UNIT TEST 1 CLASS X
SUBJECT – Mathematics (SET A)
Time : 55 Mins
Max. Marks : 30
(1 Mark)
- If one of the zero of the quadratic polynomial is 3+√2. Write the other zero.
[Correct Question: If one zero of the polynomial x² ‒ 4x + 1 is (2 + √3), write the other zero.]
- For the given pair of linear equations, write the condition for Unique Solution.
px+qy-r=0 and ay+bx-c=0 - Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -1/2.
- If the sum of the zeroes of the quadratic polynomial f(t)=kt²+2t+3k is equal to their product, find the value of k.
(2 Marks)
- Find the number of zeroes and the zeroes of the polynomial f(x).
- Find the zeroes of the polynomial x²+(1/6)x-2 and verify the relationship between the coefficients and zeroes of the polynomial.
- Solve : 37x+41y=70 , 41x+37y=86
(3 Marks)
- Find the values of a and b for which the following system of linear equations has an infinite number of solutions
2x+3y=7
2ax+(a+b)y-28=0 - If α and β are the zeroes of the polynomial f(x)=x²-x-4, find the value of (1/α)+(1/β)-αβ.
- In a two digit number, the ten’s digit is three times the unit digit. When the number is decreased by 54, the digits are reversed. Find the number.
- If α and β are the zeroes of the polynomial f(x)=kx²+4x+4 such that α²+β²=24, find the value(s) of k.
(4 Marks)
- Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other, they meet in one hour. Find the speed of the two cars.
- CASE STUDY BASED QUESTION
Amrita was very fond of reading books. Therefore, she went to the National Book Fair at Pragati Maidan in New Delhi to get some storybooks and textbooks.
When her friends asked her how many of each she has bought, she answered, four times the number of textbooks is six more than thrice the number of storybooks. Also, seven times the number of textbooks added to thrice the number of storybooks gives 27.
13(i) Taking the number of text books and story books bought by Amrita as x and y respectively, the pair of linear equations formed in this case is
(a) 4x+3y=6, 7x+3y=27
(b) 4x-3y=-6, 7x+3y=27
(c) 4x-3y=6, 7x+3y=27
(d) 4x-3y=-6, 7x-3y=27
13(ii) The number of text books and story books bought by Amrita from the fair are
(a) Text books = 4, Story books = 3
(b) Text books = 4, Story books = 6
(c) Text books = 6, Story books = 4
(d) Text books = 3, Story books = 2
13(iii) The value(s) of k for which the system of equations kx+3y=k-3 and 12x+ky=k has no solution is
(a) 6
(b) -6
(c) 6,-6
(d) none of these.
13(iv) The linear equation 2x-y=4 intersect the y-axis at the point
(a) (0,-4)
(b) (0,-8)
(c) (0,4)
(d) 0,8)