8386 . একটি ছক্কা এমনভাবে তৈরি যেন জোড় সংখ্যা আসার সম্ভাবনা বেজোড় সংখ্যা আসার সম্ভাবনার দ্বিগুণ হয়। ছক্কাটি একবার নিক্ষেপ পরীক্ষায় 4 এর কম পড়ার সম্ভাবনা কত? ( A biased die is so loaded that an even number is twice as likely to appear compared to an odd number. Find the probability of getting a number less than 4 in a single toss?)

• A. 1/9
• B. 4/6
• C. 4/9
• D. 1/6

Answer: Option A

Explanation:

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $1$

Answer: Option C

Explanation:

• A. $2+\sqrt{2}$
• B. $3-\sqrt{2}$
• C. $3+\sqrt{2}$
• D. $2-\sqrt{2}$

Answer: Option D

Explanation:

• A. $\frac{1}{8}\mathrm{\pi } {\mathrm{g}}^2$
• B. $\frac{1}{4}\mathrm{\pi } {\mathrm{g}}^2$
• C. $\frac{1}{2}\mathrm{\pi } {\mathrm{g}}^2$
• D. $\mathrm{\pi } {\mathrm{g}}^2$

Answer: Option B

Explanation:

• A. $3\sqrt{2}$
• B. $2\sqrt{3}$
• C. $10$
• D. $3\sqrt{5}$

Answer: Option C

Explanation:

• A. $x$
• B. $y$
• C. $\frac{1}{x}$
• D. $\frac{1}{y}$

Answer: Option A

Explanation:

• A. $\left[\begin{array}{ccc}5& 5& 1\\ 4& 2& 2\\ 1& 6& 6\end{array}\right]$
• B. $\left[\begin{array}{ccc}1& 5& 1\\ 4& -2& 2\\ 1& 6& 2\end{array}\right]$
• C. $\left[\begin{array}{ccc}1& 3& -1\\ 4& 0& 2\\ 1& 6& 4\end{array}\right]$
• D. $\left[\begin{array}{ccc}1& 3& -1\\ 2& -2& 0\\ -1& 4& 2\end{array}\right]$

Answer: Option B

Explanation:

• A. $-\sin \sqrt{x}$
• B. $\frac{-\sin \sqrt{x}}{2\sqrt{x}}$
• C. $\frac{-\sin \sqrt{x}}{\sqrt{x}}$
• D. $\frac{\sin \sqrt{x}}{2\sqrt{x}}$

Answer: Option B

Explanation:

• A. $1$
• B. $0$
• C. $2$
• D. $\frac{1}{2}$

Answer: Option C

Explanation:

• A. $3$
• B. $5$
• C. $\frac{47}{4}$
• D. $\frac{29}{4}$

Answer: Option D

Explanation:

• A. $\frac{1}{2}$
• B. $1$
• C. $\frac{3}{2}$
• D. $3$

Answer: Option C

Explanation:

• A. $0$
• B. $\frac{\mathrm{\pi }}{2}$
• C. $\mathrm{\pi }$
• D. $2\mathrm{\pi }$

Answer: Option C

Explanation:

• A. $2{\sin }^2\theta$
• B. $2{\cos }^2\theta$
• C. $\sin 2\theta$
• D. $\cos 2\theta$

Answer: Option D

Explanation:

• A. $-\frac{5}{2}$
• B. $-\frac{5}{12}$
• C. $\frac{5}{12}$
• D. $\frac{5}{3}$

Answer: Option D

Explanation:

• A. 30°
• B. 45°
• C. 60°
• D. 120°

Answer: Option B

Explanation: