In the given figure, PQ is a diameter of circle and RS is perpendicular to PQ, if PQ = 20 cm and PT = 4 cm, then find the length of ST?
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Solution
PO = OQ = 10 cm
∴ OT = 10 – 4 = 6 cm
∴ ST = = 8 cm
The maximum value of 24 sin2θ + 7 cos2θ is –
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Solution
24 sin2θ + 7 cos2θ = 24 [For maximum value θ = 90°]
On mixing the sugar of quality A and B (having price Rs. 32 per kg and Rs. 54 per kg respectively) the new average of sugar so formed is Rs. 48 per kg. The ratio of Quantity of A and B in the mixture is –
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Solution
Required ratio =
If 2x = 3y = 4z, find x : y : z
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Solution
2x = 3y = 4z
∴ x : y : z =
The ratio of Ages of A, B and C is 5 : 8 : 9. If the sum of the ages of A and C is 56 years. Then the age of B is-
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Solution
Let the ages of A, B and C are 5x, 8x and 9x.
∴ 5x + 9x = 56
x = 4
∴ Age of B = 4 × 8 = 32 years
The ratio of number of boys and girls in a school is 3 : 2. If 50% of the boys and 20% of the girls are scholarship holders, then what is the percentage of those students who do not get scholarship?
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Solution
Let the number of boys and girls in the class is 300 & 200.
Number of students who got scholarship = = 150 + 40 = 190
∴ Required percent =
The radius of a circle is increased by 5%, then the percentage increase in area of the circle will be-
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Solution
% increase = 5 + 5 + %
If a single discount is equivalent to three successive discount of 30%, 60% and 70% then the single discount is-
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Solution
Single discount = 100 – 100 × = 91.6%
By Selling 44 pens, a shopkeeper’s gain is equal to the selling price of 12 pens. find his gain percent :
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Solution
Profit percent =
When 17200 is divided by 18, then the remainder will be-
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Solution