1
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+3
-0.75
The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices $$\left( {0,0} \right),\left( {0,21} \right)$$ and $$\left( {21,0} \right)$$, is
A
133
B
190
C
233
D
105
2
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+2
-0.5
Coefficient of $${t^{24}}$$ in $${\left( {1 + {t^2}} \right)^{12}}\left( {1 + {t^{12}}} \right)\left( {1 + {t^{24}}} \right)$$ is
A
$${}^{12}{C_6} + 3$$
B
$${}^{12}{C_6} + 1$$
C
$${}^{12}{C_6}$$
D
$${}^{12}{C_6} + 2$$
3
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+2
-0.5
If $$\,\alpha \in \left( {0,{\pi \over 2}} \right)\,\,then\,\,\sqrt {{x^2} + x} + {{{{\tan }^2}\alpha } \over {\sqrt {{x^2} + x} }}$$ is always greater than or equal to
A
$$2\,\tan \alpha \,$$
B
1
C
2
D
$${\sec ^2}\,\alpha $$
4
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+2
-0.5
If W1, W2 and W3 represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3. IIT-JEE 2003 Screening Physics - Work Power & Energy Question 29 English
A
W1 > W2 > W3
B
W1 = W2 = W3
C
W1 < W2 < W3
D
W2 > W1 > W3
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