1
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$a = \min \{ {x^2} + 2x + 3:x \in R\} $$ and $$b = \mathop {\lim }\limits_{\theta \to 0} {{1 - \cos \theta } \over {{\theta ^2}}}$$. Then $$\sum\limits_{r = 0}^n {{a^r}{b^{n - r}}} $$ is
A
$${{{2^{n + 1}} - 1} \over {3\,.\,{2^n}}}$$
B
$${{{2^{n + 1}} + 1} \over {3\,.\,{2^n}}}$$
C
$${{{4^{n + 1}} - 1} \over {3\,.\,{2^n}}}$$
D
$${1 \over 2}({2^n} - 1)$$
2
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let a > b > 0 and I(n) = a1/n $$-$$ b1/n, J(n) = (a $$-$$ b)1/n for all n $$ \ge $$ 2, then
A
I(n) < J(n)
B
I(n) > J(n)
C
I(n) = J(n)
D
I(n) + J(n) = 0
3
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$\widehat \alpha $$, $$\widehat \beta $$, $$\widehat \gamma $$ be three unit vectors such that $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = {1 \over 2}(\widehat \beta + \widehat \gamma )$$ where $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = $$$$(\widehat \alpha \,.\,\widehat \gamma )\widehat \beta - (\widehat \alpha \,.\,\widehat \beta )\widehat \gamma $$. If $$\widehat \beta $$ is not parallel to $$\widehat \gamma $$, then the angle between $$\widehat \alpha $$ and $$\widehat \beta $$ is
A
$${{5\pi } \over 6}$$
B
$${{\pi } \over 6}$$
C
$${{\pi } \over 3}$$
D
$${{2\pi } \over 3}$$
4
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The position vectors of the points A, B, C and D are $$3\widehat i - 2\widehat j - \widehat k$$, $$2\widehat i - 3\widehat j + 2\widehat k$$, $$5\widehat i - \widehat j + 2\widehat k$$ and $$4\widehat i - \widehat j - \lambda \widehat k$$, respectively. If the points A, B, C and D lie on a plane, the value of $$\lambda$$ is
A
0
B
1
C
2
D
$$-$$ 4
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12