1
JEE Main 2021 (Online) 24th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
If $$n \ge 2$$ is a positive integer, then the sum of the series $${}^{n + 1}{C_2} + 2\left( {{}^2{C_2} + {}^3{C_2} + {}^4{C_2} + ... + {}^n{C_2}} \right)$$ is :
A
$${{n(2n + 1)(3n + 1)} \over 6}$$
B
$${{n(n + 1)(2n + 1)} \over 6}$$
C
$${{n{{(n + 1)}^2}(n + 2)} \over {12}}$$
D
$${{n(n - 1)(2n + 1)} \over 6}$$
2
JEE Main 2021 (Online) 24th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) $$ \ne $$ 0 for all x $$ \in $$ R. If $$\left| {\matrix{ {f(x)} & {f'(x)} \cr {f'(x)} & {f''(x)} \cr } } \right|$$ = 0, for all x$$ \in $$R, then the value of f(1) lies in the interval :
A
(0, 3)
B
(9, 12)
C
(3, 6)
D
(6, 9)
3
JEE Main 2021 (Online) 24th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$f:R \to R$$ be defined as

$$f(x) = \left\{ {\matrix{ { - 55x,} & {if\,x < - 5} \cr {2{x^3} - 3{x^2} - 120x,} & {if\, - 5 \le x \le 4} \cr {2{x^3} - 3{x^2} - 36x - 336,} & {if\,x > 4,} \cr } } \right.$$

Let A = {x $$ \in $$ R : f is increasing}. Then A is equal to :
A
$$( - 5,\infty )$$
B
$$( - \infty , - 5) \cup (4,\infty )$$
C
$$( - 5, - 4) \cup (4,\infty )$$
D
$$( - \infty , - 5) \cup ( - 4,\infty )$$
4
JEE Main 2021 (Online) 24th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x $$-$$ 1, then the co-ordinates of P are :
A
($$-$$2, 8)
B
(2, 8)
C
(1, 5)
D
(3, 13)
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