If A = $\left[\begin{array}{cc}3& 1\\ - 1& 2\end{array}\right]$ and B = $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, Find A² - 5A + 7I

The monthly pocket money of Ravi and Sanjeev are in the ratio 5:7. Their expenditures are in the ratio 3:5. If each saves Rs. 80 every month, find their monthly pocket money

Using the Remainder Theorem factorise completely the following polynomial.

3x³ + 2x² – 19x + 6

On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.?

ABC is an isosceles right angled triangle with ∠ABC = 90$°$. A semi-circle is drawn with AC as the diameter. If AB = BC = 7 cm, find the area of the shaded region.
Take ($\mathrm{\pi } = \frac{22}{7}$)

Given a line segment AB joining the points A(– 4, 6) and B(8, – 3). Find

(i) The ratio in which AB is divided by y-axis.

(ii) Find the coordinates of the point of intersection.

(iii) The length of AB.

In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the radius of circle.

Evaluate without using trigonometric tables:

${\cos }^2\left(26°\right) + \cos \left(64°\right)\sin \left(26°\right) + \frac{\tan \left(36°\right)}{\cot \left(54°\right)}$

Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data.

Marks	5	6	7	8	9
Number of Students	6	a	16	13	b

If the mean of the distribution is 7.2, find a and b.

Kiran deposited Rs. 200 per month for 36 months in a bank’s recurring deposit account. If the bank pays interest at the rate of 11% per annum, find the amount she gets on maturity.