Which of the following is paramagnetic ?

Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution?

Among the following, the essential amino acid is :

The incorrect statement among the following is :

If m and M are the minimum and the maximum values of 4 + {1 \over 2} sin2 2x $$-$$ 2cos4 x, x $$\in$$ R, then M $$-$$ m is equal to :

The system of linear equations $$\text{matrix}x+\lambda y-z=0\text{cr}\lambda x-y-z=0\text{cr}x+y-\lambda z=0\text{cr}$$ has a non-trivial solution for :

If A = \left[ {\matrix{ {5a} & { - b} \cr 3 & 2 \cr } } \right] and $$A$$ adj $$A=A$$ $$A^T,$$ then $$5a+b$$ is equal to :

If A = \left[ {\matrix{ { - 4} & { - 1} \cr 3 & 1 \cr } } \right], then the determinant of the matrix (A2016 − 2A2015 − A2014) is :

Let A be a 3 $$\times$$ 3 matrix such that A2 $$-$$ 5A + 7I = 0 Statement - I : A$$-$$1 = {1 \over 7} (5I $$-$$ A). Statement - II : The polynomial A3 $$-$$ 2A2 $$-$$ 3A + I can be reduced to 5(A $$-$$ 4I). Then :

The number of distinct real roots of the equation, \left| {\matrix{ {\cos x} & {\sin x} & {\sin x} \cr {\sin x} & {\cos x} & {\sin x} \cr {\sin x} & {\sin x} & {\cos x} \cr } } \right| = 0 in the interval \left[ { - {\pi \over 4},{\pi \over 4}} \right] is :

If P = \left[ {\matrix{ {{{\sqrt 3 } \over 2}} & {{1 \over 2}} \cr { - {1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right],A = \left[ {\matrix{ 1 & 1 \cr 0 & 1 \cr } } \right]\,\,\, Q = PAPT, then PT Q2015 P is :

Let two fair six-faced dice $$A$$ and $$B$$ be thrown simultaneously. If $$E_1$$ is the event that die $$A$$ shows up four, $$E_2$$ is the event that die $$B$$ shows up two and $$E_3$$ is the event that the sum of numbers on both dice is odd, then which of the following statements is $$NOT$$ true?

An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is :

If A and B are any two events such that P(A) = {2 \over 5} and P (A $$\cap$$ B) = {3 \over {20}}, hen the conditional probability, P(A $$|$$(A' $$\cup$$ B')), where A' denotes the complement of A, is equal to :

If a curve $$y=f(x)$$ passes through the point $$(1,-1)$$ and satisfies the differential equation, $$y(1+xy)dx=x$$ $$dy$$, then f\left( { - {1 \over 2}} \right) is equal to :

The solution of the differential equation {{dy} \over {dx}}\, + \,{y \over 2}\,\sec x = {{\tan x} \over {2y}},\,\, where 0 $$\le$$ x < {\pi \over 2}, and y (0) = 1, is given by :

If f(x) is a differentiable function in the interval (0, $$\infty$$) such that f (1) = 1 and $$\underset{t\to x}{\lim }$$ {{{t^2}f\left( x \right) - {x^2}f\left( t \right)} \over {t - x}} = 1, for each x > 0, then $$f\left(\text{raise}0.5ex3/\text{lower}0.25ex2\right)$$ equal to :

Two sides of a rhombus are along the lines, $$x-y+1=0$$ and $$7x-y-5=0$$. If its diagonals intersect at $$(-1,-2)$$, then which one of the following is a vertex of this rhombus?

A straight line through origin O meets the lines 3y = 10 − 4x and 8x + 6y + 5 = 0 at points A and B respectively. Then O divides the segment AB in the ratio :

A ray of light is incident along a line which meets another line, 7x − y + 1 = 0, at the point (0, 1). The ray is then reflected from this point along the line, y + 2x = 1. Then the equation of the line of incidence of the ray of light is :