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Short Answer Type

141. A manufacturer reckons that the value of machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value of it at the end of 5 years.

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142.
A square is drawn by joining the mid-points of the sides of a given square. A third square is drawn inside the second square in the same way, and the process continues indefinitely. If a side of the first square is 16 cm., determine the sum of the areas of all the squares.

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Let ABCD be the given square of side 16cm as shown in the figure. Let EFGH be the second square drawn by joining the mid-points of the sides of given square ABCD.

BF = EB = 8

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rightwards double arrow

space space EF space equals space square root of 128 space equals space 8 square root of 2

Area of first square =

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Area of 2nd square =

space space left parenthesis 8 square root of 2 right parenthesis squared space equals space 128 space sq. space cm.

Now, side of the third square =

square root of left parenthesis 4 square root of 2 right parenthesis squared plus left parenthesis 4 square root of 2 right parenthesis squared space end root space equals space square root of 32 plus 32 end root space equals space 8

∴ Area of third square =

left parenthesis 8 right parenthesis squared space equals space 64

sq. cm. Since the number of squares is infinite

∴ Sum of areas of all such squares = 256 + 128 + 64 + .......

equals fraction numerator 256 over denominator 1 minus begin display style 1 half end style end fraction

open curly brackets because space straight a space equals space 256 comma space space straight r space equals space 128 over 256 space equals space 1 half close curly brackets

space space space space space space equals fraction numerator 256 over denominator begin display style 1 half end style end fraction space equals space 512

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Multiple Choice Questions

143.

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:

46^th
59^th
52^nd
52^nd

394 Views

144.

If the 2^nd, 5^th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

272 Views

145.

If the sum of the first ten terms of the series,

$open parentheses 1 3 over 5 close parentheses squared space plus open parentheses 2 2 over 5 close parentheses squared space plus open parentheses 3 1 fifth close parentheses squared space plus space 4 squared space plus space open parentheses 4 4 over 5 close parentheses squared space plus.....$ is 16/5 m, the m is equal to

347 Views

146.

The sum of first 9 terms of the series $1 cubed over 1 space plus fraction numerator 1 cubed plus 2 cubed over denominator 1 plus 3 end fraction space plus space fraction numerator 1 cubed plus 2 cubed plus 3 cubed over denominator 1 plus 2 plus 3 end fraction space....$ is

194 Views

147.

Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

$square root of 2 plus square root of 3$
$3 plus square root of 2$
$2 minus square root of 3$
$2 minus square root of 3$

250 Views

148.

The sum of first 20 terms of the sequence 0.7,0.77,0.777...... is

$7 over 81 space left parenthesis 179 minus 10 to the power of negative 20 end exponent right parenthesis$
$7 over 9 left parenthesis 99 minus 10 to the power of negative 20 end exponent right parenthesis$
$7 over 81 left parenthesis 179 plus 10 to the power of negative 20 end exponent right parenthesis$
$7 over 81 left parenthesis 179 plus 10 to the power of negative 20 end exponent right parenthesis$

958 Views

149.

If x, y, z are in A.P. and tan⁻¹ x, tan⁻¹ y and tan⁻¹ z are also in A.P., then

x= y= z
2x =3y = 6z
6x = 3y= 2z
6x = 3y= 2z

207 Views

150.

Statement 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... + (361 + 380 +400) is 8000.
Statement 2: $sum from straight k space equals 1 to straight n equals space 1 of left square bracket straight k cubed minus left parenthesis straight k minus 1 cubed right parenthesis right square bracket space equals space straight n cubed$ , for any natural number n.

Statement 1 is false, statement 2 is true
Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

178 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

142. A square is drawn by joining the mid-points of the sides of a given square. A third square is drawn inside the second square in the same way, and the process continues indefinitely. If a side of the first square is 16 cm., determine the sum of the areas of all the squares.

Multiple Choice Questions