Recent questions tagged eamcet

$A(\alpha, \beta)=\begin {bmatrix} \cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^{\beta} \end{bmatrix} => [A(\alpha, \beta)]^{-1}=$

asked Sep 20, 2013 by meena.p

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If $x$ is real, the value of $\large\frac{x^2-3x+4}{x^2+3x+4}$ lies in the interval

asked Sep 20, 2013 by meena.p

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The value of $'\alpha'$ for which the equation $x^3+ax+1=0$ and $x^4+ax^2+1=0$ have a common root is

asked Sep 20, 2013 by meena.p

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If $\tan A $ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0,$ then $\sin^2 (A+B)$=

asked Sep 20, 2013 by meena.p

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If $a \;>\;0$ and $b^2-4ac=0,$ then the curve $y=ax^2+bx+c$

asked Sep 20, 2013 by meena.p

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$ \sum \limits ^{\infty}_{n=1} \large\frac{2n}{(2n+1)\ !} =$

asked Sep 20, 2013 by meena.p

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$\large\frac{x^2+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}$ then find $A+C=$

asked Sep 20, 2013 by meena.p

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If the coefficient of $r$th and $(r+1)$th terms in the expansion of $(3+7x)^{29}$ are equal , then $r=$

asked Sep 20, 2013 by meena.p

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If $^{(n-1)} C_3+^{n-1} C_4 \;>\;^n C_3$, then the minimum value of $n$ is

asked Sep 20, 2013 by meena.p

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$^{15}P_{8}=A+8.^{14}P_7 =>A=$

asked Sep 20, 2013 by meena.p

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The number of five digit numbers divisible by 5 that can be formed using the numbers $0,1,2,3,4,5$ without repetition is

asked Sep 20, 2013 by meena.p

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A bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement successively, until the bag is empty. If the number of ways in which each pair consists of one white and one black balls is $14,400.$ then $n=$

asked Sep 20, 2013 by meena.p

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If $a,b$ and $n$ are natural numbers then $a^{n-1}+b^{n-1}$ is divisible by:

asked Sep 20, 2013 by meena.p

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If $f :IR \to IR$ is defined by $f(x) =\bigg[\large\frac{x}{5}\bigg]$ for $ x \in IR,$ Where $[y]$ denotes the greatest integer not exceeding y, then $ (f(x):|x| < 71)=$

asked Sep 20, 2013 by meena.p

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If $f:[2, \infty) \to B$ defined by $f(x)=x^2-4x+5$ is a bijection, then B=

asked Sep 20, 2013 by meena.p

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If $y=y(x)$ is the solution of the differential equation $\bigg(\large\frac{2+ \sin x}{y+1}\bigg) \frac{dy}{dx} $$+ cos x=0$ with $y(0)=1,$ then $y\bigg(\large\frac{\pi}{2}\bigg)=$

asked Sep 20, 2013 by meena.p

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The solution of the differential equation $\large\frac{dy}{dx}=\frac{y}{x}+\frac{\phi (y/x)}{\phi ' (y/x)}$ is

asked Sep 20, 2013 by meena.p

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Let $f(0)=1,f(0.5)=\large\frac{5}{4}$$, f(1)=2,f(1.5)=\large\frac{13}{4}$ and $f(2)=5$. Using Simpson's rule, $\int \limits_0^{2} f(x) dx=$

asked Sep 20, 2013 by meena.p

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If $I_n=\int \limits _0^{\pi/4} \tan ^n \theta d \theta$ for $n=1,2,3........$ then $I_{n-1}+I_{n+1}=.............$

asked Sep 20, 2013 by meena.p

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The area (in square units) of the region bounded by the curves $x=y^2$ and $x=3-2y^2$ is

asked Sep 20, 2013 by meena.p

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$\int \large\frac{1+\cos 4x}{\cot x -\tan x}$$dx$=

asked Sep 20, 2013 by meena.p

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If $\int \large\frac{\sin ^8 x -\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x}$$dx=A \sin 2x+B,$ then $A=$

asked Sep 20, 2013 by meena.p

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$\large\int \bigg(\sqrt {\large\frac{a+x}{a-x}}+\sqrt {\large\frac{a-x}{a+x}}\bigg)$$dx= $

