1
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
+4
-1
Change Language
Let a1, a2, ......., a10 be an AP with common difference $$-$$ 3 and b1, b2, ........., b10 be a GP with common ratio 2. Let ck = ak + bk, k = 1, 2, ......, 10. If c2 = 12 and c3 = 13, then $$\sum\limits_{k = 1}^{10} {{c_k}} $$ is equal to _________.
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2
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language
Let Q be the foot of the perpendicular from the point P(7, $$-$$2, 13) on the plane containing the lines $${{x + 1} \over 6} = {{y - 1} \over 7} = {{z - 3} \over 8}$$ and $${{x - 1} \over 3} = {{y - 2} \over 5} = {{z - 3} \over 7}$$. Then (PQ)2, is equal to ___________.
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3
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language
Let $$\left( {\matrix{ n \cr k \cr } } \right)$$ denotes $${}^n{C_k}$$ and $$\left[ {\matrix{ n \cr k \cr } } \right] = \left\{ {\matrix{ {\left( {\matrix{ n \cr k \cr } } \right),} & {if\,0 \le k \le n} \cr {0,} & {otherwise} \cr } } \right.$$

If $${A_k} = \sum\limits_{i = 0}^9 {\left( {\matrix{ 9 \cr i \cr } } \right)\left[ {\matrix{ {12} \cr {12 - k + i} \cr } } \right] + } \sum\limits_{i = 0}^8 {\left( {\matrix{ 8 \cr i \cr } } \right)\left[ {\matrix{ {13} \cr {13 - k + i} \cr } } \right]} $$ and A4 $$-$$ A3 = 190 p, then p is equal to :
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4
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
+4
-1
Change Language
Let $$\lambda$$ $$\ne$$ 0 be in R. If $$\alpha$$ and $$\beta$$ are the roots of the equation x2 $$-$$ x + 2$$\lambda$$ = 0, and $$\alpha$$ and $$\gamma$$ are the roots of equation 3x2 $$-$$ 10x + 27$$\lambda$$ = 0, then $${{\beta \gamma } \over \lambda }$$ is equal to ____________.
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