Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

Posted by XIPP on Dec 09, 2013; 4:53am
URL: http://discussion-forum.276.s1.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p7584328.html

Duck, just have a doubt. Why other posts call you Nidhi? How they got to know your name? Will they also know my real name without being mentioned myself?(Also I think you have completed your masters, right?)

By the way, as Shreya's olders posts suggest, she wants to ask the prev. Amit Sir's questions :

If a < b < c < d, then the equation (x − a)(x − b) + 2(x − c)(x − d) = 0 has
(a) both the roots in the interval [a, b],
(b) both the roots in the interval [c, d],
(c) one root in the interval (a, b) and the other root in the interval (c, d),
(d) one root in the interval [a, b] and the other root in the interval [c, d].

Let f and g be two differentiable functions on (0, 1) such that f(0) = 2, f(1) = 6, g(0) = 0 and g(1) = 2. Then there exists θ ∈ (0, 1) such that f'(θ) equals
(a) (1/2)g'(θ),
(b) 2g'(θ),
(c) 6g'(θ),
(d) (1/6)g'(θ).

The minimum value of log(x)a + log(a)x, for 1 < a < x, is
(a) less than 1,
(b) greater than 2,
(c) greater than 1 but less than 2.
(d) None of these.

The value of ∫(1/(2x(1+√x)))dx over [4, 9] equals
(a) log(e)3 − log(e)2,
(b) 2log(e)2 − log(e)3,
(c) 2log(e)3 − 3log(e)2,
(d) 3log(e)3 − 2log(e)2.

Read log(x)a as log value of a when x is the base, And likewise others.
Read ∫(1/(2x(1+√x)))dx over [4, 9] as the value of definite integral of the said function over the range [4, 9]