1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
A
$$7!\, \times 5!\,\,$$
B
$$6!\, \times 5!$$
C
$$30!$$
D
$$5!\, \times 4!$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
If $${}^n{C_r}$$ denotes the number of combination of n things taken r at a time, then the expression $$\,{}^n{C_{r + 1}} + {}^n{C_{r - 1}} + 2\, \times \,{}^n{C_r}$$ equals
A
$$\,{}^{n + 1}{C_{r + 1}}$$
B
$${}^{n + 2}{C_r}$$
C
$${}^{n + 2}{C_{r + 1}}$$
D
$$\,{}^{n + 1}{C_r}$$
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The sum of the serier $${1 \over {1.2}} - {1 \over {2.3}} + {1 \over {3.4}}..............$$ up to $$\infty $$ is equal to
A
$$\log {\,_e}\left( {{4 \over e}} \right)\,\,$$
B
$$2\,\log {\,_e}2$$
C
$$\log {\,_e}2 - 1\,$$
D
$$\log {\,_e}2$$
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
A square of side a lies above the $$x$$-axis and has one vertex at the origin. The side passing through the origin makes an angle $$\alpha \left( {0 < \alpha < {\pi \over 4}} \right)$$ with the positive direction of x-axis. The equation of its diagonal not passing through the origin is :
A
$$y\left( {\cos \alpha + \sin \alpha } \right) + x\left( {\cos \alpha - \sin \alpha } \right) = a$$
B
$$y\left( {\cos \alpha - \sin \alpha } \right) - x\left( {\sin \alpha - \cos \alpha } \right) = a$$
C
$$y\left( {\cos \alpha + \sin \alpha } \right) + x\left( {\sin \alpha - \cos \alpha } \right) = a$$
D
$$y\left( {\cos \alpha + \sin \alpha } \right) + x\left( {\sin \alpha + \cos \alpha } \right) = a$$
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