Recent questions tagged sec-c

If $x^p$ occurs in the expansion of $(x^2+\large\frac{1}{x})^{2n}$.Prove that its coefficient is $\large\frac{2n!}{\Large\frac{4n-p}{3}!\frac{2n+p}{3}!}$

asked Jun 24, 2014 by sreemathi.v

1 answer

In the expansion of $(x+a)^n$ if the sum of odd terms is denoted by O and the sum of even term by E.Then prove that (ii) $4OE=(x+a)^{2n}-(x-a)^{2n}$

asked Jun 24, 2014 by sreemathi.v

1 answer

In the expansion of $(x+a)^n$ if the sum of odd terms is denoted by O and the sum of even term by E.Then prove that (i) $O^2-E^2=(x^2-a^2)^n$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find $n$ in the binomial $\big[\sqrt[3]{2} +\large\frac{1}{\sqrt[3]{3}} \big]^n$ if the ratio of $7^{th}$ term from the beginning to the $7^{th}$ term from the end is $\large\frac{1}{6}$

asked Jun 24, 2014 by sreemathi.v

1 answer

Show that the middle term in the expansion of $(x-\large\frac{1}{x})^{2n}$ is $\large\frac{1\times 3\times 5\times..... (2n-1)}{n!}$$\times (-2)^n$

asked Jun 24, 2014 by sreemathi.v

1 answer

If $p$ is a real number and if the middle term in the expansion of $(\large\frac{p}{2}$$+2)^8$ is 1120.Find $p$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the coefficient of $\large\frac{1}{x^{17}}$ in the expansion of $(x^4-\large\frac{1}{x^3})^{15}$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the coefficient of $x^{15}$ in the expression of $(x-x^2)^{10}$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the middle term in the expansion of $(3x-\large\frac{x^3}{6})^9$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the middle term in the expansion of $(\large\frac{x}{a}-\frac{a}{x})^{10}$

asked Jun 24, 2014 by sreemathi.v

1 answer

If the term free from $x$ in the expansion of $(\sqrt x-\large\frac{k}{x^2})^{10}$ is $405$,find the value of $k$.

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the term independent of $x,x\neq 0$ in the expansion of $\big(\large\frac{3x^2}{2}-\frac{1}{3x})^{15}$

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 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

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

Prove that the coefficient of $x^n$ in $(1+x)^{2n}$ is twice the coefficient of $x^n$ in $(1+x)^{2n-1}$

asked Jun 23, 2014 by sreemathi.v

1 answer

The coefficients of the $(r-1)^{th},r^{th}$ and $(r+1)^{th}$ terms in the expansion of $(x+1)^n$ are in the ratio of $1 : 3 : 5$. Find both $n$ and $r$.

asked Jun 23, 2014 by sreemathi.v

1 answer

Find the middle term in the expansion of $\big(\large\frac{3}{3}$$+9y\big)^{10}$

asked Jun 23, 2014 by sreemathi.v

1 answer

Find the middle term in the expansion of $(3-\large\frac{x^3}{6})^7$

asked Jun 23, 2014 by sreemathi.v

1 answer

Find the coefficient of $a^5b^7$ in $(a-2b)^{12}$

asked Jun 23, 2014 by sreemathi.v

1 answer

Show that $9^{n+1}-8n-9$ is divisible by 64 whenever n is a positive integer.

asked Jun 23, 2014 by sreemathi.v

1 answer

The number of ways in which one can select three distinct integers between 1 and 30 both inclusive ,whose sum is even is

asked Jun 20, 2014 by sreemathi.v

1 answer

9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes.The number of ways of arranging one ball in each of the boxes is

asked Jun 20, 2014 by sreemathi.v

1 answer

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary.The number of words that appear before the word COCHIN is

asked Jun 20, 2014 by sreemathi.v

1 answer

The number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the octagon is

asked Jun 20, 2014 by sreemathi.v

1 answer

Two numbers are chosen from 1,3,5,7.....147,149 and 151 and multiplied together in all possible ways.The number of ways which will give us the product a multiple of 5 is

asked Jun 20, 2014 by sreemathi.v

1 answer

ABCD is a convex quadrilateral 3,4,5 and 6 points are marked on the sides AB,BC,CD and DA respectively.The number of triangles with vertices on different sides is

asked Jun 20, 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

Solve the equation $\sec^22x=1-\tan 2x$

asked May 22, 2014 by sreemathi.v

1 answer

Solve the equation $\sin 9\theta=\sin \theta$

asked May 22, 2014 by sreemathi.v

1 answer

If $\tan(\cot x)=\cot(\tan x)$,prove that $\sin 2x=\large\frac{4}{(2n+1)\pi}$

asked May 22, 2014 by sreemathi.v

1 answer

Solve $3\tan(\theta-15^{\large\circ})=\tan(\theta+15^{\large\circ})$

asked May 22, 2014 by sreemathi.v

1 answer

If $\cos\theta=\large\frac{\cos\alpha-\cos\beta}{1-\cos\alpha\cos\beta}$ then prove that one of the values of $\tan\large\frac{\theta}{2}$ is $\tan \large\frac{\alpha}{2}$$\cot \large\frac{\beta}{2}$

asked May 22, 2014 by sreemathi.v

2 answers

If $\cos \theta=\cos \alpha.\cos\beta$ prove that $\tan\large\frac{\theta+\alpha}{2}$$\tan\large\frac{\theta-\alpha}{2}=$$\tan^2\large\frac{\beta}{2}$

asked May 22, 2014 by sreemathi.v

1 answer

If $\sin x+\sin y=a$ and $\cos x+\cos y=b$,show that $\sin(x+y)=\large\frac{2ab}{a^2+b^2}$

asked May 22, 2014 by sreemathi.v

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

Prove that $\tan\alpha\tan(60^{\large\circ}-\alpha)\tan (60^{\large\circ}+\alpha)=\tan 3\alpha$

asked May 21, 2014 by sreemathi.v

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

Prove that $\cos^3A\cos 3A+\sin^3A\sin 3A=\cos^32A$

asked May 21, 2014 by sreemathi.v

1 answer

Prove that $\tan\alpha+2\tan 2\alpha+4\tan 4\alpha+8\cot 8\alpha=\cot\alpha$

asked May 21, 2014 by sreemathi.v

1 answer

Prove that $\tan(60^{\large\circ}+A)\tan(60^{\large\circ}-A)=\large\frac{2\cos 2A+1}{2\cos 2A-1}$

asked May 21, 2014 by sreemathi.v

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

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