Recent questions tagged 2014

Phthalic acid reacts with resorcinol in the presence of concentrated $\;H_{2}SO_{4}\;$ to give :

asked May 22, 2014 by yamini.v

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Which of the following will not show mutarotation ?

asked May 21, 2014 by yamini.v

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Aminoglycosides are usually used as :

asked May 21, 2014 by yamini.v

1 answer

Which one of the following acids does not exhibit optical isomerism ?

asked May 21, 2014 by yamini.v

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Which of the following molecules has two sigma $\sigma\;$ and two pi $\pi\;$ bonds ?

asked May 21, 2014 by yamini.v

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Let p,q,r denote arbitrary statements . Then the logically equivalent of the statement $\;p \Rightarrow (q \lor r)\;$ is :

asked May 21, 2014 by yamini.v

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If $\;f(\theta) = \begin{vmatrix} 1 & cos\theta &1 \\[0.3em] -sin\theta & 1 & \cos \theta \\[0.3em] -1 & sin \theta & 1\end{vmatrix}\;$ and A and B are respectively the maximum and the minimum values of $\;f(\theta)\;$ , then (A ,B) is equal to :

asked May 21, 2014 by yamini.v

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Statement I : The equation $\;(sin^{-1} x)^{3} + (cos^{-1} x)^{3} - a \pi^{3}=0\;$ has a solution for all $\;a \geq \large\frac{1}{32}\;$ .\[\] Statement II : For any $\;x \in R\;, sin^{-1}x+cos^{-1}x=\large\frac{\pi}{2}\;$ and $\; 0 \leq (sin^{-1}x - \large\frac{\pi}{4})^{2} \leq \large\frac{9 \pi^{2}}{16}\;$ .

asked May 21, 2014 by yamini.v

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A number x is chosen at random from the set $\;\{ 1,2,3,4,...,100\}\;$ .Define the event : A= the chosen number x satisfies $\;\large\frac{(x-10)(x-50)}{(x-30)} \geq 0\;$ Then P(A) is :

asked May 21, 2014 by yamini.v

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Let $\;\overline{x}\;$ M.D. be the mean and the mean deviation about $\;\overline{x}\;$ on n observations $\;x_{i} , i=1,2,...,n\;$.If each of the observations is increased by 5 , then the new mean and the mean deviation about the new mean , respectively , are :

asked May 21, 2014 by yamini.v

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If $\;\hat{x} , \hat{y}\;$ and $\;\hat{z}\;$ are three unit vectors in three - dimensional space , then the minimum value of $\;|\hat{x} + \hat{y}|^{2} + |\hat{y} + \hat{z}|^{2} + |\hat{z} + \hat{x}|^{2}\;$ :

asked May 21, 2014 by yamini.v

0 answers

If the distance between planes , $\;4x - 2y -4z+1=0\;$ and $\;4x - 2y -4z+d=0\;$ is 7 , then d is :

asked May 21, 2014 by yamini.v

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A symmetrical form of the line of intersection of the planes $\;x=ay+b\;$ and $\;z=cy+d\;$ is :

asked May 21, 2014 by yamini.v

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The minimum area of a triangle formed by any tangent to the ellipse $\;\large\frac{x^{2}}{16}+\large\frac{y^{2}}{81} =1\;$ and the co - ordinate axes is :

asked May 21, 2014 by yamini.v

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Two tangents are drawn from a point (-2 ,-1) to the curve , $\;y^{2}=4x\;$ . If $\;\alpha\;$ is the angle between them , then $\;|tan \alpha|\;$ is equal to :

asked May 21, 2014 by yamini.v

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For the two circles $\;x^{2}+y^{2}=16\;$ and $\;x^{2}+y^{2}-2y=0\;$ , there is/are :

asked May 21, 2014 by yamini.v

1 answer

If the three distinct lines $\;x+2ay+a=0\;,x+3by+b=0\;$ and $\;x+4ay+a=0\;$ are concurrent , then the point (a,b) lines on a :

asked May 21, 2014 by yamini.v

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If a line intercepted between the coordinate axes is trisected at a point $\;A(4,3)\;$ , which is nearer to x - axis, then its equation is :

asked May 21, 2014 by yamini.v

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The general solution of the differential equation , $\;sin 2x (\large\frac{dy}{dx} - \sqrt{tanx})-y=0 \;$, is :

