NPAT 27th June 2021 Shift 1

If the mean of the following distribution is 22, then what will be the value of x?

Let x be the median of the data: 13, 17, 52, 56, 65, 35, 77, 39, 15, 37. If 35 is replaced by 53 in the data, then the median of the new data will bey. What is the difference between x and y?

A biased coin is such that the probability of getting a head is thrice the probability of getting a tail. If the coin is tossed 4 times, what will be the probability of getting a head all the times?

If the standard deviation of $$x_1, x_2, x_3, .... x_n \text{is} k$$, then what will be the standard deviation of $$\frac{10x_1 - 7}{2}, \frac{10x_2 - 7}{2}, ...., \frac{10x_n - 7}{2}$$?

What is the variance of the following data?

9, 10, 13, 14, 6, 11, 8, 7, 4, 18

Two persons, on either side of a tower 45 m high, obsetve the angles of elevation of the top of the tower to be $$30^\circ$$ and $$60^\circ$$, respectively. The distance (in m) between the two persons is:

$$\frac{(2 \sin^2 \theta - 1)(1 + \tan^2 \theta)(\sec \theta + \tan \theta)(1 - \sin \theta)}{(\sec^2 \theta - 1)(\tan \theta - \cot \theta)\cos^2 \theta}, 0^\circ < \theta < 90^\circ$$, is equal to:

$$\frac{\tan^2 \theta + \cot^2 \theta + 2}{\sec \theta \cosec \theta}, 0^\circ < \theta < 90^\circ$$, is equal to:

If $$\sec(5^\circ -2 \theta) = \cosec(5 \theta - 5^\circ), 0^\circ < \theta < 90^\circ$$, then what will be the value of $$\frac{\sin 3\theta + \tan 2 \theta}{\sec 2 \theta}$$?

In $$\triangle ABC, \angle B = 90^\circ, BC = 6 \text{cm} \text{and} AC = 10 \text{cm}$$. What is the value of $$\sin 2A - \cos 2A$$?