Unit Test 1 (2022-2023)
Mathematics
Class X
SET – B
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.
- State fundamental theorem of Arithmetic.
- Find a quadratic polynomial whose sum and product of zeroes are √2 and (-3/2) respectively.
- Find whether the following pair of linear equations are consistent or inconsistent. Also state whether the lines representing them intersect at a point, are parallel or are coincident.
3x+2y=5
2x-3y=7 - Find the values of ‘a’ and ‘b’ if (-2) and (5) are the zeroes of the quadratic polynomial, p(x)=x²+(a+1)x+b.
- 15 pastries and 12 biscuit packets have been donated for a school fete. These are to be packed in several smaller identical boxes with the same number of pastries and biscuits packets in each. How many biscuit packets and how many pastries will each box contain?
- Find the zeroes of the following quadratic polynomial by the factorisation method and verify the relation between zeroes and the coefficient of the polynomial 3x²+4x-4.
- Solve 3x+4y=10 and 2x-2y=2 and hence find the value of “m” for which y=mx+5.
- Given that √3 and √5 are irrational numbers, prove that √3+√5 is an irrational number.
- Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?
- Draw the graph of the pair of linear equations x-y+1=0 and 3x+2y-12=0. Determine the coordinates of the vertices of the triangles formed by these lines and the x-axis. Also, share the triangular region so obtained.