asked May 21, 2014 by yamini.v

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If for a continuous function f(x) , $\;\int \limits_{\pi}^{t} (f(x)+x) dx = \pi^{2}-t^{2}\;$ , for all $\;t \geq -\pi\;$ , then $\;f(- \large\frac{\pi}{3})\;$ is equal to :

asked May 21, 2014 by yamini.v

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If [] denotes the greatest integer function , then the integral $\;\int \limits_{0}^{\pi} [cos x] dx\;$ is equal to :

asked May 21, 2014 by yamini.v

1 answer

The integral $\;\int \large\frac{sin^{2}x cos^{2}x}{(sin^{3} x +cos^{3} x )^{2}} dx\;$ is equal to :

asked May 21, 2014 by yamini.v

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If $\;1+x^{4}+x^{5} = \sum_{i=0}^{5} a_{i} (1+x)^{i}\;$, for all x in R , then $\;a_{2}\;$ is :

asked May 21, 2014 by yamini.v

0 answers

Let f and g be two differential functions on R such that $\;f^{'}(x) > 0\;$ and $\;g^{'}(x) > 0\;$ for all $\; x \in R\;$. Then for all x :

asked May 21, 2014 by yamini.v

0 answers

If $\;f(x) = x^{2}-x+5\;,x > \large\frac{1}{2}\;$ , and $\;g(x)\;$ is its inverse function , then $\;g^{'}(7)\;$ equals :

asked May 21, 2014 by yamini.v

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Let $\;f , g :R \to R\;$be two functions defined by $\;f(x)=\{ \begin{matrix}x sin(\large\frac{1}{x}) \;, x \neq 0 \\ 0\;,x=0 \end{matrix}\;$ , and $\;g(x)=x f(x)\;$\[\] Statement I : f is a continuous function at x=0 .\[\] Statement II : g is differential function at x=0 .

asked May 21, 2014 by yamini.v

0 answers

The least positive integer n such that $\;1-\large\frac{2}{3} -\large\frac{2}{3^{2}}- ..... -\large\frac{2}{3^{n-1}} < \large\frac{1}{100}\;$, is :

asked May 21, 2014 by yamini.v

1 answer

Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of $\;\large\frac{1}{a} \;$ and $\;\large\frac{1}{b}\;$ . If $\;\large\frac{1}{M} : G \;$ is 4 : 5 , then a : b can be :

asked May 21, 2014 by yamini.v

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If $\;(2 + \large\frac{x}{3})^{55}\;$ is expanded in the ascending powers of x in two consecutive terms of the expansion are equal , then these terms are :

asked May 21, 2014 by yamini.v

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If $\; A=\begin{bmatrix} 1 & 2 & x \\[0.3em] 3 & -1 & 2\end{bmatrix}\;$ and $\; B=\begin{bmatrix} y & x & 1\end{bmatrix}\;$ be such that $\;AB= \begin{bmatrix} 6 \\[0.3em] 8 \end{bmatrix}\;$ , then :

asked May 21, 2014 by yamini.v

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If $\; \begin{vmatrix} a^{2} & b^{2} & c^{2} \\[0.3em] (a+\lambda)^{2} &(b+\lambda)^{2} & (c+\lambda)^{2} \\[0.3em] (a-\lambda)^{2} & (b-\lambda)^{2} & (c-\lambda)^{2} \\[0.3em] \end{vmatrix}=k \lambda \begin{vmatrix} a^{2} & b^{2} & c^{2} \\[0.3em] a & b& c \\[0.3em] 1 & 1 & 1 \end{vmatrix}\;,\lambda \neq 0\;$ , then k is equal to :

asked May 21, 2014 by yamini.v

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8 - digit number are formed using the digits 1,1,2,2,2,3,4,4.The number of such numbers in which the odd digits do not occupy odd places , is :

asked May 20, 2014 by yamini.v

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The sum of the roots of the equation ,$\;x^{2}+|2x-3|-4=0\;$ is :

asked May 20, 2014 by yamini.v

1 answer

Let $\;z \neq -i\;$ be any complex number such that $\;\large\frac{z-i}{z+i}\;$ is a purely imaginary number . Then $\;z+ \large\frac{1}{z}\;$ is :

