There are 350 boys in the first three standards. The ratio of the number of boys in first and second standards is 2 : 3, while that of boys in second and third standards is 4 : 5. What is the total number of boys in first and third standards?
The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for 2 years at 5% per annum is ₹ 15. What is the sum of money deposited?
A man rows down a river 18 km in 4 hours with the stream and returns in 10 hours. Consider the following statements:
1. The speed of the man against the stream is 1.8 km/hr.
2. The speed of the man in still water is 3.15 km/hr.
3. The speed of the stream is 1.35 km/hr.
Which of the above statements are correct?
If a triangle has sides 5, 13 and 12 units and \( \theta \) is the acute angle of the triangle, then what is the value of \( (\sin \theta + \cos \theta) \)?
If \( A = \frac{\sin 45^{\circ} - \sin 30^{\circ}}{\cos 45^{\circ} + \cos 60^{\circ}} \) and \( B = \frac{\sec 45^{\circ} - \tan 45^{\circ}}{\mathrm{cosec} 45^{\circ} + \cot 45^{\circ}} \), then which one of the following is correct?
