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1 mole of Rhombic sulphur is treated with conc. $HNO_{3}$ find the mass of $H_{2}O$ formed

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Let m and n be two positive integers greater than 1.If $α→0lim α_{m}e_{cosα_{n}}−e =−(2e )$ then the value of $nm $ is

let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes $P_{1}:x+2y−z+1=0$ and $P_{2}:2x−y+z−1=0$, Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane $P_{1}$. Which of the following points lie(s) on M?

In the following reactions, the structure of the major product 'X' is

For $a∈R$ (the set of all real numbers), $a=−1),$$(lim)_{n→∞}((n+1)_{a−1}[(na+1)+(na+2)+……(na+n)]1_{a}+2_{a}++n_{a} =60.1 $Then $a=$(a)$5$ (b) 7 (c) $2−15 $ (d) $2−17 $

Which of the following is (are) NOT the square of a $3×3$ matrix with real entries? (a)$⎣⎡ 100 010 00−1 ⎦⎤ $ (b) $⎣⎡ −100 0−10 00−1 ⎦⎤ $ (c)$⎣⎡ 100 010 001 ⎦⎤ $ (d) $⎣⎡ 100 0−10 00−1 ⎦⎤ $

Let x, y and z be three vectors each of magnitude V2 tion on and the angle between each pair of them is E. If a is a let non-zero vector perpendicular to x and yx z and b is a non-zero tor perpendicular to y and z x x, then 1.

Let m be the smallest positive integer such that the coefficient of $x_{2}$ in the expansion of $(1+x)_{2}+(1+x)_{3}+(1+x)_{4}+……..+(1+x)_{49}+(1+mx)_{50}$ is $(3n+1)._{51}C_{3}$ for some positive integer n. Then the value of n is

Let E1 and E2, be two ellipses whose centers are at the origin.The major axes of E1 and E2, lie along the x-axis and the y-axis, respectively. Let S be the circle $x_{2}+(y−1)_{2}=2$. The straight line x+ y =3 touches the curves S, E1 and E2 at P,Q and R, respectively. Suppose that $PQ=PR=322 $.If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are):