asked May 20, 2014 by yamini.v

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A relation on the set $\;A=\{x:|x| < 3 , x \in Z\}\;$ where Z is the set of integers is defined by $\;R=\{(x,y) : y=|x| , x \neq -1\}\;$. Then the number of elements in the power set of R is :

asked May 20, 2014 by yamini.v

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A zener diode is connected to a battery and a load as shown below : The currents $\;I,I_{Z}\;$ and $\;I_{L}\;$ are respectively

asked May 20, 2014 by yamini.v

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A radioactive nuclei with decay constant 0.5/s is being produced at a constant rate of 100 nuclei/s . If at t=0 there were no nuclei , the time when there are 50 nuclei is :

asked May 20, 2014 by yamini.v

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A photon of wavelength $\;\lambda\;$ is scattered from an electron , which was at rest .The wavelength shift $\;\bigtriangleup \lambda\;$ is three times of $\;\lambda\;$ and the angle of scattering $\;\theta\;$ is $\;60^{0}\;$ . The angle at which the electron recoiled is $\;\phi\;$ .The value of $\;tan \phi\;$ is : (electron speed is much smaller than the speed of light)

asked May 20, 2014 by yamini.v

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In a compound microscope the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm .When object is kept at 1.25 cm in front of objective , final image is formed at infinity . Magnifying power of the compound microscope should be :

asked May 20, 2014 by yamini.v

1 answer

Two monochromatic light beams of intensity 16 and 9 units are interfacing .The ratio of intensities of bright and dark parts of the resultant pattern is :

asked May 20, 2014 by yamini.v

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An object is located in a fixed position in front of a screen .Sharp image is obtained on the screen for two positions of a thin lens are separated by 10 cm .The size of the images in two situations are in the ratio 3 : 2 . What is the distance between the screen and the object ?

asked May 20, 2014 by yamini.v

1 answer

An electromagnetic field wave of frequency $\;1 \times 10^{14} \;$ hertz is propagating along z - axis . The amplitude of electric field is 4 V/m .If $\;\in_{0}=8.8 \times 10^{-12}\;C^{2}/N-m^{2}\;$ , then average energy density of electric field will be :

asked May 20, 2014 by yamini.v

0 answers

A coil of circular cross - section having 1000 turns and $\;4\;cm^{2}\;$ face area is placed with its axis parallel to a magnetic field which decreases by $\;10^{-2}\;Wb\;m^{-2}\;$ in 0.01 s. The e.m.f induced in the coil is :

asked May 20, 2014 by yamini.v

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Three identical bars A,B and C are made of different magnetic materials .When kept in a uniform magnetic field , the field lines around them look as follows : Make the correspondence of these bars with their material being diamagnetic (D) ,ferromagnetic (F) and paramagnetic (P) :

asked May 20, 2014 by yamini.v

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Three straight parallel current carrying conductors are shown in the figure . The force experienced by the middle conductor of length 25 cm is :

asked May 20, 2014 by yamini.v

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In the circuit shown , current (in A) through the 50 V and 30 V batteries are , respectively :

asked May 20, 2014 by yamini.v

1 answer

A parallel plate capacitor is made of two plates of length l , width w and separated by distance d . A dielectric slab (dielectric constant K) that fits exactly between the plates is held near the edge of the plates .It is pulled into the capacitor by a force $\;F=-\large\frac{\partial U}{\partial x}\;$ where U is the energy of the capacitor up to distance x (See figure) .If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is :

asked May 20, 2014 by yamini.v

1 answer

A cone of base radius R and height h is located in a uniform electric field rightarrow{E}$\;\over\;$ parallel to its base. The electric flux entering the cone is :

asked May 20, 2014 by yamini.v

0 answers

Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2 m/s.The velocity of sound is 320 m/s.The number of beats heard by the person in one second will be :

asked May 20, 2014 by yamini.v

0 answers

The angular frequency of the damped oscillator is given by , $\;w=\sqrt{\large\frac{k}{m}-\large\frac{r^{2}}{4m^{2}}}\;$ where k is the spring constant , m is the mass of the oscillator and r is the damping constant.If the ratio $\;\large\frac{r^{2}}{mk}\;$ is $\;8\%\;$ , the change in time period compared to the undamped oscillator is approximately as follows :

asked May 20, 2014 by yamini.v

1 answer

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