IIT-JEE Exam

The number of values of k, for which the system of
equation : (k + 1) x + 8y = 4k, kx + (k + 3) y = 3k –1,
has no solution, is -
(1) 2 (2) 3 (3) infinite (4) 1

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IIT-JEE Other Question

The real number k for which the equation, 2x^3 + 3x
+ k = 0 has two distinct real roots in [0, 1]
(1) lies between –1 and 0
(2) does not exist
(3) lies between 1 and 2
(4) lies between 2 and 3
Let Tn be the number of all possible triangles
formed by joining vertices of an n-sided regular
polygon. If Tn+1 – Tn = 10 then the value of n is -
(1) 10 (2) 8 (3) 7 (4) 5