# Maths-9-2006

**MATHS**

**IX**

**SECTION A 3 MARKS EACH**

**The marked price of the fan is 800/-. It is sold at the discount of 10%. He further allowed the discount of 5% more. Find the selling price?****prove that a**^{3}**+ b**^{3}**+ c**^{3}**– 3abc = 1/2(a + b + c)[(a – b)**^{2}**+ (b – c)**^{2}**+ (c – a)**^{2}**)]****If sin A = 3/5, find all the other ratios.****A playground is in the shape of the rectangle. It has two semicircles on the smaller sides as the diameters. If the sides of the rectangle are 36 m and 24.5 m find the area of the playground?****In the figure below, AL is the angle bisector of, < BAC prove that < ABC + < ACD = 2 < ALC.**

**Divide 195150\ between A and B in such a way that the amount A receives in 2 years is same as the amount B receives in 4 years at the rate 4%.****The mean of 100 students was found to be 40. Later it was found that 53 were misread as 83. Compute the correct mean.****Find the median of 25, 27, 19, 29, 21, 23, 25, 30, 28, and 20?****Construct a triangle whose perimeter is 10 cm and base angles are 60**^{o}**and 45**^{o}**.****Find the mean proportional between 32 and 8?**

**SECTION B 4 MARKS EACH**

**find the value of a and b**

**7 – 1 7 + 1**

**————— – ————— = a + b 7**

**7 + 1 7 – 1**

**If the selling 20 articles at the cost price of 23 articles. Find the gain or the loss percent?****In the figure below, < CPD = < BPD AD is the angle bisector of < BAC prove that CP = BP. C**

**Factorize 12x**^{2}**– 7x + 1.****In the figure below find the area of the shaded region? The radius of each circle is 7 cm.**

**Read the page of the pass below.**

**MONTH**** ****DEPOSIT**** ****WITHDRAWL**** ****BALANCE**

**July 14 4000 4000**

**Aug 3 5000 9000**

**Aug 4 3000 6000**

**Aug 23 2300 ——**

**Nov 13 5500 ——**

**Nov 15 ——– 9000**

**Dec 2 6000 15000**

**Dec 23 2400 ——–**

**Fill in the blanks and find the interest at the rate of 6%**

**if x/a = y/b then show that**

**x**^{2}** + a**^{2}** y**^{2}** + b**^{2}** (x + y)**^{2}** + (a + b)**^{2}

**———– + ———— = ————————-**

**x + a y + b [x + y] [ a + b]**

**If PMO is the right angled triangle < M = 90**^{o}**, PM = 3 cm, OP = 6 cm, find all the parts?****If a is subtracted form each of the deviations x**_{1}**, x**_{2}**, x**_{3}**,….. x**_{n }**then prove that the new mean = old mean – a.****If the median of the data is 63, find x?**

**29, 32, 48, 50, x, x + 2, 72, 78, 84, 95.**

**SECTION C 6 MARKS EACH**

**if 6pq x + 3p x + 3q**

**x = ——– then find ———– + ———–**

**p + q x – 3p x – 3q**

**In the figure OABC is a rhombus and O is the centre of the circle. If the radius is 10 cm, find the area of rhombus**

**Show that the medians of a triangle pass through the same point and divides each in the ratio of 2 : 1.**

**Show that if the line passing through the mid point of the one side of the triangle and parallel to the second side bisects the third side.**

**in the figure below, if AB is the shortest side and CD is the longest side then prove that < A > <C and < B > <D**