1
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
A rectangle with sides of lenght (2m - 1) and (2n - 1) units is divided into squares of unit lenght by drawing parallel lines as shown in the diagram, then the number of rectangles possible with odd side lengths is IIT-JEE 2005 Screening Mathematics - Permutations and Combinations Question 36 English
A
$${(m + n - 1)^2}$$
B
$${4^{m + n - 1}}$$
C
$${m^2}\,{n^2}$$
D
$$m(m + 1)\,n\,(m + 1)$$
2
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
The value of $$$\left( {\matrix{ {30} \cr 0 \cr } } \right)\left( {\matrix{ {30} \cr {10} \cr } } \right) - \left( {\matrix{ {30} \cr 1 \cr } } \right)\left( {\matrix{ {30} \cr {11} \cr } } \right) + \left( {\matrix{ {30} \cr 2 \cr } } \right)\left( {\matrix{ {30} \cr {12} \cr } } \right)....... + \left( {\matrix{ {30} \cr {20} \cr } } \right)\left( {\matrix{ {30} \cr {30} \cr } } \right)$$$
is where $$\left( {\matrix{ n \cr r \cr } } \right) = {}^n{C_r}$$
A
$$\left( {\matrix{ {30} \cr {10} \cr } } \right)$$
B
$$\left( {\matrix{ {30} \cr {15} \cr } } \right)$$
C
$$\left( {\matrix{ {60} \cr {30} \cr } } \right)$$
D
$$\left( {\matrix{ {31} \cr {10} \cr } } \right)$$
3
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
$$\cos \left( {\alpha - \beta } \right) = 1$$ and $$\,\cos \left( {\alpha + \beta } \right) = 1/e$$ where $$\alpha ,\,\beta \in \left[ { - \pi ,\pi } \right].$$
Paris of $$\alpha ,\,\beta $$ which satisfy both the equations is/are
A
0
B
1
C
2
D
4
4
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
A simple pendulum has time period T1. The point of suspension is now moved upward according to the relation y = Kt2, (K = 1 m/s2) where y is the vertical displacement. The time period now become T2. The ratio of $${{T_1^2} \over {T_2^2}}$$ is (g = 10 m/s2)
A
$${5 \over 6}$$
B
$${6 \over 5}$$
C
1
D
$${4 \over 5}$$
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