1
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
The real number $$k$$ for which the equation, $$2{x^3} + 3x + k = 0$$ has two distinct real roots in $$\left[ {0,\,1} \right]$$
A
lies between 1 and 2
B
lies between 2 and 3
C
lies between $$ - 1$$ and 0
D
does not exist.
2
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
The number of values of $$k$$, for which the system of equations : $$$\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \cr {kx + \left( {k + 3} \right)y = 3k - 1} \cr } $$$
has no solution, is
A
infinite
B
1
C
2
D
3
3
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
If z is a complex number of unit modulus and argument $$\theta $$, then arg $$\left( {{{1 + z} \over {1 + \overline z }}} \right)$$ equals :
A
$$ - \theta \,\,$$
B
$${\pi \over 2} - \theta \,$$
C
$$\theta \,$$
D
$$\,\pi - \theta \,\,$$
4
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
The expression $${{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \over {1 - \tan {\rm A}}}$$ can be written as:
A
$$\sin {\rm A}\,\cos {\rm A} + 1$$
B
$$\,\sec {\rm A}\,\cos ec{\rm A} + 1$$
C
$$\tan {\rm A} + \cot {\rm A}$$
D
$$\sec {\rm A} + \cos ec{\rm A}$$
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