Write 3/13 in decimal form and find what kind of decimal expansion it has. -Maths 9th

Write 3/13 in decimal form and find what kind of decimal expansion it has. -Maths 9th
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Find the decimal expansion of 7/22 .Explain why it is taken as the approximate value of pi -Maths 9th

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Write the following rational numbers in decimal form : -Maths 9th

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The coefficient of x in the expansion of (x + 3)3 is -Maths 9th

Description : The coefficient of x in the expansion of (x + 3)3 is -Maths 9th

Last Answer : (d) Now, (x + 3)3 = x3 + 33 + 3x (3)(x + 3) [using identity, (a + b)3 = a3 + b3 + 3ab (a + b)] = x3 + 27 + 9x (x + 3) = x3 +27 + 9x2+27x Hence, the coefficient of x in (x + 3)3 is 27.

The coefficient of x in the expansion of (x + 3)3 is -Maths 9th

Description : The coefficient of x in the expansion of (x + 3)3 is -Maths 9th

Last Answer : (d) Now, (x + 3)3 = x3 + 33 + 3x (3)(x + 3) [using identity, (a + b)3 = a3 + b3 + 3ab (a + b)] = x3 + 27 + 9x (x + 3) = x3 +27 + 9x2+27x Hence, the coefficient of x in (x + 3)3 is 27.

Which of the following rational numbers have the terminating decimal representation? -Maths 9th

Description : Which of the following rational numbers have the terminating decimal representation? -Maths 9th

Last Answer : (i) The prime factor of 5 is 5. Hence 3 / 5 has a terminating decimal representation. (ii) 20 = 4 x 5 = 22 x 5. The prime factors of 20 are both 2's and 5's. Hence 7 / 20 has a ... a terminating decimal. (vi) The prime factor of 7 is 7. Hence 23 / 7 has a non-terminating decimal representation.

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Description : Which of the following rational numbers have the terminating decimal representation? -Maths 9th

Last Answer : (i) The prime factor of 5 is 5. Hence 3 / 5 has a terminating decimal representation. (ii) 20 = 4 x 5 = 22 x 5. The prime factors of 20 are both 2's and 5's. Hence 7 / 20 has a ... a terminating decimal. (vi) The prime factor of 7 is 7. Hence 23 / 7 has a non-terminating decimal representation.

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Rationalise the denominator in each of the following and hence evaluate by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236 up to three places of decimal. -Maths 9th

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A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field. -Maths 9th

Description : A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field. -Maths 9th

Last Answer : Let the given field is in the form of a trapezium ABCD such that parallel sides are AB = 10 m and DC = 25 m Non-parallel sides are AD = 13 m and BC = 14 m. We draw BE || AD, such that BE = 13 m. ... = 112 m2 So, area of the field = area of ∆BCE + area of parallelogram ABED = 84 m2 + 112 m2 = 196 m2

A right circular cylinder just encloses a sphere of radius r (see fig. 13.22). Find (i) surface area of the sphere, (ii) curved surface area of the cylinder -Maths 9th

Description : A right circular cylinder just encloses a sphere of radius r (see fig. 13.22). Find (i) surface area of the sphere, (ii) curved surface area of the cylinder -Maths 9th

Last Answer : Surface area of sphere = 4πr2, where r is the radius of sphere (ii) Height of cylinder, h = r+r =2r Radius of cylinder = r CSA of cylinder formula = 2πrh = 2πr(2r) (using value of h) = 4πr2 (iii) Ratio ... sphere)/CSA of Cylinder) = 4r2/4r2 = 1/1 Ratio of the areas obtained in (i) and (ii) is 1:1.

