Recent questions tagged 2014

Let A and B be two events such that $\;P (\overline{A \cup B}) = \large\frac{1}{6}\;,P (\overline{A \cap B}) = \large\frac{1}{4} \;$ where $\;\overline{A}\;$ stands for the compliment of the event A .Then the events A and B are :

asked May 2, 2014 by yamini.v

0 answers

If $\;[\overrightarrow{a} \times \overrightarrow{b} \;\;\overrightarrow{b}\times \overrightarrow{c} \;\;\overrightarrow{c} \times \overrightarrow{a} ]= \lambda [\overrightarrow{a}\;\overrightarrow{b}\;\overrightarrow{c}]^{2}\;$ then $\;\lambda\;$ is equal to :

asked May 2, 2014 by yamini.v

0 answers

The angle between the lines whose direction cosines satisfy the equations $\;l+m+n=0\;$ and $\;l^{2}=m^{2}+n^{2}\;$ is :

asked May 2, 2014 by yamini.v

0 answers

The image of the line $\;\large\frac{x-1}{3} =\large\frac{y-3}{1} =\large\frac{z-4}{-5}\;$ in the plane $\;2x-y+z+3=0\;$ is the plane :

asked May 2, 2014 by yamini.v

0 answers

The slope of the line touching both the parabolas $\;y^{2}=4x\;$ and $\;x^{2}=-32y\;$ is :

asked May 2, 2014 by yamini.v

0 answers

Let C be the circle with centre at (1,1) and radius=1 . If T is the circle centred at (0,y) ,passing through origin and touching the circle C externally ,then the radius of T is equal to :

asked May 2, 2014 by yamini.v

0 answers

The locus of the foot of perpendicular drawn from the centre of the ellipse $\;x^{2}+3y^{2}=6\;$ on any tangent to it is :

asked May 2, 2014 by yamini.v

1 answer

Let a,b,c and d be non-zero numbers .If the point of intersection of the lines $\;4ax+2ay+c=0\;$ and $\;5bx+2by+d=0\;$ lies in the fourth quadrant and is equidistant from the two axis then :

asked May 2, 2014 by yamini.v

0 answers

Let PS be the median of the triangle with vertices P(2,2) , Q(6,-1) and R(7,3) . The equation of the line passing through (1,-1) and parallel to PS is :

asked May 2, 2014 by yamini.v

0 answers

Let the population of rabbits surviving at a time t be governed by the differential equation $\; \large\frac{d p(t)}{dt} = \large\frac{1}{2} p(t) -200 \;$ . If$\;p(0) = 100\;$ , then $\;p(t)\;$ equals :

asked May 2, 2014 by yamini.v

1 answer

The area of the region described by $\;A=\{(x,y) : x^{2}+y^{2} \leq 1 \;and\; y^{2} \leq 1-x\}\;$ is :

asked May 2, 2014 by yamini.v

0 answers

The integral $\; \int_{0}^{\pi} \sqrt{1+4sin^{2} \large\frac{x}{2}-4 sin \large\frac{x}{2}} dx\;$ equals :

asked May 2, 2014 by yamini.v

0 answers

The integral $\;\int (1+x-\large\frac{1}{x})\;e^{x+\large\frac{1}{x}} dx\;$ is equal to :

asked May 2, 2014 by yamini.v

0 answers

If x=-1 and x=2 are extreme points of $\;f(x) =\alpha log|x|+ \beta x^{2}+x\;$ then :

asked May 2, 2014 by yamini.v

0 answers

If f and g are differentiable functions in [0 , 1] satisfying $\;f(0)=2=g(1)\;,g(0)=0\;$ and $\;f(1)=6\;$, then for some $\;c \in ]0 ,1[\;$ :

asked May 1, 2014 by yamini.v

0 answers

If g is the inverse of a function f and $\;f^{'}(x) =\large\frac{1}{1 + x^{5}}\;$ , then $\;g^{'}(x)\;$ is equal to :

asked May 1, 2014 by yamini.v

0 answers

$\; \lim_{x \to 0} \large\frac{sin (\pi cos^{2} x)}{x^{2}}\;$ is equal to :

asked May 1, 2014 by yamini.v

0 answers

Three positive numbers from an increasing G.P. if the middle term in this G.P. is doubled , the new numbers are in A.P. Then the common ratio of the G.P. is :

asked May 1, 2014 by yamini.v

0 answers

If $\;(10)^{9} + 2 (11)^{1} (10)^{8} + 3(11)^{2} (10)^{7}+....+10 (11)^{9} = k (11)^{9}\;$, then k is equal to :

asked May 1, 2014 by yamini.v

0 answers

If the coefficients of $\;x^{2}\;$ and $\;x^{3}\;$ in the expansion of $\;(1+ax+bx^{2}) (1-2x)^{18}\;$ in powers of x are both zero , then (a,b) is equal to :

