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1) Find the error part: (a) Nobody denies /(b) that my ideas /(c) are different than yours. /(d) No error.
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2) Find the error part: He always says (a)/that he prefers to go (b)/home to stay in (c)/a hotel at night. (d)/
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3) Find the error part: (a) My mother is fond off /(b) cooking different /(c) types of dishes /(d) No error.
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4) If the sum of two numbers is 12 and their product is 35, then what will be the sum of their reciprocals?
Explanation :
Suppose the numbers are P and Q
So, according to the question -
P + Q = 12
P * Q = 35
Sum of reciprocals of P and Q is = 1/P + 1/Q
= Q + P/PQ
= 12/35
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5) If the sum and reciprocal of a number is equal to 2, the number is
Explanation :
Suppose the number is a.
So, according to the question -
a + 1/a = 2
(a^2 + 1)/a = 2
a^2 + 1 = 2a
Or, a^2 + 1 -2a = 0
We can say that (a - 1)2 = 0
So, a =1
Hence the required number is 1, whose sum and reciprocal are equal to 2.
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6) If the ratio of two positive numbers is 7 : 9 and their product is 1575, then the greatest number is
Explanation :
Given ration 7 : 9
So, let the numbers be 7a and 9a. According to the question -
7a * 9a = 1575
63a² = 1575
a² = 1575/63
Or a² = 25
And a =5
So, the two numbers will be -
7a = 7 * 5 = 35
And 9a = 9 * 5 = 45
Hence, the greater number is 45 between the given numbers.
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7) The sum of two numbers is equal to the thrice of their difference. What will be the ratio between them?
Explanation :
Let the numbers be 'a' and 'b'. According to the question -
(a + b) = 3(a - b)
(a + b) = 3a - 3b
2a = 4b
a = 2b
So, a/b = 2 : 1
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8) Which of the following is equal to x^3?
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9) The sum of four consecutive even numbers is 748, then which is the smallest number among them?
Explanation :
Let a be the smallest even number
So, according to the question -
(a) + (a + 2) + (a + 4) + (a + 6) = 748
4(a) + 12 = 748
4a = 736
Or, a = 184
So, the smallest number be 184
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10) If (64)² - (36)²= 20 * x, then what is the value of x?
Explanation :
Here, we can apply the formula of
a^2 - b^2 = (a + b) (a - b)
So, after applying the formula, we will get
(64 + 36) (64 - 36) = 20 * x
100 * 28 = 20 * x
x = 100 * 28/ 20 = 140
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