Assertion : Rayon is a semisynthetic polymer whose properties are better than natural cotton. Reason : Mechanical and aesthetic properties of cellulose can be improved by acetylation.

The transition metal ions responsible for color in ruby and emerald are, respectively :

Which one of the following species is stable in aqueous solution?

Which of the following compounds is metallic and ferromagnetic ?

The reaction of zinc with dilute and concentrated nitric acid, respectively, produces :

The bond angle H - X - H is the greatest in the compound :

The group of molecules having identical shape is :

The species in which the $\mathrm{N}$ atom is in a state of $s p$ hybridization is :

Thiol group is present in :

Observation of “Rhumann’s purple” is a confirmatory test for the presence of :

Consider the following sequence for aspartic acid : The pI (isoelectric point) of aspartic acid is :

The set of all values of $$\lambda$$ for which the system of linear equations: $$\text{matrix}2x_1-2x_2+x_3=\lambda x_1\text{cr}2x_1-3x_2+2x_3=\lambda x_2\text{cr}-x_1+2x_2=\lambda x_3\text{cr}$$ has a non-trivial solution

If A = \left[ {\matrix{ 1 & 2 & 2 \cr 2 & 1 & { - 2} \cr a & 2 & b \cr } } \right] is a matrix satisfying the equation $$A{A}^T=9\text{I},$$ where $$I$$ is $$3\times 3$$ identity matrix, then the ordered pair $$(a,b)$$ is equal to :

If $$12$$ different balls are to be placed in $$3$$ identical boxes, then the probability that one of the boxes contains exactly $$3$$ balls is :

Let $$y(x)$$ be the solution of the differential equation \left( {x\,\log x} \right){{dy} \over {dx}} + y = 2x\,\log x,\left( {x \ge 1} \right). Then $$y(e)$$ is equal to :

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $$(0,0)$$ $$(0,41)$$ and $$(41,0)$$ is :

If the angles of elevation of the top of a tower from three collinear points $$A,B$$ and $$C,$$ on a line leading to the foot of the tower, are $$30^{\circ }$$, $$45^{\circ }$$ and $$60^{\circ }$$ respectively, then the ratio, $$AB:BC,$$ is :

The sum of coefficients of integral power of $$x$$ in the binomial expansion $${\left(1-2\sqrt{x}\right)}^{50}$$ is :

The integral \int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}} equals :

Let $$O$$ be the vertex and $$Q$$ be any point on the parabola, $$x^2=8y$$. If the point $$P$$ divides the line segment $$OQ$$ internally in the ratio $$1:3$$, then locus of $$P$$ is :