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1) 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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2) Find the error part: (a) My mother is fond off /(b) cooking different /(c) types of dishes /(d) No error.
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3) 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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4) 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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5) 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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6) 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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7) What is the value of (a - b), if (a^2 - b^2)/(a + b) = 25?
Explanation :
According to the identity,
a^2 - b^2 = (a + b) (a - b)
It is given that (a^2 - b^2)/(a + b) = 25
So, it can be written as (a + b) (a - b)/(a + b) = 25
Hence, (a - b) = 25
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8) Which of the following is the unit digit in (1570)^2 + (1571)^2 + (1572)^2 + (1573)^2?
Explanation :
Pick up the unit digit of each number and multiply them;
0^2 in (1570)^2 = 0
1^2 in (1571)^2 = 1
2^2 in (1572)^2 = 4
3^2 in (1573)^2 = 9
On adding the unit digits, we will get,
0 1 4 9 = 14 (unit digit = 4)
So, on adding (1570)^2 (1571)^2 (1572)^2 (1573)^2, the unit digit will be 4.
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9) Find the odd number/letters from the given alternatives.
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10) Find the odd number / letters / word from the given alternative.
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