Number System - Study Mode

[#71] Among the following statements, the statement which is 'not correct' is :
Correct Answer

(B) Every real number is a rational number

Explanation

Solution: Every real number is a rational number

[#72] Sum of three consecutive integers is 51. The middle one is -
Correct Answer

(D) 17

Explanation

Solution: Let numbers are a, a + 1, a + 2 Then, a + a + 1 + a + 2 = 51 3a + 3 = 51 3a = 48 a = 16 Middle number : = a + 1 = 16 + 1 = 17

[#73] The sum of 10 terms of the arithmetic series is 390. If the third term of the series is 19. Find the first term :
Correct Answer

(A) 3

Explanation

Solution: Sum of A.P. = $$frac{n}{2}left[ {2a + (n - 1)d}
ight]$$ n th term = a + (n - 1)d 3 rd term : ⇒ a + (3 - 1)d = 19 ⇒ a + 2d = 19.....(i) Sum of 10 term : $$eqalign{
& Rightarrow frac{{10}}{2}left[ {2a + 9d}
ight] = 390 cr
& Rightarrow 2a + 9d = 78..... (ii) cr
& Rightarrow a + 2d = 19 cr} $$ From equation (i) and (ii) a = 3 d = 8

[#74] If p = - 0.12, q = - 0.01 and r = - 0.015, then the correct relationship among the three is :
Correct Answer

(A) p < r < q

Explanation

Solution: ∵ p = - 0.12 q = - 0.01 r = - 0.015 If all values would be positive 0.12 > 0.015 > 0.01 p > r > q But these are negative so their order will be q > r > p

[#75] The sum of squares of three positive integers is 323. If the sum of squares of two numbers is twice the third, their product is :
Correct Answer

(A) 255

Explanation

Solution: Let the integers in a, b, c a 2 + b 2 + c 2 = 323.....(i) a 2 + b 2 + = 2c.....(ii) Break the 323 in to their squares a = 5 b = 3 c = 17 So, a 2 + b 2 + c 2 = 323 and a 2 + b 2 = 2c 25 2 + 3 2 = 2 × 17 34 = 34 So, Satisfied a : b : c = 17 × 5 × 3 = 255