Recent questions in Mathematics

If the line $y=2x+c,$ is a tangent to the circle $x^2+y^2=5,$ then a value of c is

asked Sep 23, 2013 by meena.p

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If $s$ and $p$ are respectively the sum and the product of the slope of the lines $3x^2-2xy-15y^2=0,$ then $s:p=$

asked Sep 23, 2013 by meena.p

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If $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines then $\sqrt {\large\frac{g^2-ac}{f^2-bc}}=$

asked Sep 23, 2013 by meena.p

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If one of the lines in the pair of straight lines given by $4x^2+6xy+ky^2=0$ bisects the angle between the coordinate axes, then $k \in$

asked Sep 23, 2013 by meena.p

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The line joining the points $A(2,0)$ and $B(3,1)$ is rotated through an angle of $45^{\circ}$, about A in the anticlockwise direction. The coordinates of B in the new position

asked Sep 23, 2013 by meena.p

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The image of the point $(3,8)$ in the line $x+3y=7$ is

asked Sep 23, 2013 by meena.p

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The number of points $P(x,y)$ with natural numbers as coordinates that the inside the quadrilateral formed by the lines $2x+y=2,y=0$ and $x+y=5 $ is

asked Sep 23, 2013 by meena.p

1 answer

If the vectors $\bar {AB}=-3 \bar {i}+ 4 \bar {k}$ and $\bar {AC}=5 \bar {i}-2 \bar j+4 \bar {k} $ are the sides of a triangle ABC, then the length of the medium through A is

asked Sep 23, 2013 by meena.p

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The locus of a point such that the sum of its distance from the points $(0,2)$ and $(0,-2)$ is $6,$ is

asked Sep 23, 2013 by meena.p

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The probability that an individual suffers a bad reaction from an injection is 0.001. The probability that out of 2000 individuals exactly three will suffer bad reaction is

asked Sep 23, 2013 by meena.p

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The probability distribution of a random variable $X$ is given below :X=x 0 1 2 3 P(X=x) $\frac{1}{10}$ $\frac{2}{10}$ $\frac{3}{10}$ $\frac{4}{10}$ Then the variance of $X$ is

asked Sep 23, 2013 by meena.p

1 answer

Let $A$ and $B$ be events in a sample spaces $S$ such that $P(A)=0.5, P(B)=0.4$ and $P(A \cup B)=0.6$. observe the following lists:

asked Sep 23, 2013 by meena.p

1 answer

Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is

asked Sep 23, 2013 by meena.p

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A class has fifteen boys and five girls. Suppose three students are selected at random from the class. The probability that three are two boys and one girl is

asked Sep 23, 2013 by meena.p

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Let $\bar {v}=2 \bar{i}+\bar {j}-\bar {k}$ and $\bar {w}=\bar {i}+3 \bar{k}$. If $ \bar u$ is any unit vector then the maximum value of the scalar triple product $(\bar {u} \; \bar {v}\; \bar {w})$ is

asked Sep 23, 2013 by meena.p

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If $|\bar {a}|=1$,$ |\bar {b}|=2$ and the angle between $\bar {a} $ and $\bar {b}$ is $120^{\circ},$ then $\{(\bar {a}+ 3 \bar {b}) \times (3 \bar {a}-\bar {b})\}^2=$

asked Sep 23, 2013 by meena.p

1 answer

For any vector $\bar r,\bar {i} \times (\bar {r} \times \bar {i}) \div \bar {j} \times (\bar {r} \times \bar {j})+ \bar k \times (\bar {r} \times {\bar k})=$

asked Sep 23, 2013 by meena.p

1 answer

If the vector $\bar {i}-2x \bar {j}-3 y \bar{k}$ and $\bar {i}+3 x \bar{ j}+2 y \bar {k}$ are orthogonal to each other, then the locus of the point $(x,y)$ is

asked Sep 23, 2013 by meena.p

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The magnitude of the projection of the vector $\bar {a}=4 \bar {i}-3 \bar {j}+2 \bar k $ on the line which makes equal angles with the coordinate axes is

asked Sep 23, 2013 by meena.p

1 answer

The angle of elevation of a stationary cloud from a point 2500 m above a lake is $15^{\circ}$ and from the same point the angle of depressed its reflection in the lake is $45^{\circ}$. The height (in meters) of the cloud above the lake , given that $\cot 15^{\circ}=2+\sqrt {3}$, is

asked Sep 23, 2013 by meena.p

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In a triangle $ABC$ if $\large\frac{\cos A}{a}=\frac {\cos B}{b} =\frac{\cos C}{c}$, then $\Delta ABC$ is

asked Sep 20, 2013 by meena.p

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In triangle ABC if $a \cos ^2 \large\frac{C}{2}$$+c \cos ^2 \large\frac{A}{2}=\frac{3b}{2}$, then the sides of the triangle are in

asked Sep 20, 2013 by meena.p

1 answer

For $0 < x \leq \pi, \sin h^{-1} (\cot x)=$

asked Sep 20, 2013 by meena.p

1 answer

$(\tan ^{-1}x)^2+(\cot ^{-1}x)^2=\large\frac{5 \pi^2}{8}$$=>x=$

asked Sep 20, 2013 by meena.p

1 answer

The most general value of $\theta$ which satisfies both the equations $\tan \theta=-1$ and $\cos \theta=\large\frac{1}{\sqrt 2}$ is :

asked Sep 20, 2013 by meena.p

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If $f(x)=\sin ^6 x+ \cos ^6x$ for $x \in IR,$ then $f(x)$ lies in the interval

asked Sep 20, 2013 by meena.p

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$\cos A =\large\frac{3}{4}$$=>32 \sin \bigg(\large\frac{A}{2}\bigg)$$ \sin \bigg(\large\frac{5A}{2}\bigg)=$

asked Sep 20, 2013 by meena.p

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If $f:IR \to IR$ is defined by $f(x)=7+ \cos (5x+3)$ for $ x \in IR,$ then the period of f is :

asked Sep 20, 2013 by meena.p

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$\large\frac{(1+i)^{2011}}{(1-i)^{2009}}=$

asked Sep 20, 2013 by meena.p

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The locus of the complex number z such that $arg \bigg (\large\frac{z-2}{z+2}\bigg)=\frac{\pi}{3}$ is :

asked Sep 20, 2013 by meena.p

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Let $z=a-\large\frac{i}{2};$$ \alpha \; \in IR.$ Then $|i+z|^2-|i-z|^2=$

asked Sep 20, 2013 by meena.p

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$\begin{vmatrix} 24 & 25 & 26\\ 25 & 26 & 27 \\ 26 & 27 & 27\end{vmatrix}=$

asked Sep 20, 2013 by meena.p

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$A=\begin{bmatrix} 1 & 0 & 1\\ 0 & 1 & 1 \\ 0 & 1 & 0\end{bmatrix} \;=>\;A^2-2A=$

asked Sep 20, 2013 by meena.p

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If A is a matrix such that $\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} A\begin{bmatrix} 1 & 1 \end{bmatrix} =\begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}$ then A=

asked Sep 20, 2013 by meena.p

1 answer

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

asked Sep 20, 2013 by meena.p

1 answer

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

1 answer

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

1 answer

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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