The perimeter of a right triangle is 30 cm. If its hypotenuse is 13 cm, then what are two sides? -Maths 9th

Description : The perimeter of a right triangle is 30 cm. If its hypotenuse is 13 cm, then what are two sides? -Maths 9th

Last Answer : The other two sides of the triangle are 12 cm and 5 cm Explanation: Let the other two sides of triangle be x and y It's hypotenuse is 13 cm Perimeter of triangle = Sum of all sides ... When y = 12 x=17-y = 17-12 =5 So, the other two sides of the triangle are 12 cm and 5 cm

Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. -Maths 9th

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Last Answer : Here, the arranged data is 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43 Total number of observations = 10 Here, 10 is an even number , therefore median will be the mean of (10 / 2)th and (10 / 2 + 1)th observation. ... ⇒ 3x + 12 / 2 = 24 ⇒ 3x - 12 = 48 ⇒ 3x = 60 ⇒ x = 20 ∴ The value of x = 20

Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. -Maths 9th

Description : Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. -Maths 9th

Last Answer : Here, the arranged data is 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43 Total number of observations = 10 Here, 10 is an even number , therefore median will be the mean of (10 / 2)th and (10 / 2 + 1)th observation. ... ⇒ 3x + 12 / 2 = 24 ⇒ 3x - 12 = 48 ⇒ 3x = 60 ⇒ x = 20 ∴ The value of x = 20

The mean of 25 observations is 36. Out of these observations, if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is -Maths 9th

Description : The mean of 25 observations is 36. Out of these observations, if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is -Maths 9th

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The mean of 25 observations is 36. Out of these observations, if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is -Maths 9th

Description : The mean of 25 observations is 36. Out of these observations, if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is -Maths 9th

Last Answer : (b) Given, mean of 25 observations = 36 ∴ Sum of 25 observations = 36 x 25 = 900 Now, the mean of first 13 observations = 32 ∴ Sum of first 13 observations = 13 x 32 = 416 and the mean of last 13 ... - (Sum of 25 observations) = (520 + 416)-900 = 936 - 900 = 36 Hence, the 13th observation is 36.

In the linear equation y = 4x + 13, if x is the number of hours a labourer is on work and y are his wages in rupees then draw the graph. Also find the wages when work is done for 6 hours. -Maths 9th

Description : In the linear equation y = 4x + 13, if x is the number of hours a labourer is on work and y are his wages in rupees then draw the graph. Also find the wages when work is done for 6 hours. -Maths 9th

Last Answer : when the work is done for 6 hours x=6 y=4(6)+13 y=24+13 y=37 the labourer gets Rs.37 if he works for 6hrs

Find the length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm. -Maths 9th

Description : Find the length of a chord which is at a distance of 12 cm from the centre of a circle of radius 13 cm. -Maths 9th

Last Answer : Let AB be a chord of circle with centre O and radius 13cm. Draw OM perpendicular AB and join OA. In the right triangle OMA, we have OA2 = OM2 + AM2 ⇒ 132 = 122 + AM2 ⇒ AM2 = 169 - 144 ... . As the perpendicular from the centre of a chord bisects the chord.Therefore, AB = 2AM = 2 x 5 = 10cm.

The radius of a circle is 13 cm and the length of one of its chords is 24 cm. Find the distance of the chord from the centre. -Maths 9th

Description : The radius of a circle is 13 cm and the length of one of its chords is 24 cm. Find the distance of the chord from the centre. -Maths 9th

Last Answer : Let PQ be a chord of a circle with centre O and radius 13cm such that PQ = 24cm. From O, draw OM perpendicular PQ and join OP. As, the perpendicular from the centre of a circle to a chord bisects the chord. ∴ PM ... Hence, the distance of the chord from the centre is 5cm.

