Recent questions tagged easy

Integrate : $ \int \sqrt {2x^2-5x +6 } $$dx$

asked Dec 23, 2013 by meena.p

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An X-ray tube operates on $30\: kV$. The minimum wavelength emitted is :

asked Dec 23, 2013 by thanvigandhi_1

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Which of the following radiations has least wavelength?

asked Dec 23, 2013 by thanvigandhi_1

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The time taken by a photoelectron to come out after the photon strikes is approximately

asked Dec 23, 2013 by thanvigandhi_1

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The threshold frequency for a metallic surface corresponds to energy of $6.2\: eV$ and the stopping potential for a radiation incident on this surface is $5V$. The incident radiation lies in

asked Dec 23, 2013 by thanvigandhi_1

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If $\lim\limits_{x\to 0}(1+ax)^{\Large\frac{b}{x}}=e^2\qquad(a,b\in N)$ then

asked Dec 23, 2013 by sreemathi.v

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Compute the typical de Broglie wavelength of an electron $(\lambda)$ in a metal at $ 27^{\circ}C$ and compare it with the mean separation between two electrons(r) in a metal which is given to be about $2 \times 10^{-10}m$

asked Dec 23, 2013 by thanvigandhi_1

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The function $f(x)=\sin^{-1}(\cos x)$ is

asked Dec 23, 2013 by sreemathi.v

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The work function of the following metals are : $Na = 2.75\: eV; K = 2.3\: eV ; Mo = 4.17\: eV ; Ni = 5.15 \: eV$. Which of these metals will not give photoelectric emission for a radiation of wavelength $3300\: A^{\circ}$ the photocell? from a $ He – Cd$ laser placed $1m$ away from

asked Dec 23, 2013 by thanvigandhi_1

1 answer

What is the de Broglie wavelength of a dust particle of mass $1 \times 10^{-9}$ kg drifting with a speed of $\;2.2 m/s$

asked Dec 23, 2013 by thanvigandhi_1

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$\lim\limits_{x\to 1}\large\frac{x^3+x^2-2}{\sin(x-1)}$ is

asked Dec 23, 2013 by sreemathi.v

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Integrate : $\int\large\frac{\log _e \tan ^{-1} (3x)}{4 (1+gx^2)}$

asked Dec 23, 2013 by meena.p

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$\lim\limits_{x\to 0}\big(\large\frac{a^x+b^x+c^x}{3}\big)^{\Large\frac{1}{x}}$ is

asked Dec 23, 2013 by sreemathi.v

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The work function for a certain metal is $4.2 eV$. Will this metal give photoelectric emission for incident radiation of wavelength $589 nm$?

asked Dec 23, 2013 by thanvigandhi_1

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$\lim\limits_{x\to 0}\large\frac{(\cos x)^{1/2}-(\cos x)^{1/3}}{\sin^2x}$ is

asked Dec 23, 2013 by sreemathi.v

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Integrate : $\int x^5 \sec^2 (7x^6+9) dx$

asked Dec 23, 2013 by meena.p

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$\lim\limits_{x\to \infty}\big(\large\frac{x+1}{x+2}\big)^{2x+1}$ is

asked Dec 23, 2013 by sreemathi.v

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The threshold frequency for a certain metal is $3.3 \times 1014Hz$. If light of frequency $8.2 \times 1014 Hz$ is incident on the metal, predict the cutoff voltage for the photoelectric emission.

asked Dec 23, 2013 by thanvigandhi_1

1 answer

Integrate : $\int \large\frac{\sqrt {\cos^{-1}(4x)}}{\sqrt {1-16x^2}}$$dx$

asked Dec 23, 2013 by meena.p

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A 100 W sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on him. The $ \lambda$ of sodium light is 589 nm. At what rate are the photons delivered to the sphere ?

asked Dec 23, 2013 by thanvigandhi_1

1 answer

$\lim\limits_{n\to\infty}\bigg[\large\frac{1}{1-n^4}+\frac{1}{1-n^4}+.........+\frac{n^3}{1-n^4}\bigg]$

asked Dec 23, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}(\log_33x)^{\log_x3}$ is

asked Dec 23, 2013 by sreemathi.v

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If $f(x)=\mid x-25\mid$ and $g(x)=f(f(x))$,find $g'(x)$ for $x > 50$

asked Dec 23, 2013 by sreemathi.v

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Integrate : $ \int x^2. e^{\Large x^3}. \cos (e^{\Large x^3}).dx$

asked Dec 23, 2013 by meena.p

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Evaluate :$\lim\limits_{x\to 0}(\cos x)^{\large\frac{1}{x^2}}$

asked Dec 23, 2013 by sreemathi.v

1 answer

Evaluate :$\lim\limits_{x\to \Large\frac{\pi}{4}}\large\frac{\sqrt 2-\cos x-\sin x}{(4x-\pi)^2}$

asked Dec 23, 2013 by sreemathi.v

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The energy flux of sunlight reaching the surface of the earth is $ 1.388 \times 10^3 \: W/m^2$. How many photons per square meter are incident on earth per second ? Assume that the photons in the sunlight have an average wavelength of 550 nm.

