Recent questions tagged sec-c

Prove that the value of $5\cos \theta+3\cos (\theta+\large\frac{\pi}{3})+$$3$ lies between -4 and 10

asked May 21, 2014 by sreemathi.v

1 answer

If $\alpha$ and $\beta$ are the solution of the equation $a\sec\theta+b\tan\theta=c$,then show that $\tan(\alpha+\beta)=\large\frac{2bc}{b^2-c^2}$

asked May 21, 2014 by sreemathi.v

1 answer

Prove that $\cos^2A+\cos ^2B-2\cos A\cos B.\cos(A+B)=\sin^2(A+B)$

asked May 21, 2014 by sreemathi.v

1 answer

Prove that $\tan 70^{\large\circ}=2\tan 50^{\large\circ}+\tan 20^{\large\circ}$

asked May 21, 2014 by sreemathi.v

1 answer

Evaluate :$\sin(n\pi+(-1)^n\large\frac{\pi}{4})$ where $n$ is an integer,

asked May 21, 2014 by sreemathi.v

1 answer

In right-angled triangle, the difference between the two acute angles is $(\large\frac{\pi}{15})^c$.Find the angles in degrees

asked May 20, 2014 by sreemathi.v

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

In a circle of diameter 50cm,the length of a chord is 25cm.Find the length of the minor arc of the chord

asked May 20, 2014 by sreemathi.v

1 answer

True-or-False :If $\tan(\pi \cos \theta)=\cot (\pi \sin \theta)$,then $\cos(\theta-\large\frac{\pi}{4})$$=\pm \large\frac{1}{2\sqrt 2}$

asked May 20, 2014 by sreemathi.v

1 answer

$3(\sin x-\cos x)^4+6(\sin x+\cos x)^2+4(\sin ^6x+\cos ^6x)$=_______

asked May 20, 2014 by sreemathi.v

1 answer

In a triangle ABC with $\angle C=90^{\large\circ}$ the equation whose roots are $\tan A$ and $\tan B$ is ___________

asked May 20, 2014 by sreemathi.v

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

Find the general solution of the equation $(\sqrt 3+1)\cos \theta+(\sqrt 3-1)\sin \theta=2$

asked May 20, 2014 by sreemathi.v

1 answer

Prove that $\cos \theta \cos\large\frac{\theta}{2}-$$\cos 3\theta\cos \large\frac{9\theta}{2}=$$\sin 7\theta\sin 8\theta$

asked May 20, 2014 by sreemathi.v

1 answer

In a polygon no three diagonals are concurrent.If the total number of points of intersection of diagonals interior to the polygon be 70,then the number of diagonals of the polygon is

asked May 20, 2014 by sreemathi.v

1 answer

The number of words of four letters containing equal number of vowels and consonants ,repetition allowed is

asked May 19, 2014 by sreemathi.v

1 answer

A team of four students is to be selected from a total of 12 students.Total number of ways in which team can be selected such that two particular students refuse to be together and other two particular students wish to be together only is equal to

asked May 19, 2014 by sreemathi.v

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

If $p$ is the length of perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$, then show that $ \large\frac{1}{p^2}$$= \large\frac{1}{a^2}$$ +\large\frac{1}{b^2}$

asked May 18, 2014 by thanvigandhi_1

1 answer

A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women . In how many different ways can this be done if two particular women refuse to serve on the same committee.

asked May 16, 2014 by sreemathi.v

1 answer

If $nC_{r-1}=36,nC_r=84$ and $nC_{r+1}=126$ then find $rC_2$

asked May 15, 2014 by sreemathi.v

1 answer

A box contain two white,three black and four red balls. In how many ways can three balls be drawn from the box,if atleast one black ball is to be includedin the draw

asked May 15, 2014 by sreemathi.v

1 answer

Out of 18 points in a plane,no three are in the same line except five points which are collinear.Find the number of lines that can be formed joining the points

asked May 15, 2014 by sreemathi.v

1 answer

A candidate is required to answer 7 questions out of 12 questions,which are divided into two groups,each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

asked May 15, 2014 by sreemathi.v

1 answer

Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.

asked May 14, 2014 by sreemathi.v

1 answer

From a class of 25 students 10 are to be chosen for an excursion party.There are 3 students who decide that either all of them will join or none of them will join.In how many ways can the excursion party be chosen?

