The value of \(k\) for which the function \(f(x)=\left\{\begin{array}{ll}\frac{1-\cos 8 x}{16 x^2} & , \text { if } x \neq 0 \\ k & , \text { if } x=0\end{array}\right.\) is continuous at \(x=0\) is :

\(\int\left(\frac{1}{\log _e x}-\frac{1}{\left(\log _e x\right)^2}\right) d x\) is equal to

The slope of tangent to the curve \(x=t^2+3 t-8, y=2 t^2-2 t-5\) at the point (2, -1) is:

If \(x y+\frac{x^2}{y}=x^3 y+y\), then \(\frac{d y}{d x}\) is equal to

Area of the region bounded by the curve \(y^2=4 x, y\)-axis and the line \(y=3\) is equal to:

If \(f:[3, \infty) \rightarrow A\) defined by \(f(x)=x^2\) is an onto function, then \(A\) is:

The value of a washing machine purchased two years ago depreciates at the annual rate of 10%. If its present value is ₹ 50,000, then its value after two years will be :

Identify the autosome-linked recessive disorder.

A long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is \(4 \times 10^{-3} Wb\). The self-inductance of the solenoid is

Question based on the following passage :
P-Block elements are placed in group 13 to 18 in the periodic table. Group 15 is nitrogen family.
Nitrogen can react with hydrogen, oxygen, halogens etc. It shows multiple oxidation states in its various oxides i.e. \(N_2O, N_2O_3, N_2O_5\) etc. Important allotropic forms of phosphorus are white, red and black phosporus. Various compounds of phosphorus are phosphine, \(PCl_3, PCl_5\) and oxoacids of phosphorus. Oxidation states \(+1\) to \(+5\) are seen in various oxoacids of phosphorus. Group 17 elements are collectively known as halogens. Bond dissociation enthalpy of \(F_2\) is smaller than \(Cl_2\).
The gases present in group 18 are chemically unreactive, they form only few compounds. Neil Bartlett (in 1962) observed the reaction of a noble gas. Since then, many noble gas compounds have been synthesised.
The process used for the preparation of Oleum is :

\(\text{[NiCl}_2\text{(PPh}_3)_2\text{]}\) is named as :

The side of an equilateral triangle increases at the rate of \(3 cm / sec\), then the rate at which the area of the triangle increases when the side is 4 cm , is :

The rate of biomass production is called productivity and it is expressed in terms of __________ to compare the productivity of different ecosystems.