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In an equilateral triangle PQR, if p, q and r denote the lengths perpendiculars from P, Q, R respectively on the opposite sides, then –

Arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is ___.

If sum and product of the zeroes of the polynomial ax^2-5x+c equal to 10 each. Find a and c

If the function are defined as $f\left(x\right)=\sqrt{x}$ and $g\left(x\right)=\sqrt{1-x},$ then what is the common domain of the following functions: $f+g,f-g,\frac{f}{g},\frac{g}{f},g-f$ where $(f\pm g)\left(x\right)=f\left(x\right)\pm g\left(x\right),\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$

Solve each of the following quadratic equations:
$\frac{1}{x-2}+\frac{2}{x-1}=\frac{6}{x},x\ne 0,1,2$

$△PQR$, right-angled at Q, if PR = 24 cm, QR = 12 cm, then find the value of $\angle QRP$.

Show that none of the following is an identity :

(i) $co{s}^2\theta +cos\theta =1$ (ii) $si{n}^2\theta +sin\theta =2$ (iii) $ta{n}^2\theta +sin\theta =co{s}^2\theta$

If $tanA=ntanB$ and $sinA=msinB$, prove that $co{s}^{2}A=\frac{(m^2-1)}{(n^2-1)}.$

Solve each of the following systems of eqautions by the method of cross-multiplication:

3x+2y+25=0

2x+y+10=0

Question 1

Both u and v vary directly with each other. When u is 10, v is 15, which of the following is not a possible pair of corresponding values of u and v?

(a) 2 and 3

(b) 8 and 12

(c) 15 and 20

(d) 25 and 37.5

What is the value of cot B in terms of a,b,c?

If A = {3, 6, 9, 12, 15, 18, 21}

B = {2, 4, 6, 8, 10, 12, 14, 16}

C = {5, 10, 15, 20}, then match the following.

$\begin{array}{cc}A& B\\ 1.B-C& A.\{5,10,20\}\\ 2.A-C& B.\{3,9,15,21\}\\ 3.C-(A-B)& C.\{3,6,9,12,18,21\}\\ 4.C\cap (A-B)& D.\{15\}\\ & E.\{2,4,6,8,12,14,16\}\end{array}$

Find a solution of the equation 4 sin$\theta$= 3 cosec$\theta$

The smallest positive values of x and y which satisfy $tan(x–y)=1,sec(x+y)=\frac{2}{\sqrt{3}}$ are

A person observes the angle of elevation of the top of a 60m tower from a point on the level ground to be 60${}^{\circ }$. Find the distance between the person and the foot of the tower.

Value of ‘a’ so that (x + 6) is a factor of the polynomial x³ + 5x² - 4x + a.

If one root of the equation 2$x^2$ + ax + 6 = 0 is 3, then find the value of a

The equation of the straight line passing through the point of intersection of lines 3x – 4y – 7 = 0 and 12x – 5y – 13 = 0 and perpendicular to the line 2x – 3y + 5 = 0 is

The following distribution represents the number of hours spent per year by a group of sports person in going to the gym. Find the median number of hours spent per by the sports persons in going to the gym.

Which of the following is always irrational?

The area of a right-angled triangle is 165 sq metres. Determine its base and altitude if the latter exceeds the former by 7 metres.

Black aces and black queens are removed from a pack of 52 cards.remaining cards are reshuffled and a card is drawn. Find the probability of getting

1) a black card

2) an ace

In $△ABC,\angle B=\angle C.D$ and $E$ are mid points of $AB$ and $AC$, respectively. Find the value of the ratio $\frac{BE}{CD}$.

If 1K × K1 = K2K, the letter K stands for the digit

A. 1

B. 2

C. 3

D. 4

The sum of first ten terms of an A.P. is four times the sum of its first five terms. What is the ratio of first term and common difference?

The traffic signals at 3 different road crossing chages after evry 48 s,72s,and 108s respectively.If they all change simultaneously at 8 hours, then what time will they again change simultaneously?

A tree standing on a horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top are respectively $\alpha and\beta$. Prove that the height of the top from the ground is $\frac{(b-a)tan\alpha tan\beta }{tan\alpha -tan\beta }$.