Find the area of a trapezium whose parallel sides are 25 cm and 13 cm long and the distance between them is 8 cm. -Maths 9th

Description : Find the area of a trapezium whose parallel sides are 25 cm and 13 cm long and the distance between them is 8 cm. -Maths 9th

Last Answer : Area of a trapezium = 1/2(sum of parallel sides) x (perpendicular diatance between them) = 1/2(25 + 13) x 8 = 152cm2

The lengths of the sides of a triangle are 7 cm, 13 cm and 12 cm. -Maths 9th

Description : The lengths of the sides of a triangle are 7 cm, 13 cm and 12 cm. -Maths 9th

Last Answer : Let, a = 7 cm, b = 13 cm, c = 12 cm ∴ s = (a + b + c)/2 = (7 +13 +12)/2 = 32/2 = 16 cm Area of △ ABC = under root( √s(s -a) (s - b)(s -c)) = under root( √16(16 - 7)(16 - 13)(16 - 12) = ... 24 √3 cm2 Also, Area of △ ABC = 1/2AC.BD 24 √3 = 1/2 x 12 x BD ⇒ BD = (24 √3 x 2)/12 = 4 √3 cm

Ten observations 6, 14, 15, 17, x+1, 2x -13, -Maths 9th

Description : Ten observations 6, 14, 15, 17, x+1, 2x -13, -Maths 9th

Last Answer : 6, 14, 15, 17, x + 1, 2x -13, 30, 32, 34, 43, Here, n = 10 Since the number of observations is 10 (an even number), therefore, the median = (10/2)th observation + (10/2 + 1)th observation/2 = 5th observation + 6th ... = x + 1 + 2x - 13/2 ⇒ 48 = 3x - 12 ⇒ 3x = 48 + 12 = 60 ⇒ x = 20

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Last Answer : 1. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold ? (1000 cm3 = 1 l) . 2. The inner diameter of a cylindrical ... with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients ?

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Last Answer : Below you will find MCQ Questions of Chapter 13 Surface Areas and Volumes Class 9 Maths Free PDF Download that will help you in gaining good marks in the examinations and also cracking competitive ... Areas and Volumes MCQ Questions will help you in practising more and more questions in less time.

A right DABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. What is the volume of the solid so obtained ? -Maths 9th

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Last Answer : From the figure it is clear that a cone is formed. Here, h = 12 cm, r = 5 cm Volume of cone = = 314 cm3

A right triangular prism of height 18 cm and of base sides 5 cm, 12 cm and 13 cm is transformed into another right triangular prism on a base -Maths 9th

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Last Answer : Vol. of △ ular prism = Area of △ ular base × height. ∴ Area of triangular base = area of triangle PQR By heron's formula. S=S(s−a)(s−b)(s−c)​where S=2a+b+c​∴Areaof△PQR= S=23+4+5​=6 S=6(6−3)(6−4)(6−5)​=3×2×3×2×1​=6cm2 ∴ vol. of Prism =6×10 =60cm3Answer.

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When x^13 + 1 is divided by x –1, the remainder is : -Maths 9th

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If the polynomial x^19 + x^17 + x^13 + x^11 + x^7 + x^5 + x^3 is divided by (x^2 + 1), then the remainder is : -Maths 9th

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Point A(5, 1) is the centre of the circle with radius 13 units. AB ⊥ chord PQ. B is (2, –3). The length of chord PQ is -Maths 9th

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Last Answer : (c) ParallelogramAB = \(\sqrt{(4-7)^2+(5-6)^2}\) = \(\sqrt{9+1}\) = \(\sqrt{10}\)BC = \(\sqrt{(7-4)^2+(6-3)^2}\) = \(\sqrt{9+9}\) = \(3\sqrt2\)CD =\(\sqrt{(4-1)^2+(3-2) ... = \(2\sqrt{13}\)AB = CD, BC = AD and AC ≠ BD ⇒ opposite sides are equal and diagonals are not equal. ⇒ ABCD is a parallelogram.

