Sequences and Series Arithmetic Progression What is AP ? When the sequences or series number increase or decreases by the fixed quantity , then the sequence or series is known Arithmetic progression. General Expression of A.P. : a , a+d , a + 2d , a+3d ......... where a is the first term and d is common difference nth term (a n ) : It represent the nth term of an A.P. , and it can be write down as a n = a + (n-1)d NOTE : The difference between consecutive terms is always d Sum of first n terms of an A.P. S n = a + (a+d) + (a+2d) + ....... + (a + (n-1)d) Arithmetic Mean (AM) : When three numbers are in A.P. , then middle one is called arithmetic mean of other two. If a and b are two number and AM is the arithmetic mean of a and b , it means a , AM , b are in A.P. How to insert n arithmetic means between two numbers AM 1 , AM 2 , AM 3 .....AM n are n arithmetic means between two numbers a and b , So the seque...

permutation and combination Question no. 31 In a plane , there are 10 points out of which 4 are collinear , then the number of triangles that can be formed by joining these points are looks_one 60 looks_two 116 looks_3 120 looks_4 None of these Answer Option looks_two 116 Solution Solution : No. of triangles = n C 3 - p C 3 = 10 C 3 - 4 C 3 = 120 - 4 = 116 Question no. 32 The number of straight lines joining 8 points on a circle is looks_one 8 looks_two 16 looks_3 24 looks_4 28 Answer Option looks_4 28 Solution Solution : No. of straight line = n(n-1)/2 = 8 *7 / 2 = 28 Question no. 33 The number of diagonals in a polygon of m sides is looks_one m(m-5)/2! looks_two m(m-1)/2! looks_3 m(m-3)/2! looks_4 m(m-2)/2! Answer Option looks_3 m(m-3)/2! Solution Solution : The number of diagonals in a polygon of m sides is m(m-3)/2! Question no. 34 How many ...

Sequence , Series and Logarithm Question no. 1 What is the eighth term of the sequence 1, 4, 9, 16, 25.... ? looks_one 8 looks_two 128 looks_3 64 looks_4 None of these Answer Option looks_3 64 Solution Solution : Given series consists of the perfect square terms , so given sequence is 1 , 4 ,9 , 16 ,25 , 36 , 49 , 64 ..... so the 8th term is 64 Question no. 2 The value of (1 3 +2 3 +3 3 +....+15 3 ) – (1+2+3+.... 15) is: looks_one 14280 looks_two 14400 looks_3 12280 looks_4 None of these Answer Option looks_one 14280 Solution Solution : For cubic power terms (1 3 +2 3 +3 3 +....+15 3 ) – (1+2+3+.... 15) = 14400 - 120 = 14280 Question no. 3 Iflog a b= 1/2, log b c= 1/3 and log c a = K/5 , then the value of K looks_one 25 looks_two 35 looks_3 20 looks_4 30 Answer option looks_4 30 Solution Solution : log a b = 1/2 log b c = 1/3 log a c = K/5 log a b * lo...

Boat and stream Question no. 1 A person can swim in still water at 4 km/h. If the speed of water is 2 km/h, how many hours will the man take to swim back against the current for 6 km. looks_one 3 looks_two 4 looks_3 4.5 looks_4 None of these Answer Option looks_one 3 Solution Solution : Speed of swim = 4 km/hr Speed of water = 2 km/ hr against the water speed of swim = 2 km/hr Time taken by man = distance/ speed = 6 / 2 = 3 hr Question no. 2 A man can swim in still water at 4.5 km/h, buttakes thrice as long to swim upstream than downstream. The speed of the stream is looks_one 2.25 looks_two 2 looks_3 3 looks_4 None of these Answer Option looks_one 2.25 Solution Solution : speed of swim = 4.5 km/hr Time taken to downstream = x hr Time taken to upstream = 3x hr Speed of stream = z distance of upstream = distance of downstream (4.5 - z) * 3x = (4.5 + z )* x ( 4.5 - z )* 3 = 4.5 + z 4.5 + z = 13.5 - 3...

Active And Passive Voice Question no. 11 Dogs always chase cats. looks_one Cats are always chasing dogs. looks_two Cats have been always chased by dogs. looks_3 Cats are always chased by dogs. looks_4 Cats are being always chased by dogs Question no. 12 She gave me a pen. looks_one I was given a pen by her. looks_two She was given a pen. looks_3 A pen is given by her to me. looks_4 I was given her a pen. Question no. 13 You should not offer meat to vegetarians. looks_one Vegetarians should not be offered meat. looks_two Meat should be offered to non-vegetarians. looks_3 Vegetarians should not offer meat. looks_4 You should offer no meat to non-vegetarians. Question no. 14 Post the letter. looks_one The letter is posted. looks_two The letter was posted. looks_3 Let the letter be posted. looks_4 The letter will be posted. Question no. 15 Can we send this big parcel by air...