Recent questions tagged 2009

The locus of center of a circle which passes through the origin and cuts off a length of 4 units from the line $x=3$ is :

asked Oct 10, 2013 by meena.p

1 answer

The equation of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x- and y- axis respectively, are :

asked Oct 10, 2013 by meena.p

1 answer

The pair of straight line $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2+x-2=0$ form a:

asked Oct 10, 2013 by meena.p

1 answer

The area (in square units) of the triangle formed by $x+y+1=0$ and the pair of straight lines $x^2-3xy+2y^2=0$ is :

asked Oct 10, 2013 by meena.p

1 answer

The value of $\lambda$ with $|\lambda| < 16$ such that $2x^2-10xy+12y^2+5x+\lambda y -3=0$ represents a pair of straight lines, is :

asked Oct 10, 2013 by meena.p

1 answer

The equation of the straight line perpendicular to the straight line $3x+2y=0$ and passing through the point of intersection of the lines $x+3y-1=0$ and $x-2y+4=0$ is :

asked Oct 10, 2013 by meena.p

1 answer

The points on the line $3x+4y=5$ which is equidistant from (1,2) and (3,4) is :

asked Oct 10, 2013 by meena.p

1 answer

The area (in square units) of the circle which touches the lines $4x+3y=15$ and $4x+3y=5$ is :

asked Oct 10, 2013 by meena.p

1 answer

The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle $36^{\circ}$ is :

asked Oct 10, 2013 by meena.p

0 answers

If $X$ is a binomial variate with the range $\{0,1,2,3,4,5,6\}$ and $P(X=2)=4P(X=4),$ then the parameter p of X is :

asked Oct 9, 2013 by meena.p

1 answer

If $m$ and $\sigma^2$ are the mean and variance of the random variable X, whose distribution is given by: X=x: 0 1 2 3 P(X=x): 1/3 1/2 0 1/6 then:

asked Oct 9, 2013 by meena.p

1 answer

Suppose that $E_1$ and $E_2$ are two events of a random experiment such that $P(E_1)=\large\frac{1}{4},$$ P(E_2/E_1)=\large\frac{1}{4},$ Observe the lists given below:

asked Oct 9, 2013 by meena.p

1 answer

The probability of choosing randomly a number c from the set {1,2,3,......,9} such that the quadratic equation $x^2+4x+c=0$ has real roots is :

asked Oct 9, 2013 by meena.p

1 answer

If $A$ and $B$ are events of a random experiment such that $P(A \cup B)=\large\frac{4}{5},$$ P(\bar {A} \cup \bar {B})=\large\frac{7}{10}$ and $P(B)=\large\frac{2}{5},$ then $P(A)=$

asked Oct 9, 2013 by meena.p

1 answer

The volume of the tetrahedron having the edges $\overrightarrow {i}+2 \overrightarrow {j}-\overrightarrow {k},\overrightarrow {i}+\overrightarrow {j}+ \overrightarrow {k},\overrightarrow {i}+\overrightarrow {j}+ \lambda \overrightarrow {k}$ as coterminous, is $\large\frac{2}{3} $ cubic units. Then $\lambda=$

asked Oct 9, 2013 by meena.p

1 answer

Suppose $\overrightarrow {a}= \lambda \overrightarrow {i}- 7 \overrightarrow {j}+3 \overrightarrow {k}, \overrightarrow {b}= \lambda \overrightarrow {i}+\overrightarrow {j}+2 \lambda \overrightarrow {k}$. If the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$ is greater than $90^{\circ},$ then $\lambda$ satisfies the inequality:

asked Oct 9, 2013 by meena.p

1 answer

If $m_1,m_2,m_3$ and $m_4$ are respectively the magnitudes of the vectors $\overrightarrow{a_1}=2 \overrightarrow{i}-\overrightarrow{j}+\overrightarrow{k},\;\;\overrightarrow{a_2}=3 \overrightarrow{i}-4\overrightarrow{j}-4\overrightarrow{k},\;\;\overrightarrow{a_3}=\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k}$ and $\overrightarrow{a_4}=-\overrightarrow{i}+3 \overrightarrow{j}+\overrightarrow{k}$ then the correct order of $m_1,m_2,m_3,m_4$ is :

asked Oct 9, 2013 by meena.p

1 answer

If $\overrightarrow {a}=-\overrightarrow {i}+\overrightarrow {j}+2\overrightarrow {k} , \overrightarrow {b}=2\overrightarrow {i}-\overrightarrow {j}-\overrightarrow {k}$ and $\overrightarrow {c}=-2 \overrightarrow {i}+\overrightarrow {j}+3 \overrightarrow {k},$ then the angle between $2 \overrightarrow {a}-\overrightarrow {c}$ and $\overrightarrow {a}+\overrightarrow {b}$ is :

asked Oct 9, 2013 by meena.p

1 answer

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0,l^2+m^2-n^2=0$ is :

asked Oct 9, 2013 by meena.p

1 answer

In a quadrilateral $ABCD,$ the point P divides DC in the ratio $1:2$ and Q is the mid point of AC.If $\overrightarrow {AB}+2 \overrightarrow {AD}+\overrightarrow {BC}-2 \overrightarrow {DC}=k \overrightarrow {PQ}$, then $k= $

asked Oct 9, 2013 by meena.p

1 answer

$P$ is a point on the segment joining the feet of two vertical poles of heights $a$ and $b$. The angles of elevation of the tops of the poles from P are $45^{\circ}$ each. Then the square of the distance between the tops of the poles is :

asked Oct 9, 2013 by meena.p

1 answer

In a $\Delta ABC \; \large\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$$=$

