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Q1PhysicsEasyGeometrical Optics
An observer looks at a distant tree of height $10$ m with a telescope of magnifying power $20$ . To the observer the tree appears:
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Answer: D
A telescope produces angular magnification: the image subtends an angle $20$ times larger, which the eye interprets as the object being brought $20$ times nearer (not literally taller). So it appears $20$ times nearer.
Q2PhysicsHardGravitation
Two planets are at mean distances $d_{1}$ and $d_{2}$ from the sun and their frequencies are $n_{1}$ and $n_{2}$ . Then:
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Answer: B
Kepler: $T^{2} \propto d^{3} \Rightarrow \frac{1}{n ^{2}} \propto d^{3} \Rightarrow n^{2} d^{3} =$ const. So $n_{1}^{2} d_{1}^{3} = n_{2}^{2} d_{2}^{3}$ .
Q3PhysicsHardSemiconductor
The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature:
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Answer: A
The occupation probability goes as $exp (- E_{g} /2 k T)$ , so it falls exponentially as the band gap increases.
Q4ChemistryHardChemical Equilibrium
For $S n O_{2} (s) + 2 H_{2} (g) ⇌ S n (s) + 2 H_{2} O (g)$ , the equilibrium mixture contains 40% water vapour by volume. Find $K_{p}$ if the total pressure at equilibrium is 5 atm.
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Answer: B
For gases, volume % = mole %. $p_{H_{2} O} = 0.4 \times 5 = 2$ atm; $p_{H_{2}} = 0.6 \times 5 = 3$ atm. $K_{p} = (p_{H_{2} O})^{2} / (p_{H_{2}})^{2} = 4/9$ .
Q5ChemistryMediumAlcohols, Phenols and Ethers
Phenyl isopropyl ether ( $C_{6} H_{5} - O - C H (C H_{3})_{2}$ ) is heated with conc. HI to give a hydroxy compound A, which is further heated with Zn dust to give compound B. Identify A and B.
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Answer: D
Conc. HI cleaves the aryl alkyl ether to give phenol (A) and isopropyl iodide. The aryl-O bond is not cleaved, so phenol forms. Phenol heated with Zn dust gives benzene (B).
Q6MathematicsMediumInverse Trigonometric Functions
The set of all values of $k$ for which $(tan^{- 1} x)^{3} + (cot^{- 1} x)^{3} = k π^{3}$ , $x \in R$ , is the interval:
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Answer: A
$S = (tan^{- 1} x)^{3} + (cot^{- 1} x)^{3} = \frac{3 π}{2} (tan^{- 1} x - \frac{π}{4})^{2} + \frac{π ^{3}}{32}$ . So $\frac{π ^{3}}{32} \leq S < \frac{7}{8} π^{3} \Rightarrow \frac{1}{32} \leq k < \frac{7}{8}$ .
Q7MathematicsMediumStraight Lines and Pair of Straight Lines
If $L : a x + b y + c = 0$ is a variable straight line, where $a$ , $b$ and $c$ are the second, fourth and seventh term of an AP respectively, then $L$ passes through the fixed point:
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Answer: B
Let $a = p + q$ , $b = p + 3 q$ , $c = p + 6 q$ ( $p$ = first term, $q$ = common difference). Then $a x + b y + c = p (x + y + 1) + q (x + 3 y + 6) = 0$ . Solving $x + y + 1 = 0$ and $x + 3 y + 6 = 0$ gives $x = \frac{3}{2}$ , $y = - \frac{5}{2}$ .
Q8BiologyMediumTransport in Plants
If we place a twig bearing white flowers in coloured water, it turns colour; on examining the T.S. of the twig, what would we be able to demonstrate?
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Answer: D
The coloured water travels through the xylem in the vascular bundles, which become stained; a transverse section demonstrates that the path of water movement is through the vascular bundles.
Q9BiologyMediumPrinciples of Inheritance and Variation
Select the unsuitable option regarding sex determination in birds:
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Answer: C
In birds the male is homogametic (ZZ) and produces only one type of gamete, while the female is heterogametic (ZW) with two types of sex chromosomes. So 'males have two types of sex chromosomes' is the incorrect statement.

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