1
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.

Then
A
f(x) has 13 non-zero real roots
B
f(x) has exactly one real root
C
f(x) has exactly one pair of imaginary roots
D
f(x) has no real root
2
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The area of the region

$$\{ (x,y):{x^2} + {y^2} \le 1 \le x + y\} $$ is
A
$${{{\pi ^2}} \over 2}$$
B
$${\pi \over 4}$$
C
$${\pi \over 4}$$$$ - $$$${1 \over 2}$$
D
$${{{\pi ^2}} \over 3}$$
3
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Change Language
In open interval $$\left( {0,\,{\pi \over 2}} \right)$$
A
cos x + x sin x < 1
B
cos x + x sin x >1
C
no specific order relation can be ascertained between cos x + x sin x and 1
D
$$\cos \,x + x\,\sin \,x < {1 \over 2}$$
4
WB JEE 2020
MCQ (Single Correct Answer)
+2
-0.5
Change Language
If the line y = x is a tangent to the parabola y = ax2 + bx + c at the point (1, 1) and the curve passes through ($$ - $$1, 0), then
A
a = b = $$ - $$1, c = 3
B
a = b = $${1 \over 2}$$, c = 0
C
a = c = $${1 \over 4}$$, b = $${1 \over 2}$$
D
a = 0, b = c = $${1 \over 2}$$
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