^{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?

**Use Euclid’s algorithm to find the HCF of 4052 and 12576.**

^{2} – 6x – 2 = 0 has real roots and if it has, find them by the method of completing the square. Also verify that roots obtained satisfy the given equation.

^{2} and x + ky = 1 have infinitely many solutions.

**The following frequency distribution shows the distance (in metres) thrown by 68 students in a Javelin throw competition.**

**Draw a less than type Ogive for the given data and find the median distance thrown using this curve.**

^{2}h to find the volume of milk in the mug and charges Rs. 43.12 for it. The dairy owner B is of the view that the price of actual quantity of milk should be charged. What according to him should be the price of one mug of milk? Which value is exhibited by the dairy owner B? (Use π = 22/7)

Find the mode of the following distribution of marks obtained by the students in an examination:

Given the mean of the above distribution is 53, using empirical relationship estimate the value of its median.

**Show that exactly one of the numbers n, n + 2 or n + 4 is divisible by 3.**

**A box contains cards numbered 11 to 123. A card is drawn at random from the box. Find the probability that the number on the drawn card is **

**a square number****a multiple of 7**

**If two positive integers p and q are written as p = a ^{2}b^{3} and q = a^{3}b; a, b are prime numbers, then verify:**

**If sin θ + cos θ = √2, then evaluate: tan θ + cot θ**

**In given figure ∠1 = ∠2 and ΔNSQ ≅ ΔMTR , then prove that ΔPTS ~ ΔPRQ.**