If 100 times the 100^th term of an AP with non zero common difference equals the 50 times its 50^th term, then the 150^th term of this AP is

•  –150

• 150

• times its 50th term

• times its 50th term

Let x1, x2, ......, x_n be n observations, and let be their arithmetic mean and σ2 be their variance.
Statement 1: Variance of 2x1, 2x2, ......, 2xn is 4 σ².
Statement 2: Arithmetic mean of 2x1, 2x2, ......, 2xn is 4.

• Statement 1 is false, statement 2 is true

• Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

• 18 Months

• 19 Months

• 20 Months

• 20 Months

A person is to count 4500 currency notes. Let a denote the number of notes he counts in the nth minute. If a₁ = a₂ = ... = a₁₀ = 150 and a₁₀, a₁₁, ...are in an A_P with common difference -2, then the time taken by him to count all notes is

• 24 min

• 34 min

• 125 min

• 125 min

155.

Statement-1: S₃ = 55 × 2⁹.
Statement-2: S₁ = 90 × 2⁸ and S2 = 10 × 2⁸.

• Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is true; statement-2 is not a correct explanation for Statement-1. 

• Statement-1 is true, Statement-2 is false.

• Statement-1 is true, Statement-2 is false.

For any three positive real numbers a, b and c, (25a² + b²) + 25(c² – 3ac) = 15b(3a + c), Then

• b , c and a are in G.P

• b, c and a are in A.P

• a, b and c are in A.P

• a, b and c are in A.P

Let a, b, c ∈ R. If f(x) = ax² + bx + c is such
that a + b + c = 3 and f(x + y) = f(x) + f(y) + xy, ∀x,y ∈ R,then  is equal to

• 225

• 330

• 165

• 165

The sum to infinity of the series 

• 2

• 3

• 4

• 4

Statement 1: The variance of first n even natural numbers is 
Statement 2: The sum of first n natural numbers is  and the sum of squares of first n natural numbers is 

• Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1

• Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.

• Statement–1 is true, statement–2 is false.

• Statement–1 is true, statement–2 is false.

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals