In Figure, ABCD is a rectangle. Find the values of x and y.

Two different dice are tossed together. Find the probability:

- of getting a doublet
- of getting a sum 10, of the numbers on the two dice

An integer is chosen at random between 1 and 100. Find the probability that it is:

- divisible by 8
- not divisible by 8

^{4} – 9x^{3} + 5x^{2} + 3x – 1) if two of its zeroes are (2 + √3) and (2 – √3).

If the area of two similar triangles are equal, prove that they are congruent.

If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.

The table below shows the salaries of 280 persons:

Salary (In thousand Rs.) | No. of persons |

5-10 | 49 |

10-15 | 133 |

15-20 | 63 |

20-25 | 15 |

25-30 | 6 |

30-35 | 7 |

35-40 | 4 |

40-45 | 2 |

45-50 | 1 |

Calculate the median salary of the data.

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:

- The area of the metal sheet used to make the bucket.
- Why we should avoid the bucket made by ordinary plastic? [Use π = 3.14]

The mean of the following distribution is 18. Find the frequency f of the class 19 - 21.

Class | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |

Frequency | 3 | 6 | 9 | 13 | f | 5 | 4 |

The following distribution gives the daily income of 50 workers of a factory.

Daily income (in Rs.) | 100-120 | 120-140 | 140-160 | 160-180 | 180-200 |

Number of workers | 12 | 14 | 8 | 6 | 10 |

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

^{1}/_{13} hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank?

^{1}/_{3} BC. Prove that 9AD^{2} = 7AB^{2}

If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, then find the value of k.

Two different dice are thrown together. Find the probability that the numbers obtained have

- even sum
- even product

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

How many two-digit numbers are divisible by 3?

Determine the AP whose 3rd term is 5 and the 7th term is 9.

^{2} + 7x + 10, and verify the relationship between the zeroes and the coefficients.

Find the HCF and LCM of 6, 72 and 120, using the prime factorisation method.

Find the HCF of 96 and 404 by the prime factorisation method. Hence, find their LCM.

*kaju barfis* and 130 *badam barfis*. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the number of that can be placed in each stack for this purpose?