The line L is given by x/5 + y/b = 1 passes through the point (13, 32). The line K is parallel to L and has the equation -Maths 9th

Description : The line L is given by x/5 + y/b = 1 passes through the point (13, 32). The line K is parallel to L and has the equation -Maths 9th

Last Answer : (a) 45º The equations of the given lines are: A\(x\) + By = A + B ⇒ By = -A\(x\) + (A + B) ⇒ y = \(-rac{A}{B}x\) + \(rac{(A+B)}{B}\) ....(i)and A(\(x\) - y) + B(\(x\) ... (ii) = m2 = \(rac{(A+B)}{B-A}\)Let θ be the angle between both the lines, then∴ tan θ = 1 ⇒ θ = tan-1 (1) = 45°.

A straight line passes through the points (a, 0) and (0, b). The length of the line segment contained between the axes is 13 and the product of -Maths 9th

Description : A straight line passes through the points (a, 0) and (0, b). The length of the line segment contained between the axes is 13 and the product of -Maths 9th

Last Answer : (d) \(rac{23}{\sqrt{17}}\)The given lines are:L : \(rac{x}{5}+rac{y}{b}=1\) ....(i)K : \(rac{x}{c}+rac{y}{3}=1.\) ...(ii)Since line L passes through (13, 32),\(rac{13}{ ... between parallel lines ax + by + c1 = 0 and ax + by c2 = 0 is d = \(rac{|c_2-c_1|}{\sqrt{a^2+b^2}}\bigg)\)

If 2x + 3y = 13 and xy = 6, find the value of 8x3 + 21y3. -Maths 9th

Description : If 2x + 3y = 13 and xy = 6, find the value of 8x3 + 21y3. -Maths 9th

Last Answer : 2x +3y = 13-----(1) xy =6-----(2) 8x³ +27y³ = (2x)³ +(3y)³ = (2x+3y)³ - 3*2x*3y(2x+3y) [using (a+b)³ = a³+b³+3ab(a+b)] = (13)³- 18 * 6 *13 [ using (1) and (2)] = 2197 - 1404 =793

Cbqs (case base study ) of chapter 13 surface areas and volume of maths class 9th -Maths 9th

Description : Cbqs (case base study ) of chapter 13 surface areas and volume of maths class 9th -Maths 9th

Last Answer : CBQs Ch- 13 Surface area and volume - Maths Class 9th 1 . Dev was doing an experiment to find the radius r of a sphere.For this he took a cylindrical container with radius R = 7 cm and height 10 cm. He filled the container ... .14)*6²*8 = 301.44 m³ area of the floor = πR² = 3.14 (6)² = 113.04 m²

Let cost of a pen and a pencil be “x” and “y” respectively. A girl pays ₹16 for 2 pens and 3 pencils. Write the given data in the form of a linear equation in two variables. Also represent it graphically. -Maths 9th

Description : Let cost of a pen and a pencil be “x” and “y” respectively. A girl pays ₹16 for 2 pens and 3 pencils. Write the given data in the form of a linear equation in two variables. Also represent it graphically. -Maths 9th

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Write the simple form of a rational number 177/413. -Maths 9th

Description : Write the simple form of a rational number 177/413. -Maths 9th

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Write three pairs of form (x,y) that satisfy the equation x + y = 5 . Use these ordered pairs to draw the graph of the equation x + y = 5 . -Maths 9th

Description : Write three pairs of form (x,y) that satisfy the equation x + y = 5 . Use these ordered pairs to draw the graph of the equation x + y = 5 . -Maths 9th

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Write three pairs of form (x,y) that satisfy the equation x = y . Use these ordered pairs to draw the graph of the equation x = y . -Maths 9th

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Last Answer : Given equation is x−3y=4 for y=−1 x−(3×−1)=4 x=1 therefore ordered pair of points is (1,−1)

The decimal expansion of the rational number 23/(2 2 . 5) will terminate after (a) one decimal place (b) two decimal places (c) three decimal places (d) more than 3 decimal places

Description : The decimal expansion of the rational number 23/(2 2 . 5) will terminate after (a) one decimal place (b) two decimal places (c) three decimal places (d) more than 3 decimal places

Last Answer : (b) two decimal places