Algebra
Practice Questions on Algebra
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Q11) If 9x + 15xy + 35y = 123, for all real x, y, then find the minimum value of 3x + 5y. 1) 12 2) 10 3) 8 4) 14
We have 9x + 15xy + 35y = 123 Adding 21 on both sides we get 9x + 15xy + 35y + 21 = 144 3x(3 + 5y) + 7 (3 + 5y) = 144 (3x + 7) (3 + 5y) = 144 we know that AM ≥ GM (3x + 7 + 3 + 5y)/2 ≥ √ (3x + 7)(3 + 5y) 3x + 5y + 10 ≥ 24 3x + 5y ≥ 14 Minimum value of 3x + 5y is 14. Hence, option 4. Q12) Find the 5th term of an A.P. whose sum upto n terms is given by Sn = n(n + 4). 1) 45 2) 32 3) 13 4) None of these
T5 = S5 - S4 = 45 - 32 = 13 Hence, option 3. Q13) A tank is 1/5th full of water. When 22 liters of water is added to the tank, then it is 3/4th full of water. Find the capacity of the tank. 1) 50 liters 2) 30 liters 3) 36 liters 4) 40 liters
Let 'c' be the capacity of the tank. ATQ c/5 + 22 = 3c/4 On solving, c = 40 liters Hence, option 4. Q14) If  , what is the value of  ?1) 32 2) 31 3) 2 4) None of these
If then,  , for all values of n.Hence, option 3. Q15) If 2x.2y = 8, 9x.3y = 81. Then which of the following is true. 1) x + y = 2 2) xy = 2 3) x = 2y 4) None of these
2x.2y = 8, 9x.3y = 81 2x + y = 23, 32x + y = 34 x + y = 3, 2x + y = 4 On solving, x = 1, y = 2 Hence, option 2. |