If \((t+1)dx=(2x+(t+1)^3)dt\) and \(x(0)=2\), then \(x(1) \)is equal to:
Let S = {1,2,3,..., 20}, R1 = {(a, b): a divide b}, R2 = {(a, b): a is integral multiple of b} and a, b ∈ S. n(R1 - R2) = ?
Number of radial nodes present in 3p are
Which of the following compounds have colour due to d-d transition?
Given: \(5f (x) 4f(\frac 1x) = x^2 - 4 \) & \(y = 9f(x) × x^2\) If y is strictly increasing, then find interval of \(x\).