PART - 2 CH - 12 Limits and Derivatives — MATHS STD 11 Science — Question

In a non-leap year, the probability of having 53 tuesdays or 53 wednesdays is:

1. $\frac{1}{7}$

2. $\frac{2}{7}$

3. $\frac{3}{7}$

4. none os these.

1. $\frac{5\pi}{6}$
   
2. $\frac{2\pi}{3}$
   
3. $\frac{\pi}{6}$
   
4. $\frac{\pi}{3}$
   

One vertex of the equilateral triangle with centroid at the origin and one side as x + y - 2 = 0 is:

1. (-1, -1)
2. (2, 2)
3. (-2, -2)
4. (2, -2)

[Hint: Let ABC be the equilateral triangle with vertex A (h, k) and let $\text{D}(\alpha,\beta)$ be the point on BC. Then $\frac{2\alpha+\text{h}}{3}=0=\frac{2\beta+\text{k}}{3}.$ Also $\alpha+\beta-2=0$ and $\frac{\text{k}-0}{\text{h}-0}\times(-1)=-1\Big].$

The value of $\cot\Big(\frac{\pi}{4}+\theta\Big)\cot\Big(\frac{\pi}{4}-\theta\Big)$ is:

1. -1

2. 0

3. 1

4. Not defined

1. $\frac{1}{3}$
   
2. $\frac{1}{4}$
   
3. $\frac{5}{12}$
   
4. $\frac{2}{3}$