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See figure 2.14.In ∆ PQR,∠PQR = 90°, seg QS ⊥seg PR then find x, y, z.
A chord PQ of a circle with radius 15 cm subtends an angle of 60° with the centre of the circle. Find the area of the minor as well as the major segment. (π = 3.14)
Write the denominator of the rational number $\frac{257}{5000}$ in the form $2^m \times 5^n$^, where m, n are non-negative integers. Hence, write the decimal expansion, without actual division.
→A ladder on the platform of a fire brigade van can be elevated at an angle of 70° to the maximum. The length of the ladder can be extended upto 20m. If the platform is 2m above the ground, find the maximum height from the ground upto which the ladder can reach. (sin 70° = 0.94)
In a tree plantation programme, the number of trees planted by students of different classes is given in the following table. Draw a pie diagram showing the information.
→| Standard | $5^{\text {th }}$ | $6^{\text {th }}$ | $7^{\text {th }}$ | $8^{\text {th }}$ | $9^{\text {th }}$ | $10^{\text {th }}$ |
| No of tree | 40 | 50 | 75 | 50 | 70 | 75 |
The rain water from a roof of 44m × 20m drains into a cylindrical tank having diameter of base 4m and height 3.5m. If the tank is just full, then find the rainfall in cm.
If $\sin (\text{A} − \text{B}) = \sin \text{A} \cos \text{B} − \cos \text{A} \sin \text{B}$ and $\cos (\text{A − B}) = \cos\text{A} \cos\text{B} + \sin \text{A} \sin \text{B},$ find the values of sin 15° and cos 15°.
→The denominator of a fraction is $3$ more than its numerator. The sum of the fraction and its reciprocal is $2\frac{9}{10}.$ Find the fraction.
→Show graphically that the following systems of equations is in-consistent (i.e. has no solution):
$3\text{x}-4\text{y}-1=0$
$2\text{x}-\frac{8}{3}\text{y}+5=0$
→$3\text{x}-4\text{y}-1=0$
$2\text{x}-\frac{8}{3}\text{y}+5=0$
Find the roots of the following equations, if they exist, by applying the quadratic formula:
$2x^2 + ax - a^2 = 0$
→$2x^2 + ax - a^2 = 0$