NPAT Common 2020 QP3

The mean deviation about the mean of the dataset 22, 24, 30, 27, 29, 31, 25, 28, 41, 43, 30 is:

Consider the following distribution:

The mean of the distribution is 8.84 years. The value of xis:

Let x be the median of the data:
20,50,60,53, 77,88,90, 40,30, 70,25,45,64, 72,8, 15,85,60,55,28.
Ify is the median of the same dataset when 25 and 28 are replaced by 52 and 82 respectively, then what is the value of $$\mid x-y \mid$$ ?

An integer is selected at random from the set { 100, 101, 102, .... , 999 }. What is the probability that the sum of the digits of the selected number is the same as the product of its digits?

What is the standard deviation of the given data set: 25, 50, 45, 30, 70, 42, 36, 48, 34, 60 (correct to two decimal places).

From the top of a tower of height 18 m, a bullet is shot at an angle of depression of 60° to hit a target lying on the ground. The bullet missed the target and hit a point in between the line j oining the foot of the tower and the target, which is 6 m away from the target. What is the tangent of the angle of depression at which the bullet should have been shot so as to hit the target?

If $$\cos^{2}\theta( \tanh^{2}\theta-\sin^{2}\theta)\times (\tan^{2}\theta+\cot^{2}\theta+2)=k-1$$, then k = ?

$$\frac{sin\theta}{sec\theta+tan\theta-1}-\frac{cos\theta}{cosec\theta+cot\theta-1}$$ is equal to:

If $$3\tan\theta+5\cosec\theta$$, where $$0^\circ < 9 < 90^\circ$$, then the value of $$\large\frac{\cos\theta+\sin\theta}{\cos\theta-\sin\theta}$$ is:

The value of $$\large\frac{\sin^{2}1^{\circ}+\sin^{2}3^{\circ}+\sin^{2}5^{\circ}+....+\sin^{2}89^{\circ}}{\cosec^{2}62^{\circ}-\tan 28^{\circ}\cot 62^{\circ} + (\sec^{2}37^{\circ} - \cot^{2}53^{\circ})}$$ is: