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The sum of the digits of a number consisting of three digits is 12. The middle digit is equal to half of the sum of the other two. If the order of the digit be reversed, the number diminished by 198. Find the number.
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→The following pie diagram represents the number of valid votes obtained by four students who contested for school captain. The total of valid votes polled was 720. Answer the following questions.
(i) Who has won the election?
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(i) Who has won the election?
(ii) What is the minimum no. of votes? Who got it?
(iii) By how many votes did the winner defeat the nearest contestant?
The following data gives the distribution of total monthly household expenditure of $200$ families of a village. .Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:
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Expenditure (in ₹)
|
Frequency
|
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$1000-1500$
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$24$
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$1500-2000$
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$40$
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$2000-2500$
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$33$
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$2500-3000$
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$28$
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$3000-3500$
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$30$
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$3500-4000$
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$22$
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$4000-4500$
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$16$
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$4500-5000$
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$7$
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Prove that if a positive integer is of the form 6q + 5, then it is of the form 3q + 2 for some integer q, but not conversely.
Find the lengths of the medians of a triangle whose vertices are A(-1,1), B(5, -3) and C(3, 5).
By using the method of completing the square, show that the equation $2x^2 + x + 4 = 0$ has no real roots.
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Solve the following system of equations by the method of cross-multiplication:
2(ax - by) + a + 4b = 0
2(bx + ay) + b - 4b = 0
In two concentric circles, a chord of length 8cm of the larger circle touches the smaller circle. If the radius of the larger circle is $5\ cm$ then Find the radius of the smaller circle.
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