1
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
The equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has:
A
infinite number of real roots
B
no real roots
C
exactly one real root
D
exactly four real roots
2
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:
A
880
B
629
C
630
D
879
3
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
If $$n$$ is a positive integer, then $${\left( {\sqrt 3 + 1} \right)^{2n}} - {\left( {\sqrt 3 - 1} \right)^{2n}}$$ is :
A
an irrational number
B
an odd positive integer
C
an even positive integer
D
a rational number other than positive integers
4
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

Statement-1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) +.....+ (361 + 380 + 400) is 8000.

Statement-2: $$\sum\limits_{k = 1}^n {\left( {{k^3} - {{(k - 1)}^3}} \right)} = {n^3}$$, for any natural number n.

A
Statement-1 is false, Statement-2 is true.
B
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
C
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
D
Statement-1 is true, Statement-2 is false.
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