Unit Test 1 (2022-2023)
Mathematics
Class X
SET – A
Time: 1 Hour
MM: 25
General Instructions :
All questions are compulsory.
Q.1 is of 1 mark, Q.2-Q.5 are of 2 marks each, Q.6-Q.9 are of 3 marks each and Q.10 is of 4 marks.
- The HCF of the two numbers is 145 and their LCM is 2175. If one number is 725, find the other.
- Find a quadratic polynomial whose sum and product of zeroes are 21/8 and 5/16.
- Find the LCM of 90 and 144 by the prime factorisation method.
- Two brands of chocolates are available in packs of 24 and 15 respectively. If I need to buy an equal number of chocolates of both kinds, what is the least number of chocolates of each kind I need to buy?
- If α and β are the zeroes of the polynomial x²+x+1, then find the value of 1/α+1/β-2αβ.
- Find the zeroes of the following quadratic polynomial by the factorisation method and verify the relation between zeroes and coefficients of the polynomial.
5y²+8y-4 - Check whether the given pair of linear equations has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, then find it by any algebraic method.
5x-4y+8=0
7x+6y-9=0 - Prove that √5 is an irrational number.
- The sum of a two digit number and the number obtained formed by interchanging the digits is 110. If 10 is subtracted from the original number, the new number is 4 more than 5 times the sum of the digits of the original number. Find the original number.
- Draw the graph of the equation x-y-1=0 and 3x+y-11=0. Determine the coordinates of the vertices of the triangle formed by these lines and the y-axis. Also, shade the triangular region so obtained.