Prove that a ÷ (b÷c) is not same as (a÷b)÷c if,
a=27
b=(- 18)
c=(-3)
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Answers
Answer:
Let k be one of the root of the given equation.
According to the problem,
1/k will be the other root of the given equation.
We know that, product of the roots of the equation = c/a.
Therefore, k × 1/k = c/a.
or, 1 = c/a.
or, a = c [multiplying a on both sides].
The roots of the equation ax2 + bx + c = 0 will be reciprocal if a = c.
Therefore, a = c or c = a.
Answer: (c)
3. If 8 ∙ 2x = 5(y+8), then when y = -8, x =
(a) -4, (b) -3, (c) 0, (d) 4, (e) 8
Solution:
8 ∙ 2x = 5(y+8).
or, 8 ∙ 2x = 5(-8+8).
or, 2x = 50.
or, 2x = 1 [anything to the power 0 is 1 then, 50 = 1].
Taking log on both sides,
log 2x = log 1.
or, x log 2 = 0 [since log 1 = 0].
or, x = 0/log 2 [dividing log 2 on both sides].
Therefore, x = 0.
Answer: (c)
4. A circle of radius 10 inches has its center at the vertex C of an equilateral triangle ABC and passes through the other two vertices. The side AC extended through C intersects the circle at D. The number of degrees of angle ADB is:
(a) 15, (b) 30, (c) 60, (d) 90, (e) 120
2Save
Answer: (b)
5. The expression 1 – 1/(1 + √3) + 1/(1 - √3) equals:
(a) 1 - √3, (b) 1, (c) - √3, (d) √3, (e) 1 + √3.
Solution: