Recent questions tagged misc

The mean and standard deviation of six observations are $8$ and $4$ respectively. If each observation is multiplied by $3$, find the new mean and new standard deviation of the resulting observation.

asked Jul 1, 2014 by meena.p

1 answer

The mean and variance of $7$ observation are $8$ and $16$ respectively.If six of the observations are $2,4,10,12,14$. Find the remaining two observations.

asked Jul 1, 2014 by meena.p

1 answer

The mean and variance of eight observation are $9$ and $9.25$ respectively.If six of the observations are $6,7,10,12,12$ and $13$. Find the remaining two observations.

asked Jul 1, 2014 by meena.p

1 answer

Find the expansion of $(3x^2-2ax+3a^2)^3$ using Binomial theorem

asked Jun 24, 2014 by sreemathi.v

1 answer

Expand using Binomial theorem $(1+\large\frac{x}{2}-\frac{2}{x})^4$$\;\;x\neq 0$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find $x$ if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of $(4\sqrt 2+\large\frac{1}{4\sqrt 3})^n$ is $\sqrt 6 :1$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find an approximation of $(0.99)^5$ using the first three terms of its expansion.

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the value of $(a^2+\sqrt{a^2-1})^4+(a^2-\sqrt{a^2-1})^4$

asked Jun 24, 2014 by sreemathi.v

1 answer

Evaluate $(\sqrt 3+2)^6-(\sqrt 3-\sqrt 2)^6$

asked Jun 24, 2014 by sreemathi.v

1 answer

If $a$ and $b$ are distinct integers,prove that $a-b$ is a factor of $a^n-b^n$,whenever $n$ is a positive integer.

asked Jun 23, 2014 by sreemathi.v

1 answer

Find the coefficient of $x^5$ in the expansion of the product $(1+2x)^6(1-x)^7$

asked Jun 23, 2014 by sreemathi.v

1 answer

Find a if the coefficients of $x^2$ and $x^3$ in the expansion of $(3+ax)^9$ are equal.

asked Jun 23, 2014 by sreemathi.v

1 answer

Find $a,b$ and $n$ in the expansion of $(a+b)^n$ if the first three terms of the expansion are $729,7290$ and $30375$ respectively.

asked Jun 23, 2014 by sreemathi.v

1 answer

A person standing at the junction (crossing) of two straight paths represented by the equations $2x – 3y + 4 = 0$ and $3x + 4y – 5 = 0 $ wants to reach the path whose equation is $6x – 7y + 8 = 0$ in the least time. Find equation of the path that he should follow.

asked May 23, 2014 by thanvigandhi_1

1 answer

Prove that the product of the lengths of the perpendiculars drawn from the points $ ( \sqrt{a^2-b^2}, 0)$ and $ ( -\sqrt{a^2-b^2}, 0)$ to the line $ \large\frac{x}{a}$$ \cos \theta + \large\frac{y}{b}$$ \sin \theta = 1$ is $b^2$

asked May 23, 2014 by thanvigandhi_1

1 answer

A ray of light passing through the point (1, 2) reflects on the $x$ - axis at point $A$ and the reflected ray passes through the point (5, 3). Find the coordinates of $A$

asked May 23, 2014 by thanvigandhi_1

1 answer

Find equation of the line which is equidistant from parallel lines $9x + 6y – 7 = 0$ and $3x + 2y + 6 = 0.$

asked May 23, 2014 by thanvigandhi_1

1 answer

If sum of the perpendicular distances of a variable point $P (x, y)$ from the lines $ x + y – 5 = 0$ and $3x – 2y +7 = 0$ is always 10. Show that $ P$ must move on a line

asked May 22, 2014 by thanvigandhi_1

1 answer

If the lines $ y = 3x +1$ and $2y = x + 3$ are equally inclined to the line $y = mx + 4$, find the value of $m$.

asked May 22, 2014 by thanvigandhi_1

1 answer

Find the image of the point (3, 8) with respect to the line $x +3y = 7$ assuming the line to be a plane mirror

asked May 21, 2014 by thanvigandhi_1

1 answer

Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line $ x + y = 4$ may be at a distance of 3 units from this point

asked May 21, 2014 by thanvigandhi_1

1 answer

Find the distance of the line $4x + 7y + 5 = 0$ from the point (1, 2) along the line $2x-y=0$

asked May 21, 2014 by thanvigandhi_1

1 answer

In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

asked May 21, 2014 by thanvigandhi_1

1 answer

Show that the equation of the line passing through the origin and making an angle $ \theta $ with the line $y=mx+c$ is $ \large\frac{y}{x}$$ = \large\frac{m \pm \tan \theta}{1 \mp m \tan \theta}$

asked May 21, 2014 by thanvigandhi_1

1 answer

Find the equation of the line passing through the point of intersection of the lines $4x + 7y – 3 = 0$ and $2x – 3y + 1 = 0$ that has equal intercepts on the axes.

asked May 21, 2014 by thanvigandhi_1

1 answer

Find the equation of the lines through the point (3, 2) which make an angle of $45^{\circ}$ with the line $x-2y=3.$

asked May 20, 2014 by thanvigandhi_1

1 answer

If three lines whose equations are $y = m_1, x+ c_1, y = m_2, x+c_2$ and $y = m_3, x+c_3$ are concurrent, then show that $m_1(c_2-c_3)+m_2(c_3-c_1)+m_3(c_1-c_2)=0$

asked May 20, 2014 by thanvigandhi_1

1 answer

Find the value of $p$ so that the three lines $3x + y – 2 = 0, px + 2 y – 3 = 0$ and $2x – y – 3 = 0$ may intersect at one point.

asked May 20, 2014 by thanvigandhi_1

1 answer

Find the area of the triangle formed by the lines $y – x = \theta, x + y = \theta$ and $x – k = \theta$

asked May 20, 2014 by thanvigandhi_1

1 answer

Find the equation of a line drawn perpendicular to the line $ \large\frac{x}{4}$$+\large\frac{y}{6}$$=1$ through the point, where it meets the $y$ - axis

asked May 20, 2014 by thanvigandhi_1

1 answer

Find the equation of the line parallel to $y$ - axis and drawn through the point of intersection of the lines $x – 7y + 5 = 0$ and $3x + y = \theta.$

asked May 20, 2014 by thanvigandhi_1

1 answer

Find perpendicular distance from the origin to the line joining the points $ (\cos \theta, \sin \theta) $ and $(\cos \phi, \sin \phi)$

asked May 20, 2014 by thanvigandhi_1

1 answer

What are the points on the $y$ - axis whose distance from the line $ \large\frac{x}{3}$$+ \large\frac{y}{4}$$=1$ is 4 units.

asked May 18, 2014 by thanvigandhi_1

1 answer

Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and – 6, respectively

asked May 18, 2014 by thanvigandhi_1

1 answer

Find the values of $ \theta$ and $p$, if the equation $x\: \cos \theta + y \sin \theta = p$ is the normal form of the line $ \sqrt 3 x+y+2=0.$

asked May 18, 2014 by thanvigandhi_1

1 answer

Find the values of $k$ for which the line $(k-3)x-(4-k^2)y+k^2-7k+6=0$ is passing through the origin.

asked May 18, 2014 by thanvigandhi_1

1 answer

Find the values of $k$ for which the line $(k-3)x-(4-k^2)y+k^2-7k+6=0$ is Parallel to the $y$ axis.

asked May 18, 2014 by thanvigandhi_1

1 answer