1
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

Two dices are rolled. If both dices have six faces numbered $$1,2,3,5,7$$ and $$11$$ then the probability that the sum of the number on the top faces is less than or equal to 8 is

A
$$\frac{4}{9}$$
B
$$\frac{17}{36}$$
C
$$\frac{5}{12}$$
D
$$\frac{1}{2}$$
2
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

The solution of $$\frac{d y}{d x}=1+x+y+x y$$ is

A
$$\log (1+y)=x+\frac{x^2}{2}+C$$
B
$$x+y=C(1+x y)$$
C
$$\log (1+x)+x+y=C$$
D
None of the above
3
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

$$\cos (x+y), \cos x, \cos (x-y)$$ are in HP, then $$\cos x \sec \frac{y}{2}$$ is

A
$$\sqrt{3}$$
B
$$\sqrt{2}$$
C
1
D
$$\frac{1}{\sqrt{2}}$$
4
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{2}=\alpha$$ where $$-1 \leq x \leq 1, -2 \leq y \leq 2, x \leq \frac{y}{2}$$, then for all $$x, y, 4 x^2-4 x y \cos \alpha+y^2$$ is equal to

A
$$2 \sin ^2 \alpha$$
B
$$4 \cos ^2 \alpha+2 x^2 y^2$$
C
$$4 \sin ^2 \alpha$$
D
$$4 \sin ^2 \alpha-2 x^2 y^2$$
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