Sequence & Series Set 1

If x>0 then, 1+ log_e² x/1! +log_e² x/2! + ….... =

• x

• x2

• 2x

• √x

If A, B, C are the angles of a triangle and e^ia ,e^ib, e^ic are in A.P. Then the triangle must be

• right angled

• isosceles

• equilateral

• Pluto

Find the geometric mean of numbers 7, 7^2, 7^3 ,.......,7^n

• 7 ^ (n+1/2)

• 5 ^ (n+1/2)

• 2 ^ (n+1/2)

• 3 ^ (n+1/2)

Sum of 20 terms of 1.3² + 2.5² + 3.7² + …

• 178090

• 168090

• 188090

• 198090

4. If ∑_k=1ton k(k + 1) (k — I) = pn^4 + qn^3 + fn^2 + sn where p, q, t and s are constants, then the value of s is equal to

• -1/4

• -1/2

• 1/2

• 1/4

After striking the floor a certain ball rebounds 1/4th of its height from which it has fallen. The total distance that the ball travels before coming to rest if it is gently released from a height of l20m is

• 960m

• 1000m

• 1080m

• Indefinite

If cos (x - y), cos x and cos (x —y) are in HP, then cos x sec (y / 2) is equal to

• +/-√2
• +/-1/√2
• +/-2
• None of the above

The sum to n terms of the series 1/2 +3/4 + 7/8 + 15/16 + …

• n — 1 — 2-n
• 1
• n-1 + 2-n
• 1+2-n

If a²,b, c are in GP then

• a² , b², c² are in GP

• a²(b+c),b²(a+c), c²(a+b) are in GP

• a/b+c, b/c+a, c/a+b are in GP

• None of the above

If log a, log b, and log c are in A.P, and also log a— log 2b, log 2b— log 3c, log 3c —log a are in A.P., then     

• a,b,c are in HP

• a,2b, 3c are in HP

• a,b,c are sides of triangle

• None of the above