Recent questions tagged easy

$\lim\limits_{x\to a}\large\frac{\log(x-a)}{\log(e^x-e^a)}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \large\frac{\cos 2 x}{\sin ^2 x \cos ^2 x }$$dx$

asked Dec 30, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{1- x \sin x +\cos x }{x(1- \cos x )}$$dx$

asked Dec 30, 2013 by meena.p

1 answer

If $f(x)=\large\frac{1}{\sqrt{18-x^2}}$ then $\lim\limits_{x\to 3}\large\frac{f(x)-f(3)}{x-3}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

Integrate : $\int \large\frac{\sec x cosec x}{\log (\tan x )}$$dx$

asked Dec 30, 2013 by meena.p

1 answer

$\lim\limits_{x\to {-1}}\large\frac{\sqrt{\pi}-\sqrt{\cos^{-1}x}}{\sqrt{x+1}}$ is given by

asked Dec 30, 2013 by sreemathi.v

1 answer

If $f(9)=9,f'(9)=4$ then $\lim\limits_{x\to 9}\large\frac{\sqrt{f(x)}-3}{\sqrt x-3}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

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

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \large\frac{\pi}{4}}\large\frac{\cos x-\sin x}{(\Large\frac{\pi}{4}-\normalsize x)(\large\cos x+\sin x)}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

If $f(x)=\large\frac{x^2-10x+25}{x^2-7x+10}$ for $x\neq 5$ and $f$ is continuous at $x=5$ then $f(5)=$

asked Dec 30, 2013 by sreemathi.v

1 answer

Among 5 numbers a, b, c, d and e the relationships are: a, b, c are in AP and b, c, d are in GP and c, d, e are in HP. Find b, c, d if a = 2 and e = 18.

asked Dec 30, 2013 by yamini.v

2 answers

$\lim\limits_{x\to \large\frac{\pi}{4}}\big(\large\frac{1-\tan x}{1\sqrt 2\sin x}\big)$=

asked Dec 30, 2013 by sreemathi.v

1 answer

If $\lim\limits_{x\to k}\large\frac{x^k-5^k}{x-5}$$=500$ then positive value of k is

asked Dec 30, 2013 by sreemathi.v

1 answer

$f(x)=\left\{\begin{array}{1 1}\large\frac{x^5-32}{x-2}&x\neq 2\\k&x=2\end{array}\right.$ is continuous at $x=2$ then $k=$

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to\large\frac{-\pi}{4}}\large\frac{1+\tan x}{\cos 2x}$=

asked Dec 30, 2013 by sreemathi.v

1 answer

If $f$ is continuous on $[0,1]$ and $f\big(\large\frac{1}{3}\big)$$=1$ then $\lim\limits_{n\to \infty}f(\large\frac{n}{\sqrt{9n^2+1}}\big)$=

asked Dec 30, 2013 by sreemathi.v

1 answer

If $x_1=1$ and $x_{n+1}=\large\frac{4+3x_n}{3+2x_n}\qquad$$n \geq 1$ and if $\lim\limits_{n\to \infty}x_n=l$ then l is

asked Dec 30, 2013 by sreemathi.v

1 answer

If $\lim\limits_{x\to \infty}\big(\large\frac{x^3+1}{x^2+1}$$-(ax+b)\big)=2$ then

asked Dec 30, 2013 by sreemathi.v

1 answer

If $\log (x+y)=2xy$ then $y'(0)=$

asked Dec 30, 2013 by sreemathi.v

1 answer

In a GP, the first term is $312\large\frac{1}{2}$, the common ratio is $\large\frac{1}{2}$. Find the sum of the series to $\infty$ terms.

asked Dec 30, 2013 by yamini.v

1 answer

$\lim\limits_{h\to 0}\large\frac{f(2h+2+h^2)-f(2)}{f(h-h^2+1)-f(1)}$ given that $f'(2)=6$ and $f'(1)=4$

asked Dec 30, 2013 by sreemathi.v

1 answer

Let $f:R\to R$ be such that $f(1)=3$ and $f'(1)=6$.Then $\lim\limits_{x\to 0}\bigg[\large\frac{f(1+x)}{f(1)}\bigg]^{1/x}$ equals

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{\sin(\pi\cos^2x)}{x^2}$=

asked Dec 30, 2013 by sreemathi.v

1 answer

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

asked Dec 30, 2013 by sreemathi.v

1 answer

The value of $\lim\limits_{x\to 0}\int\limits_{0^{x^2}}\large\frac{\cos t^2dt}{x\sin x}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \infty}\large\frac{x^n}{e^x}$$=0$ for

asked Dec 30, 2013 by sreemathi.v

1 answer

If $G(x)=-\sqrt{25-x^2}$ then $\lim\limits_{x\to 1}\large\frac{G(x)-G(1)}{x-1}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

If the equation of the plane containing the line $\large\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$ is $a(x-x_1)+b(y-y_1)+c(z-z_1)=0$, then ?

