1
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

The area of the region bounded by the parabola $$y=x^2+1$$ and lines $$y=x+1, y=0, x=\frac{1}{2}$$ and $$x=2$$ is

A
$$\frac{23}{6}$$
B
$$\frac{23}{16}$$
C
$$\frac{79}{24}$$
D
$$\frac{79}{16}$$
2
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

Let $$\mathbf{a}=2 \mathbf{i}+\mathbf{j}+\mathbf{k}, \mathbf{b}=\mathbf{i}+2 \mathbf{j}-\mathbf{k}$$ and $$a$$ unit vector $$\mathbf{c}$$ be coplanar. If $$\mathbf{c}$$ is perpendicular to $$\mathbf{a}$$, then c equals to

A
$$\frac{1}{\sqrt{5}}(\hat{\mathbf{i}}-2 \hat{\mathbf{j}})$$
B
$$\frac{1}{\sqrt{2}}(-\hat{\mathbf{j}}+\hat{\mathbf{k}})$$
C
$$\frac{1}{\sqrt{3}}(\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}})$$
D
$$\frac{1}{\sqrt{3}}(-\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}})$$
3
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

A six faced die is a biased once. It is thrice more likely to show an odd number, then show an even number. It is thrown twice. The probability that the sum of the number in two throws is odd, is

A
$$\frac{5}{8}$$
B
$$\frac{1}{8}$$
C
$$\frac{7}{8}$$
D
$$\frac{3}{8}$$
4
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

If $$n$$ is the number of solutions of the equation $$2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1, x \in[0, \pi]$$ and $$S$$ is the sum of all these solutions, then the ordered pair $$(n, S)$$ is

A
$$(3,13 \pi / 9)$$
B
$$(2,2 \pi / 3)$$
C
$$(2,8 \pi / 9)$$
D
$$(3,5 \pi / 3)$$
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