Algebra

For how many integers ‘a’ is at least one root of the equation x³ – ax + a + 11 = 0 is a positive integer?
i) 0
ii) 2
iii) 4
iv) 5
v) More than 5

Geometry

A quadrilateral PQRS is formed by the intersection of angle bisectors of a quadrilateral ABCD. If ∠ QPS = 80º, then find the measure of the ∠ QRS.

Numbers

If a and b are two real numbers which satisfy a + b − ab = 1 and a is not an integer, then b

(a) is never an integer
(b) must be some positive integer
(c) must be some negative integer 
(d) must be equal to 0
(e) may either be an integer or a non-integer

Numbers

Which one of the following integers can be represented as the sum of 100 consecutive positive integers ?

A. 357911100
B. 23450910
C. 1005050
D. 78658925

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Arithmetic 

Virat is between his home and the Jawahar Lal Nehru stadium . To get to the stadium he can walk directly to the stadium or else he can walk home and then ride a bicycle to the stadium . He rides seven times as fast as he walks and both choices require same amount of time . What is the ratio of Virat’s distance from his home to his distance  to the stadium  ?

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Counting

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions ?

A. 16
B. 36
C. 60
D. 180

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Geometry

The parallel sides of Trapezium is 6 and 8 units respectively. Find the length of the line segment parallel to these sides and which divides the area of trapezium in equal halves.

A. 4 √3
B. 5 √ 2
C. 7
D. 7/√2

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Arithmetic 

Gaurav bought three apples , five mangoes and eight bananas for ₹87 , had he bought five apples , seven mangoes and six bananas , it would have cost him ₹121 . By how much do an apple and a mango together cost more than banana .

A. 15
B. 17
C. 19
D. 20