In the circuit shown L= 1μ H, C= 1μ F, and R= 1 kΩ. They are connected in series with an AC source V= V_{0} sinωt as shown. Which of the following options is/are correct?

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1

In the circuit shown L= 1μ H, C= 1μ F, and R= 1 kΩ. They are connected in series with an AC source V= V_{0} sinωt as shown. Which of the following options is/are correct?

ω

2

A photoelectric material having work-function Φ_{0} is illuminated with light of wavelength λ $(\lambda <\frac{hc}{\phi_{0}})$ . The fastest photoelectron has de-Broglie wavelength λ_{d}. A change in wavelength of the incident light by Δλ results in a change Δλ_{d} in λ_{d}

Then, the ratio $\frac{\triangle \lambda_{d}}{\triangle\lambda}$ is proportional to

3

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T= 0.01s$ and he measures the depth of the well to be L=20 m. Take the acceleration due to gravity g=10 ms^{-2} and the velocity of sound is 300 ms^{-1}. Then the fractional error in the measurement

$\frac{\delta L}{L}$is closet to

4

If $f:R\rightarrow R$ is twice differentablr function such that f''(x)>0, for all xε R, and $f(\frac{1}{2})=\frac{1}{2}$ , f(1)=1, then

5

If the line $x=\alpha$ divides the area of region R={(x,y) $\in$ R^{2} : x^{3}≤ y≤ x, o≤x≤1 } into two equal parts, then

6

Let α and β be non zero real numbers such $2(\cos\beta-\cos\alpha)+\cos\alpha\cos\beta=1$ . Then which of the following is/are true?

7

Let O be the origin and OX, OY, OZ be three unit vectors in the directions of the sides QR,RP,PQ respectively of triangle PQR.

(ox × oy)=

8

For how many values of p, the circle $x^{2}+y^{2}+2x+4y-p=0$ and the coordinate axes have exactly three common points?

9

Let f:R→ R be a differentable function such that f(0)=0, $f(\frac{\pi}{2})=3$ and f ' (0)=1

if $g(x)=\int_{0}^{\frac{\pi}{2}} f'(t) cosec$ $ t f(t)-\cot $ $ t cosec$ $ t f(t)] dt$

for $x\epsilon(0,\frac{\pi}{2}]$, then $\lim_{x \rightarrow0 }g(x)=$

10

The IUPAC name(s) of the following compound

11

For a solution formed by mixing liquids L and M, the vapor pressure of L plotted against the mole fraction of M in solution is shown in the following figure. Here X_{L} and X_{M} represent mole fractions of L and M respectively, In the solution. The correct statement(s) applicable to this system is (are)→

12

The color of the X_{2} molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to

13

The order of the oxidation state of the phosphorous atom in H_{3}PO_{2} , H_{3}PO_{4} , H_{3}PO_{3} and H_{4}P_{2}O_{6} is

14

The option (s) with only amphoteric oxides is (are)

15

The correct statement(s) about surface properties is (are)

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