1
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The chord of the curve $$y = {x^2} + 2ax + b$$, joining the points where x = $$\alpha$$ and x = $$\beta$$, is parallel to the tangent to the curve at abscissa x is equal to
A
$${{a + b} \over 2}$$
B
$${{2a + b} \over 3}$$
C
$${{2\alpha + \beta } \over 3}$$
D
$${{\alpha + \beta } \over 2}$$
2
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 19$$. Then, f(x) = 0 has
A
13 real roots
B
only one positive and only two negative real roots
C
not more than one real root
D
has two positive nd one negative real rot
3
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $$f(x) = \left\{ {\matrix{ {{{{x^p}} \over {{{(\sin x)}^q}}},} & {if\,0 < x \le {\pi \over 2}} \cr {0,} & {if\,x = 0} \cr } } \right.$$, $$(p,q \in R)$$. Then, Lagrange's mean value theorem is applicable to f(x) in closed interval [0, x]
A
for all p, q
B
only when p > q
C
only when p < q
D
for no value of p, q
4
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
$$\mathop {\lim }\limits_{x \to 0} {(\sin x)^{2\tan x}}$$ is equal to
A
2
B
1
C
0
D
does not exist
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