Six students, named Ajay, Bharat, Chandan, Dinesh, Gaurav and Hitesh secured 10, 20, 30, 40, 50 and 60 marks in an examination (in no particular order). Names of their fathers were Ajit, Bhushan, Chandrakant, Dattaray, Gangadhar and Hari (in no p...

Algebra

a,b,c and d are four real numbers such that a2 – b = b2 – c = c2 – d = d2 – a . Find the value of (a+b) (b+ c)(c+d)(d + a).
A. -1
B. 1
C. 0
D. None of these

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Geometry

The angle bisectors BD and CE of a triangle ABC are divided by the incentre I in the ratios 3 : 2 and 2 : 1 respectively. Then the ratio in which I divides the angle bisector through A is-

(A) 3 : 1
(B) 11 : 4
(C) 6 : 5
(D) 7 : 4


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Numbers

If x, y are natural numbers such that 2013 + x2 = y2, then the minimum possible value of xy is

A. 671
B. 668
C. 658
D. 645

Numbers

For how many positive integers p, is (30 – p)/(p-10) is a prime number ?

For how many of the following values of k can F( x ) = ( k + 10) x2 + ( k + 10) x – 9 = 0 have equal roots?

(i) −46 (ii) −25 (iii) −10 (iv) −3 (v) 10

A. 1
B. 2
C. 3
D. 0

If the ratio of the lengths of two trains is 2 : 3 and the ratio of the times taken by them to cross each other when travelling in the same direction and when travelling in opposite directions is 4 : 1, the ratio of the speed of the faster train ...

Lalu ’s daughter, Misa, has twice as many sisters as brothers, whereas her brother, Tejasvi, has thrice as many sisters as brothers. How many children does Lalu have?

A.  8
B.  9
C. 11
D. 13.

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