Class 10 Maths Polynomial DPP
CLASS - 10
General Instructions:
1. All Questions are compulsory.
2. Draw neat figures wherever required.
Section A (1x10-10)
1. Find the number of zeroes lying between -4 to 4 of the
polynomial f (x), whose graph is given below.
2. How many zeroes, the polynomial p (x) = (x-2)²-4 can have?
3. Identify, which of the following is not irrational?
(2+√5) or (2-√5) or (2+√5) (2-√5) or 2√5
4. If two positive integers a and b are written as a = x²y and b =
x²y³, where x, y are prime numbers, then find HCF(a,b).
5. How many solutions are possible for the pair of equations y = 0
and y = -7?
6. If the system of equations 3x+y=1 and (2k-1)x + (k-1)y = 2k+1
is inconsistent, then find k?
7. What is the nature of the graphs of system of equations having
infinitely many solutions?
8. Find the zeroes of the quadratic polynomial x²-3x-4.
9. If product of two numbers is 5780 and their HCF is 17, then find
their L.C.M.
10. If the sum of the zeroes of the quadratic polynomial x²-2kx+8 is
2 then what is the value of k.
Section B (2x4=8)
11. Express 3276 as a product of its prime factors.
12. Given that √3 is irrational, prove that 5 + 2√3 is irrational.
13. For what values of k will the following pair of linear equations
have infinitely many solutions?
kx+3y-(k-3)=0 12x+ky-k=0.
14. Find a quadratic polynomial the sum and product of whose
zeroes are 3 and -2/5 respectively.
OR
14. Find a quadratic polynomial whose zeroes are 5-3√2 and 5+3√2.
Section C (3x3=9)
15. Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of
'm' for which y = mx+3.
16. Prove that √2 is irrational.
or
16. Check whether 4" can end with the digit 0 for any natural
number "n".
17. Find the zeroes of the quadratic polynomial 6x²-3-7x and verify
the relationship between the zeroes and the coefficients.
Section D (3x5=15)
18. a) On a morning walk three persons step off together and their
steps measure 40 cm, 42 cm, 45 cm, what is the minimum
distance each should walk so that each can cover the same
distance in complete steps?
b) There are 576 boys and 448 girls in a school that are to be
divided into equal sections of either boys or girls alone. Find
the total number of sections thus formed.
19. If a and β are zeroes of the polynomial x² - 5x + 4, then find the
value of -
a) 1/a+ 1/β b) (a - β)
20. A number consists of two digits. When the number is divided by
the sum of its digits. the quotient is 7. If 27 is subtracted from the
number, the digits interchange their places. Find the number.
OR
20. Draw the graphs of x - 3y = 6 and 2x - 3y = 12. Shade the area
bounded by these lines and the x-axis.
Section E (2x4=8)
21. Basketball and soccer are played with a
spherical ball. Even though an athlete
dribbles the ball in both sports, a
basketball player uses his hands and a
soccer player uses his feet. Usually,
soccer is played outdoors on a large field
and basketball is played indoor on a court
made out of wood. The projectile (path traced) of soccer ball and
basketball are represented by a quadratic polynomial.
1) The graph of parabola opens upwards, if _______
2) In the graph, how many zeroes are there for the polynomial?
3) The two zeroes shown on the graph above are _________
22. A test consists of 'True' or 'False' questions. One mark is awarded
for every correct answer while ¼ mark is deducted for every
wrong answer. A student knew answers to some of the questions.
Rest of the questions he attempted by guessing. He answered
120 questions and got 90 marks.
Type of question Marks given for Marks deducted for
correct answer wrong answer
True/False 1 0.25
1. If answer to all questions he attempted by guessing were
wrong, then how many questions did he answer correctly?
2. How many questions did he guess?
3. If answer to all questions he attempted by guessing were
wrong and answered 80 correctly, then how many marks he got?
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