asked Oct 9, 2013 by meena.p

1 answer

In any $\Delta ABC,a(b \cos C-c \cos B)=$

asked Oct 9, 2013 by meena.p

0 answers

$ \sin h^{-1} 2+ \sin h^{-1}3=x => \cos h\; x=$

asked Oct 9, 2013 by meena.p

1 answer

$\cos ^{-1}\bigg(\large\frac{-1}{2}\bigg)$$-2 \sin ^{-1} \bigg(\large\frac{1}{2}\bigg)$$+3 \cos ^{-1} \bigg(\large\frac{-1}{\sqrt 2}\bigg)$$-4 \tan ^{-1}(-1)=$

asked Oct 9, 2013 by meena.p

1 answer

If $3 \cos x \neq 2 \sin x,$ then the general solution of $\sin ^2 x -\cos 2x=2 -\sin 2x$ is $x=$

asked Oct 9, 2013 by meena.p

1 answer

$\cos A \cos 2A \cos 4A....... \cos 2^{n-1} A=$

asked Oct 9, 2013 by meena.p

1 answer

$\large\frac{\cos x}{\cos (x-2y)}$$=\lambda => \tan (x-y) \tan y=$

asked Oct 9, 2013 by meena.p

1 answer

The period of $\sin ^4 x+\cos ^4x $ is :

asked Oct 9, 2013 by meena.p

1 answer

If $n$ is an integer which leaves remainder one when divided by three, then $(1+\sqrt {3}i)^n+(1-\sqrt {3}i)^n=$

asked Oct 9, 2013 by meena.p

1 answer

The locus of z satisfying the inequity $\bigg|\large\frac{z+2i}{2z+i}\bigg| < 1,$ where $z=x+iy,$ is :

asked Oct 9, 2013 by meena.p

1 answer

If $\alpha$ and $\beta$ are the roots of $x^2-2x+4=0,$ then the value of $\alpha ^6+\beta ^6$ is :

asked Oct 9, 2013 by meena.p

1 answer

If $\begin{bmatrix} 1 & -1 & x \\ 1 & x & 1 \\ x & -1 &1 \end {bmatrix}$ has no inverse, then the real value of x is :

asked Oct 9, 2013 by meena.p

1 answer

If $x,y,z$ are all positive and are the $p$th, $q$th and $r$th terms of a geometric progression respectively, then the value of the determinant $\begin{vmatrix} \log x & p & 1 \\ \log z & r &1 \\ \log z & r & 1 \end{vmatrix}=$

asked Oct 9, 2013 by meena.p

1 answer

If one of the roots of $\begin {vmatrix} 3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3 \end {vmatrix}=0$ is $-10,$ then the other roots are :

asked Oct 9, 2013 by meena.p

1 answer

Let A and B be two symmetric matrices of same order. Then the matrix $AB-BA$ is :

asked Oct 9, 2013 by meena.p

1 answer

If $f(x) =2x^4-13 x^2+ax+b$ is divisible by $x^2-3x+2$, then $(a,b) = $

asked Oct 9, 2013 by meena.p

2 answers

If $\alpha, \beta,\gamma$ are the roots of $x^3+4x+1=0,$ then the equation whose roots are $\large\frac{\alpha^2}{\beta +\gamma},\frac{\beta^2}{\gamma+\alpha},\frac{\gamma^2}{\alpha+\beta}$ is :

asked Oct 9, 2013 by meena.p

1 answer

Let $f(x)=x^2+ax+b,$ where $a,b \in R$. If $f(x) =0$ has all its roots imaginary, then the roots of $f(x)+f'(x)+f''(x)=0$ are:

asked Oct 9, 2013 by meena.p

1 answer

The roots of $(x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0,a \in R$ are always:

asked Oct 9, 2013 by meena.p

1 answer

$\large\frac{1}{e^{3x}}$$(e^x+e^{5x})=a_0+a_1x+a_2x^2+.........=>\; 2a_1+2^3a_3+2^5a_5+........=$

asked Oct 9, 2013 by meena.p

1 answer

For $|x| < 1$, the constant term in the expansion of $\large\frac{1}{(x+1)^2(x-2)}$ is :

asked Oct 9, 2013 by meena.p

1 answer

If x is numerically so small so that $x^2$ and higher powers of x can be neglected, then $\bigg(1+ \large\frac{2x}{3}\bigg)^{\large\frac{3}{2}}$$.(32+5x)^{\large\frac{-1}{5}}$ is approximately equal to :

asked Oct 8, 2013 by meena.p

1 answer

The coefficient of $x^{24}$ in the expansion of $(1+x^2)^{12}(1+x^{12}) (1+x^{24})$ is :

asked Oct 8, 2013 by meena.p

1 answer

A binary sequence is an array of 0's and 1's. The number of n-digit binary sequences which contain even number of 0's is :

asked Oct 8, 2013 by meena.p

1 answer

A binary sequence is an array of $0's $ and $1's$. The number of n-digit binary sequences which contain even number of $0's$ is:

asked Oct 8, 2013 by meena.p

1 answer

$p$ points are chosen on each of the three co planar lines. The maximum number of triangles formed with vertices at these points is :

asked Oct 8, 2013 by meena.p

1 answer

The number of subsets of $\{1,2,3......,9\}$ containing at least one odd number is :

asked Oct 8, 2013 by meena.p

1 answer

Using mathematical induction, the numbers $a_n\;'s$ are defined by, $a_0=1,a_{n+1}=3n^2+n+a_n( n \geq 0)$. Then $a_n=$

asked Oct 8, 2013 by meena.p

1 answer

$\bigg \{ x \in R :\large\frac{2x-1}{x^3+4x^2+3x} \in $$R \bigg \} =$

asked Oct 8, 2013 by meena.p

1 answer

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