**IMPORTANT QUESTIONS (CHAPTER 1 – 5)**

**(LEVEL 1)**

- State Euclid division lemma.
- State Fundamental Theorem of Arithmetic.
- Find the HCF of 105 and 245 by Euclid division algorithm.
- Express 296 as a product of its primes
- Find the HCF and LCM of 75 and 160 by Fundamental theorem of Arithmetic and verify LCM x HCF = product of two numbers
- If HCF of 30 and 45 is 15. Find the LCM.
- Prove 5 + 2√3 is irrational
- Check whether 17/210 is terminating or non-terminating. x x’
- Find the zeros and verify the relation between zeros and

coefficients of (i) x^{2} + 11x + 30 (ii) x^{2} – 9

- Find the number of zeros of in fig (i) fig (i)
- Find a quadratic polynomial whose sum and product of zeros are 1/3 and -1/3
- Divide 3x
^{2}– x^{3}– 3x + 5 by x – 1 – x^{2}and verify the division algorithm - On dividing 2x
^{3}+ 4x^{2}+ 5x + 7 by g(x) the quotient and remainder are 2x and 7 – 5x respectively. Find g(x) - State the condition so that the pair of linear equations a
_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2}= 0 have no solution, unique solution or infinite solution. - For what value of k the eq. kx + 3y – (k – 3) = 0 and 12x + ky – k have infinite many solution
- Check whether 7x + 3y = 27 and 2x + 5y = 16 have unique solution, no solution or infinite many solution.
- Check whether 2x + 3y = 7 and 4x + 6y = 16 are consistent or inconsistent.
- Find k if kx + 3y + 1 = and 2x + y + 3 =0 has unique solution.
- Check whether 5x – 3y = 11 and -10x + 6y = -22 represent an intersecting lines, parallel lines or coincident lines.
- Solve: 2/x + 2/3y = 1/6 and 3/x + 2/y = 0
- Solve graphically x – y + 1 =0 and 3x + 2y – 12 = 0
- Solve 6x + 3y = 6xy and 2x + 4y = 5xy
- Check whether x = -1 is a solution of equation 4x
^{2}– 3x – 1 = 0 - Find k if one root of equation x
^{2}+ kx – 4 = 0 - Solve by factorization: 9x
^{2}– 3x – 20 = 0 - Solve by completing square method: 6x
^{2}– 13x – 5 = 0 - Find the nature of roots of equation 9x
^{2}+ 12x + 4 = 0 - Find k if 2kx
^{2}+ 6x + 5 = 0 has equal roots. - Solve x – 1/x = 3
- Find the 20
^{th}term of the AP 7, 3, -1, -5 …… - Write the AP whose 3
^{rd}term is 5 and 7^{th}term is 9. - Determine 15
^{th}term from the end of the AP 8, 13, 18, …….. 153 - n
^{th}term of an AP is given by 5n – 3. Find the AP - Find the sum of 20 terms of the AP 5, 8, 11, 14
- Which term of the AP 3, 8, 13, …… is 78.
- Check whether 301 is a term of A.P. 5, 11, 17, 23