List of practice Questions

The value(s) of k for which the equations x² - kx - 21 = 0 and x² - 3kx + 35 = 0 will have a common root is/are

If the ratio of the roots of the equation $p{x}^2+qx+r=0$ is $a:b,$ then $\frac{ab}{(a+b{)}^2}=$

The sum of n terms of an AP is n² + n; the common difference will be:

If sum of the coefficients of x⁷ and x⁴ in the expansion of ${(\frac{x^2}{a}-\frac{b}{x})}^{11}$ is zero, then

If p + q + r = a + b + c = 0, then the determinant $\mathrm{\Delta }=\left|\begin{array}{lll}pa& qb& rc\\ qc& ra& pb\\ rb& pc& qa\end{array}\right|$ equals

Diborane undergo unsymmetrical cleavage reactions with:

Evaluate:$\underset{x\to -2}{lim}\frac{x^5+2x^4+x^2+3x+2}{x^4+2x^3+3x^2-5x-22}$

If ¹⁸C15 + 2(¹⁸C16) + ¹⁷C16 + 1 = ⁿC3, then n is equal to

The forces with magnitudes 5,3 and 1 unit are acting on a particle in the direction of the vectors $6\hat{i}+2\hat{j}+3\hat{k};3\hat{i}-2\hat{j}+6\hat{k}$ and $2i-3\hat{j}-6\hat{k},$ respectively. They remain constant while the particle is displaced from the point $A(2,-1,-3)$ to $B(5,-1,1)$. The work done is

If $\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k}$ and $\overrightarrow{b}=\hat{i}\times (\overrightarrow{a}\times \hat{i})+\hat{j}\times (\overrightarrow{a}\times \hat{j})+\overrightarrow{k}\times (\overrightarrow{a}\times \hat{k})$ then length of $\overrightarrow{b}$ isequal to

The area (in sq. units) bounded by the parabola y = 2 – x² and the line x + y = 0 is

The equation of the plane parallel to the planes x + 2y + 3z – 5 = 0 and x + 2y + 3z – 7 = 0 and equidistant from them is

The solution of $\frac{dy}{dx}=\frac{x\log x^2+x}{\sin y+y\cos y}$

A particle oscillates in simple harmonic motion such that its speed and acceleration at distance 2 m from mean position are 4 m/s and 16 m/s² respectively. Find the amplitude of oscillation of the particle.

If two primary spermatocytes and two primary oocytes undergo meiosis simultaneously, what will be the ratio of spermatozoa and ova produced at the end of the gametogenesis?

If the wavelength of incident light changes from 400 nm to 300 nm, then the stopping potential of photoelectrons emitted from a surface becomes (approximately)

Which of the following statements is/are correct?

$\sqrt{4},\sqrt[4]{4},\sqrt[8]{4},\sqrt[16]{4},\dots \dots \dots$up to ∞ are roots of the equation

$\int \frac{a^{x/2}}{\sqrt{a^{-x}-a^x}}\mathrm{dx}$ is equal to

If fourth term of an A.P. is zero, then $\frac{t_{25}}{t_{11}}$ is, where $t_n$ denotes the $n^{\text{th }}$ term of AP.

If in a triangle ABC, sin A, sin B, sin C are in A.P., then 

The coordinates of a moving point p are (2t² + 4, 4t + 6). Then  its locus will be a

The number of real solutions of the equation |x|² + 5|x| + 4 = 0 is