A square is drawn by joining the mid-points of the sides of a given square. A third square is drawn inside the second square in the same way, and the process continues indefinitely. If a side of the first square is 16 cm., determine the sum of the areas of all the squares.

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:

• 46^th

• 59^th

• 52^nd

• 52^nd

If the 2^nd, 5^th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

• 8/5

• 4/3

• 1

• 1

If the sum of the first ten terms of the series,

is 16/5 m, the m is equal to

• 102

• 101

• 100

• 100

The sum of first 9 terms of the series  is

• 71

• 96

• 142

• 142

Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

148.

The sum of first 20  terms of the sequence 0.7,0.77,0.777...... is

• 
• 
• 
• 

If x, y, z are in A.P. and tan⁻¹ x, tan⁻¹ y and tan⁻¹ z are also in A.P., then

• x= y= z

• 2x =3y = 6z

• 6x = 3y= 2z

• 6x = 3y= 2z

Statement 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... + (361 + 380 +400) is 8000.
Statement 2: , for any natural number n.

• 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