asked May 14, 2014 by sreemathi.v

1 answer

In an examination a question paper consists of 12 questions divided into two parts (i.e) Part I and Part II.Containing 5 and 7 questions respectively.A student is required to attempt 8 question in all,selecting at least 3 from each part.In how many ways can a student select the questions 2

asked May 14, 2014 by sreemathi.v

1 answer

The English alphabet has 5 vowels and 21 consonants.How many words with two different vowels and two different consonants can be formed from the alphabet?

asked May 14, 2014 by sreemathi.v

1 answer

If the different permutations of all the letters of the word EXAMINATION are listed as in dictionary,how many words are there in this list before the first word starting with E?

asked May 14, 2014 by sreemathi.v

1 answer

How many words with or without meaning can be formed with letters of the word EQUATION at a time so that vowels and consonants occur together?

asked May 14, 2014 by sreemathi.v

1 answer

How many words,with or without meaning,each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

asked May 14, 2014 by sreemathi.v

1 answer

In the triangle ABC with vertices A(2,3), B(4,-1) and C(1,2), find the equation and length of altitude from the vertex A.

asked May 14, 2014 by thanvigandhi_1

1 answer

In how many ways can the letters of the word PERMUTATIONS be arranged if the There are always $4$ letters between $P$ and $S$?

asked May 13, 2014 by sreemathi.v

1 answer

If $p$ and $q$ are the lengths of perpendiculars from the origin to the lines $ x \cos \theta - y \sin \theta = k \cos 2\theta$ and $ x \sec \theta + y \: cosec \theta -k$, respectively, prove that $ p^2+4q^2=k^2$

asked May 13, 2014 by thanvigandhi_1

1 answer

Find the 4-digit numbers that can be formed using the digits 1,2,3,4,5 if no digit is repeated.How many of will be even?

asked May 13, 2014 by sreemathi.v

1 answer

Two lines passing through the point (2,3) intersects each other at an angle of $60^{\circ}$. If slope of one line is 2, find equation of the other line.

asked May 13, 2014 by thanvigandhi_1

1 answer

Prove that the line through the point $(x_1, y_1)$ and parallel to the line $Ax+By+C=0$ is \[\] $\qquad \qquad A(x-x_1)+B(y-y_1)=0$.

asked May 13, 2014 by thanvigandhi_1

1 answer

Find the lengths of medians of the triangle $ABC$ where $A(0,0,6),\:B(0,4,0)\:and\:C(6,0,0)$

asked May 11, 2014 by rvidyagovindarajan_1

1 answer

If $\sec x=-2$ and $\pi < x < \large\frac{3\pi}{2}$,find the value of all other five trigonometric functions.

asked Apr 22, 2014 by sreemathi.v

1 answer

If $\sin x=-\large\frac{2\sqrt 6}{5}$ and $x$ lies in quadrant III,find the values of $\cos x$ and $\cot x$

asked Apr 22, 2014 by sreemathi.v

1 answer

If $\sin x+\cos x=a$,then $|\sin x-\cos x|=$________

asked Apr 22, 2014 by sreemathi.v

1 answer

If $\sin x+\cos x=a$ then $\sin ^6x+\cos ^6x$=_______

asked Apr 22, 2014 by sreemathi.v

1 answer

If $\tan A=\large\frac{1-\cos B}{\sin B}$,then $\tan 2A$=_______

asked Apr 22, 2014 by sreemathi.v

1 answer

If $K=\sin\large\frac{5\pi}{8}$$\sin \large\frac{5\pi}{18}$$\sin \large\frac{7\pi}{18}$,then the numerical value of $K$ is _____

asked Apr 22, 2014 by sreemathi.v

1 answer

If $\tan \theta=\large\frac{a}{b}$,then $b\cos 2\theta+a\sin 2\theta$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\tan\alpha=\large\frac{1}{7}$$,\tan \beta=\large\frac{1}{3}$,then $\cos 2\alpha$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\sin\large\frac{\pi}{18}$$+\sin \large\frac{\pi}{9}$$+\sin \large\frac{2\pi}{9}$$+\sin \large\frac{5\pi}{18}$ is given by

asked Apr 21, 2014 by sreemathi.v

1 answer

Number of solutions of the equation $\tan x+\sec x=2\cos x$ lying in the interval $[0,2\pi]$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\alpha+\beta=\large\frac{\pi}{4}$,then the value of $(1+\tan \alpha)-(1+\tan \beta)$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

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