JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT
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A Carnot engine has efficiency of \(50 \%\). If the temperature of sink is reduced by \(40^{\circ} \mathrm{C}\), its efficiency increases by \(30 \%\). The temperature of the source will be:
Match List - I with List - II.
| List - I Reaction |
List - II Catalyst |
||
|---|---|---|---|
| (A) | $$4N{H_3}(g) + 5{O_2}(g) \to 4NO(g) + 6{H_2}O(g)$$ | (I) | $$NO(g)$$ |
| (B) | $${N_2}(g) + 3{H_2}(g) \to 2N{H_3}(g)$$ | (II) | $${H_2}S{O_4}(l)$$ |
| (C) | $${C_{12}}{H_{22}}{O_{11}}(aq) + {H_2}O(l) \to \mathop {{C_6}{H_{12}}{O_6}}\limits_{Glu\cos e} + \mathop {{C_6}{H_{12}}{O_6}}\limits_{Fructose}$$ | (III) | $$Pt(s)$$ |
| (D) | $$2S{O_2}(g) + {O_2}(g) \to 2S{O_3}(g)$$ | (IV) | $$Fe(s)$$ |
Choose the correct answer from the options given below :
Consider the sequence \(a_{1}, a_{2}, a_{3}, \ldots\) such that \(a_{1}=1, a_{2}=2\) and \(a_{n+2}=\frac{2}{a_{n+1}}+a_{n}\) for \(\mathrm{n}=1,2,3, \ldots .\) If \(\left(\frac{\mathrm{a}_{1}+\frac{1}{\mathrm{a}_{2}}}{\mathrm{a}_{3}}\right) \cdot\left(\frac{\mathrm{a}_{2}+\frac{1}{\mathrm{a}_{3}}}{\mathrm{a}_{4}}\right) \cdot\left(\frac{\mathrm{a}_{3}+\frac{1}{\mathrm{a}_{4}}}{\mathrm{a}_{5}}\right) \ldots\left(\frac{\mathrm{a}_{30}+\frac{1}{\mathrm{a}_{31}}}{\mathrm{a}_{32}}\right)=2^{\alpha}\left({ }^{61} \mathrm{C}_{31}\right)\), then \(\alpha\) is equal to :
In the case of amplitude modulation to avoid distortion the modulation index \((\mu)\) should be :
Which of the following statement is incorrect?
The foot of the perpendicular from a point on the circle \(x^{2}+y^{2}=1, z=0\) to the plane \(2 x+3 y+z=6\) lies on which one of the following curves?