Algebra
Practice Questions on Algebra
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Q6) Find the sum of n terms of an A.P. whose nth term is given by 4n + 3. 1) 4n2 + 3n 2) 4n2 + 5n 3) 2n2 + 5n 4) 2n2 - 5n
Tn = 4n + 3 So, T1 = 7, T2 = 11, T3 = 15 and soon. So we have an A.P. where a = 7, d = 4  Hence, option 3. Q7) If α and β are the roots of the quadratic equation ax2 + bx + c = 0, find the equation whose roots are 1/α and 1/β. 1) cx2 + bx + a = 0 2) cx2 - bx + a = 0 3) ax2 - bx - c = 0 4) ax2 - bx + c = 0
Sum of roots = α + β = -b/a Product of roots = αβ = c/a Required sum of roots = 1/α + 1/β = (α + β)/(αβ) = -b/c Product of the roots = 1/(αβ) = a/c Required equation = cx2 + bx + a = 0 Hence, option 1. Q8) These is a number y such that y ∈ (100, 1000) and y is divisible by 2, 3, 4 and 5. How many values of y exist. 1) 60 2) 16 3) 15 4) 59
If a number is divisible by 2, 3, 4 and 5, then it must be divisible by their LCM i.e. 60 also. Numbers between 100 and 1000 which are divisible by 60 are 120, 180,..., 960. This is an A.P where a = 120, d = 60 and  = 960 960 = 120 + (n - 1)×60 On solving, n = 15 Hence, option 3. Q9) An amphitheater had 28 seats in first row, 31 seats in the second row, 34 seats in the third row, and so on. How many students can be seated in the 15th row of the amphitheater? 1) 70 2) 56 3) 68 4) 75
T15 = 28 + (15 - 1)×3 = 70 Hence, option 1. Q10) A vessel, full of water weighs 11.5 kg. When the vessel is 25% full, it weighs 4.75 kg. Find the weight of vessel that is 60% full of water. 1) 9 kg 2) 5.4 kg 3) 7.9 kg 4) 8.1 kg
Let V be the weight of the empty vessel and W be the weight of water in the vessel.  On solving, V = 2.5 kg, W = 9 kg. weight of vessel when it is 60% full of water  Hence, option 3. |