asked Sep 20, 2013 by meena.p

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$u=u(x,y)=\sin (y+ax)-(y+ax)^2=>$

asked Sep 20, 2013 by meena.p

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The length of the sub tangent at any point $(x_1,y_1)$ on the curve$y=5^x$

asked Sep 20, 2013 by meena.p

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If the distance travelled by a particle in time $t$ is given by $s=t^2-2t+5$ then its acceleration is

asked Sep 20, 2013 by meena.p

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If $1^{\circ}=\alpha$ radians then the approximate value of $\cos(60^{\circ}1')$ is

asked Sep 20, 2013 by meena.p

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If $ y =\large\frac{\log_{\Large e}x}{x}$ and $z= \log_ ex,$ then $\large\frac{d^2y}{dz^2}+\frac{dy}{dx}=$

asked Sep 20, 2013 by meena.p

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If $f(x) =|x|+ | \sin x|$ for $x \in \bigg(-\large\frac{\pi}{2},\frac{\pi}{2}\bigg),$ then its left hand derivative at $x=0$ is

asked Sep 20, 2013 by meena.p

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If $\cos^{-1}\bigg(\large\frac{x^2-y^2}{x^2+y^2}\bigg)=k$ (a constant ), then $\large\frac{dy}{dx}=$

asked Sep 20, 2013 by meena.p

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If $y=(1+x)(1+x^2)(1+x^4)........(1+x^{2^{n}}),$ then $\bigg(\large\frac{dy}{dx}\bigg)_{x =0}=$

asked Sep 20, 2013 by meena.p

1 answer

If [x] denotes the greatest integer not exceeding x and if the function f defined by \[f(x) = \left\{ \begin{array}{l l} \frac{a+2 \cos x}{x^2} & \quad ( x < 0) \\ b\;\tan \frac{\pi}{[x+4]} & \quad (x \geq 0) \end{array} \right. \] is continuous at $x=0,$ then the ordered pair $(a,b)=$

asked Sep 20, 2013 by meena.p

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$\lim\limits_{x \to 8} \large\frac{\sqrt {1+\sqrt {1+x}}-2}{x-8}=$

asked Sep 19, 2013 by meena.p

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Identify Phenacetin from the following :

asked Sep 19, 2013 by meena.p

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The number of hydrogen bonds between Guanine & Cytosine; and between Adenine & Thymine in DNA is :

asked Sep 19, 2013 by meena.p

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Example of a biodegradable polymer pair is :

asked Sep 19, 2013 by meena.p

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Identify $X$and $Y$ in the following reactions:

asked Sep 19, 2013 by meena.p

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The $pK_a$ values of four carboxylic acids are given below. Identify the weakest carboxylic acid.

asked Sep 19, 2013 by meena.p

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The structure of PCC is :

asked Sep 19, 2013 by meena.p

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The product formed in the reaction of phenol with $Br_2$ dissolved in $CS_2$ at $0^{\circ}$ are :

asked Sep 19, 2013 by meena.p

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Heating chloroform with aqueous sodium hydroxide solution forms:

asked Sep 19, 2013 by meena.p

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In which of the following properties, the two enantiomers of lactic acid differ from each other?

asked Sep 19, 2013 by meena.p

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Assertion (A): $-NH_2$ group of aniline is ortho, para directing in electrophilic substitutions. Reason (R) : $-NH_2$ group stabilizes the arenium ion formed by the ortho, para attack of the electrophile.

asked Sep 19, 2013 by meena.p

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$C_2H_6 \to C_2H_4+H_2$ above reaction is called as ___________ .

asked Sep 19, 2013 by meena.p

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Which one of the following gives Prussion blue colour?

asked Sep 19, 2013 by meena.p

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Cataract and skin cancer are caused by _________ .

asked Sep 19, 2013 by meena.p

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Which of the following is not added during the extraction of silver by cyanide process?

asked Sep 19, 2013 by meena.p

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A compound absorbs light in the wavelength region 490-500 nm. Its complementary colour is:

asked Sep 19, 2013 by meena.p

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Liquid $\underline{X}$ is used in Bubble chamber to detect neutral mesons and gamma photons. Then ,$\underline{X}= \underline{X}$

asked Sep 19, 2013 by meena.p

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The role of copper diaphragm in Whytlaw-Gray's method is :

asked Sep 19, 2013 by meena.p

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