asked Dec 23, 2013 by thanvigandhi_1

1 answer

Integrate: $ \int \large\frac{x^3 \tan ^{-1} x^4 }{1+x^8}$$dx$

asked Dec 23, 2013 by meena.p

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Evaluate : $\lim\limits_{x\to\large\frac{\pi}{2}}\large\frac{\sin(\cos x)\cos x}{\sin x-cosec x}$

asked Dec 23, 2013 by sreemathi.v

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Integrate : $ \int \sec^4 x dx$

asked Dec 23, 2013 by meena.p

1 answer

Evaluate : $\lim\limits_{x\to 0}\large\frac{e^x-e^{x\cos x}}{x+\sin x}$

asked Dec 23, 2013 by sreemathi.v

1 answer

Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW. How many photons per second, on the average, arrive at a target irradiated by this beam ? (Assume the beam to have uniform cross - section which is less than the target area )

asked Dec 23, 2013 by thanvigandhi_1

1 answer

Evaluate : $\lim\limits_{x\to 0}(1+\sin x)^{\Large\frac{1}{x^2}}$

asked Dec 23, 2013 by sreemathi.v

1 answer

The photoelectric cut-off voltage in a certain experiment is 1.5 V. What is the maximum kinetic energy of photoelectrons emitted ?

asked Dec 23, 2013 by thanvigandhi_1

1 answer

Evaluate : $\lim\limits_{h\to 0}\large\frac{(a+h)^2\sin(a+h)-a^2\sin a}{h}$

asked Dec 23, 2013 by sreemathi.v

1 answer

If function $f(x)$ is differentiable at $x=a$ then $\lim\limits_{x\to a}\large\frac{x^2f(a)-a^2f(x)}{x-a}$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

Let $f : R\rightarrow [0,\infty]$ be such that $\lim\limits_{x\to 5}f(x)$ exists and $\lim\limits_{x\to 5}\large\frac{(f(x))^2-9}{\sqrt{|x-5|}}$ = 0. Then $\lim\limits_{x\to 5}f(x)$ equals

asked Dec 23, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 2}\big(\large\frac{\sqrt{1-\cos 2(x-2)}}{x-2}\big)$

asked Dec 23, 2013 by sreemathi.v

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Let $f : R\rightarrow R$ be a positive increasing function with $\lim\limits_{x\to 0}\large\frac{f(3x)}{f(x)}$$=1$. Then $\lim\limits_{x\to \infty}\large\frac{f(2x)}{f(x)}$ = ?

asked Dec 23, 2013 by sreemathi.v

1 answer

Let $f$ be differentiable for all $x$. If $f(1)=-2$ and $f'(x)\geq 2$ for $x\in [1,6]$ then

asked Dec 23, 2013 by sreemathi.v

1 answer

The work function of caesium metal is $2.14 \;eV$. When light of frequency $ 6 \times 10^{14}Hz$ is incident on the metal surface , photoemmision of electron occurs. What is the stopping potential of the emitted photoelectrons ?

asked Dec 23, 2013 by thanvigandhi_1

1 answer

The value of $\lim\limits_{x\to 0}\large\frac{\int\limits_0^{x^2} \sec^2tdt}{x\sin x}$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

The maximum frequency of X-rays produced by 30 kv electrons is

asked Dec 23, 2013 by thanvigandhi_1

1 answer

If $\lim\limits_{x\to 0}\large\frac{\log(3+x)-\log(3-x)}{x}$$=K$ the value of $K$ is

asked Dec 23, 2013 by sreemathi.v

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$\lim\limits_{n\to\infty}\large\frac{1+2^4+3^4+......n^4}{n^5}$ - $\lim\limits_{n\to\infty}\large\frac{1+2^3+3^3+......n^3}{n^5}$ =

asked Dec 23, 2013 by sreemathi.v

1 answer

If $f(x+y)=f(x).f(y) \forall x,y$ and $f(5)=2,f'(0)=3$ then $f'(5)$ is

asked Dec 23, 2013 by sreemathi.v

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If $f(1)=1,f'(1)=2$ then $\lim\limits\large\frac{\sqrt{f(x)-1}}{\sqrt x-1}$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{\log x^n-[x]}{[x]}$ $n\in N$ ($x$ denotes greatest integer less than or equal to $x$)

asked Dec 23, 2013 by sreemathi.v

1 answer

Find the area enclosed by the curve $y^2+1=x,x\leq 2$ and the line $x=2$.

asked Dec 22, 2013 by balaji.thirumalai

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Evaluate: $ \begin{vmatrix} (x-2)^2 & (x-1)^2 & x^2 \\ (x-1)^2 & x^2 & (x+1)^2 \\ x^2 & (x+1)^2 & (x+2)^2 \end{vmatrix}$

asked Dec 22, 2013 by balaji.thirumalai

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