List of practice Questions

 If ⁿC4, ⁿC5 and ⁿC6 are in A.P., then n is 

If the coefficients of 5th, 6th and 7th terms in the expansion of (1+x)n are in A.P. then n =

The radius of a circle is increasing at the rate of 0.1 cm/s. When the radius of the circle is 5 cm, the rate of change of its area is

The door of a running refrigerator inside a closed room was left open. Which of the following observations will be seen?

The percentage of carbon in acetic acid is

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

In a triangle ABC, tan C < 0. Then

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

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

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:

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

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

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

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

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?

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.

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