Let the shortest distance between the lines $\frac{x-3}{3} = \frac{y-\alpha}{-1} = \frac{z-3}{1}$ and $\frac{x+3}{-3} = \frac{y+7}{2} = \frac{z-\beta}{4}$ be $3\sqrt{30}$. Then the positive value of $5\alpha + \beta$ is
If $\lim_{x \to 1} \frac{(x-1)(6+\lambda \cos(x-1)) + \mu \sin(1-x)}{(x-1)^3} = -1$, where $\lambda, \mu \in \mathbb{R}$, then $\lambda + \mu$ is equal to
Let $f: [0, \infty) \to \mathbb{R}$ be a differentiable function such that $f(x) = 1 - 2x + \int_0^x e^{x-t} f(t) \, dt$ for all $x \in [0, \infty)$. Then the area of the region bounded by $y = f(x)$ and the coordinate axes is
0.5 g of an organic compound on combustion gave 1.46 g of $ CO_2 $ and 0.9 g of $ H_2O $. The percentage of carbon in the compound is ______ (Nearest integer) $\text{(Given : Molar mass (in g mol}^{-1}\text{ C : 12, H : 1, O : 16})$
Given: $ \Delta H_f^0 [C(graphite)] = 710 $ kJ mol⁻¹ $ \Delta_c H^0 = 414 $ kJ mol⁻¹ $ \Delta_{H-H}^0 = 436 $ kJ mol⁻¹ $ \Delta_{C-H}^0 = 611 $ kJ mol⁻¹ The \(\Delta H_{C=C}^0 \text{ for }CH_2=CH_2 \text{ is }\) _____\(\text{ kJ mol}^{-1} \text{ (nearest integer value)}\)
Consider the following reactions $ A + HCl + H_2SO_4 \rightarrow CrO_2Cl_2$ + Side Products Little amount $ CrO_2Cl_2(vapour) + NaOH \rightarrow B + NaCl + H_2O $ $ B + H^+ \rightarrow C + H_2O $ The number of terminal 'O' present in the compound 'C' is ______
Match the LIST-I with LIST-II
Choose the correct answer from the options given below:
Among $ 10^{-10} $ g (each) of the following elements, which one will have the highest number of atoms? Element : Pb, Po, Pr and Pt
Which of the following statements are correct? A. The process of the addition an electron to a neutral gaseous atom is always exothermic B. The process of removing an electron from an isolated gaseous atom is always endothermic C. The 1st ionization energy of the boron is less than that of the beryllium D. The electronegativity of C is 2.5 in $ CH_4 $ and $ CCl_4 $ E. Li is the most electropositive among elements of group 1 Choose the correct answer from the options given below
Which of the following properties will change when system containing solution 1 will become solution 2 ?
In the figure shown below, a resistance of 150.4 $ \Omega $ is connected in series to an ammeter A of resistance 240 $ \Omega $. A shunt resistance of 10 $ \Omega $ is connected in parallel with the ammeter. The reading of the ammeter is ______ mA.
Given below are two statements: Statement I : The N-N single bond is weaker and longer than that of P-P single bond Statement II : Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions. In the light of above statements, choose the correct answer from the options given below
The metal ions that have the calculated spin only magnetic moment value of 4.9 B.M. are A. $ Cr^{2+} $ B. $ Fe^{2+} $ C. $ Fe^{3+} $ D. $ Co^{2+} $ E. $ Mn^{2+} $ Choose the correct answer from the options given below