asked Dec 29, 2013 by rvidyagovindarajan_1

1 answer

The direction ratio of the normal to the plane through $(1,0,0),(0,1,0)$, which makes $\large\frac{\pi}{4} $ with the plane $x+y=3$ is ?

asked Dec 28, 2013 by rvidyagovindarajan_1

1 answer

The line $\overrightarrow r=(4\hat i+2\hat j+\alpha \hat k)+\lambda(\hat i+\hat j+2\hat k)$ lies on the plane $2x-4y+z=7$ if $\alpha=?$

asked Dec 28, 2013 by rvidyagovindarajan_1

1 answer

If the lines $x=1+s,\:y=3-\lambda s,\:z=1+\lambda s\:\:and\:\:x=\large\frac{t}{2}$, $y=1+t,\:z=2-t$ where $s\:\:and\:\:t$ are parameters, are $coplanar$, then $\lambda=?$

asked Dec 28, 2013 by rvidyagovindarajan_1

1 answer

If a line $\overline {AB}$ makes angle $45^{\circ}$ with positive $x-axis$ and $120^{\circ}$ with positive $y-axis$, then the angle $\theta$ made by the line with positive $z-axis$ is ?

asked Dec 27, 2013 by rvidyagovindarajan_1

1 answer

If the lines $\overrightarrow r=(\hat i-\hat j+\hat k)+\lambda(2\hat i+3\hat j+4\hat k)\:\:and\:\:\overrightarrow r=(3\hat i+k\hat j)+\mu(\hat i+2\hat j+\hat k)$ intersect then $k=?$

asked Dec 26, 2013 by rvidyagovindarajan_1

1 answer

The intercepts cut off by the plane $\overrightarrow r.(2\hat i+\hat j-\hat k)=5$ with the axes are ?

asked Dec 24, 2013 by rvidyagovindarajan_1

1 answer

Which of the following is correct?

asked Dec 24, 2013 by thanvigandhi_1

1 answer

Emission of photoelectrons from a metal plate illuminated with monochromatic electromagnetic radiation will always take place provided

asked Dec 24, 2013 by thanvigandhi_1

1 answer

A point source of light is taken away from the experimental setup of photoelectric effect, then which is the most appropriate statement?

asked Dec 24, 2013 by thanvigandhi_1

1 answer

The $KE$ of an electron with de-Broglie wavelength of $0.3\: nm$ is

asked Dec 24, 2013 by thanvigandhi_1

1 answer

Consider two light sources of wavelengths $ \lambda_1\: and\: \lambda_2 (\lambda_1 > \lambda_2)$ which are emitting $n_1\: and \: n_2$ photons respectively, in a given time. Assume equal power for both sources, then

asked Dec 24, 2013 by thanvigandhi_1

1 answer

Sodium and Copper have work functions $2.3\: eV\: and \: 4.5\: eV$ respectively. Then the ratio of the wavelengths is nearest to

asked Dec 24, 2013 by thanvigandhi_1

1 answer

$\lim\limits_{\theta \to \Large\frac{\pi}{2}}(\sec\theta-\tan\theta)$=

asked Dec 24, 2013 by sreemathi.v

1 answer

The work function of a substance is $4\: eV$. The longest wavelength of light that can cause photoelectron emission from this substance is approximately

asked Dec 24, 2013 by thanvigandhi_1

1 answer

A source of light is placed at a distance $x$ from a photocell and cut off potential is $V$. If the distance of the same source from the photocell is doubled, then cut off potential will be :

asked Dec 24, 2013 by thanvigandhi_1

1 answer

$\lim\limits_{x\to 0}\large\frac{\tan x-\sin x}{x^3}$=

asked Dec 24, 2013 by sreemathi.v

1 answer

Blue light can cause photoelectric emission from a metal, but yellow light cannot. If red light is incident on the metal, then

asked Dec 24, 2013 by thanvigandhi_1

1 answer

The maximum energy of the electrons released in photocell is independent of

asked Dec 24, 2013 by thanvigandhi_1

1 answer

$\lim\limits_{x\to \infty}[x-\sqrt{x^2+x}]$=

asked Dec 24, 2013 by sreemathi.v

1 answer

The energy $E$ and the momentum $p$ of photon are given by $E=hn\: and\: p=h/\lambda$ respectively. The velocity of photon will be

asked Dec 24, 2013 by thanvigandhi_1

1 answer

A photodetector used to detect the wavelength of 1700 nm, has energy gap of about

asked Dec 24, 2013 by thanvigandhi_1

1 answer

If $f(x)=\large\frac{1-\tan x}{4x-\pi}\qquad $$x\neq \large\frac{\pi}{4}$,$x \in [0,\large\frac{\pi}{2}]$ and f(x) is continuous in $[0,\large\frac{\pi}{2}]$ then $f(\large\frac{\pi}{4})$

asked Dec 24, 2013 by sreemathi.v

1 answer

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