asked May 1, 2014 by yamini.v

0 answers

If A is an $\;3 \times 3\;$ non - singular matrix such that $\;A^{'}A=AA^{'}\;$ and $\;B=A^{-1}A^{'}\;$ , then $\;BB^{'} =\;$ :

asked May 1, 2014 by yamini.v

0 answers

Let $\;\alpha\;$ and $\;\beta\;$ be the roots of equation $\;px^{2} +qx + r=0\;,p \neq 0\;$ .if p ,q ,r are in A.P. and $\;\large\frac{1}{\alpha} + \large\frac{1}{\beta}=4\;$ then the value of $\;|\alpha - \beta|\;$ is :

asked May 1, 2014 by yamini.v

0 answers

If $\; a \in R\;$ and the equation $\;-3(x-[x])^{2} + 2(x-[x]) + a^{2} =0\;$ (where [x] denotes the greatest integer $\; \leq x )\;$ has no integral solution , then all possible values of a lie in the interval :

asked May 1, 2014 by yamini.v

0 answers

If z is a complex number such that $\;|z| \geq 2\;$ , then the minimum value of $\;|z + \large\frac{1}{2}|\;$ :

asked May 1, 2014 by yamini.v

0 answers

If $\; (X =4^{n} -3n-1) : n \in N \;$ and $\;Y=9(n-1) : n \in N\;$ where N is the set of natural numbers then $\;X \cup Y\;$ is equal to :

asked May 1, 2014 by yamini.v

0 answers

In the reaction , $\;CH_{3}OOH\; \underrightarrow{LiAlH_{4}}\; A \; \underrightarrow{PCl_{5}}\;B\;\underrightarrow{Alc.KOH}\;C \; $ , the product C is :

asked May 1, 2014 by yamini.v

0 answers

Which one of the following bases is not present in DNA ?

asked May 1, 2014 by yamini.v

0 answers

Which one is classified as a condensation polymer ?

asked May 1, 2014 by yamini.v

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Considering the basic strength of amines in aqueous solution , which one has the smallest $\;pK_{b}\;$ value ?

asked May 1, 2014 by yamini.v

0 answers

The major organic compound formed by the reaction of 1 ,1 ,1 - trichloroethane with silver powder is :

asked May 1, 2014 by yamini.v

1 answer

The most suitable reagent for the conversion of $\;R - CH_{2} - OH \to R - CHO \; $ is :

asked May 1, 2014 by yamini.v

0 answers

On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide , the organic compound formed is :

asked May 1, 2014 by yamini.v

1 answer

In $\;S_{N}2\;$ reactions , the correct order of reactivity for the following compounds : $\;CH_{3}Cl\;,CH_{3}CH_{2}Cl\;,(CH_{3})_{2}CHCl\;$ and $\;(CH_{3})_{3}CCl\;$ is :

asked May 1, 2014 by yamini.v

0 answers

The equation which is balanced and represents the correct product(s) is :

asked May 1, 2014 by yamini.v

0 answers

Which series of reactions correctly represents chemical reactions related to iron its compound ?

asked May 1, 2014 by yamini.v

0 answers

Given below are the half - cell reactions : $\;Mn^{2+}+2e^{-} \to Mn\;:E^{0}=-1.18\;V\;$ $\qquad \qquad \qquad \qquad\;$ $\qquad \qquad \qquad \qquad\;$ $\;2(Mn^{3+}+e^{-} \to Mn^{2+})\;:E^{0}=+1.51\;V\;$ $\qquad \qquad \qquad \qquad\;$ $\qquad \qquad \qquad \qquad\;$ $\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad\;$ The $\;E^{0}\;$ for $\;3Mn^{2+} \to Mn +2Mn^{+}\;$

asked May 1, 2014 by yamini.v

0 answers

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture 1:4 . The ratio of number of their molecule is :

asked May 1, 2014 by yamini.v

0 answers

The correct statement for the molecule , $\;CsI_{3}\;:$ is

asked May 1, 2014 by yamini.v

0 answers

In which of the following reactions $\;H_{2}O_{2}\;$ acts as a reducing agent ?\[\] (1) $H_{2}O_{2}+2H^{+}+2e^{-} \to 2H_{2}O$\[\] (2) $H_{2}O_{2}-2e^{-} \to O_{2} + 2H^{+}$\[\] (3) $H_{2}O_{2}+2e^{-} \to 2OH^{-}$\[\] (4) $H_{2}O_{2}+2OH^{-}-2e^{-} \to O_{2} + 2H^{2}O$

asked May 1, 2014 by yamini.v

0 answers

Which one of the following properties is not shown by NO ?

asked May 1, 2014 by yamini.v

0 answers

The octahedral complex of a metal ion $\;M^{3+}\;$ with four monodentate ligands $\;L_{1}\;,L_{2}\;,L_{3}\;$ and $\;L_{4}\;$ absorb wavelengths in the region of red ,green ,yellow and blue respectively .The increasing order of ligand strength of the four ligands is :

asked May 1, 2014 by yamini.v

0 answers