jac.nic.in Mathematics Model Question Paper : Jharkhand Academic Council
Name of the Organisation : Jharkhand Academic Council
Standard : Secondary
Document Type : Model Question Paper
Name of the Subject : Number System
Website : http://jac.nic.in/Com%20Model%20question.htm
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Mathematics Model Question Paper :
One mark :
1. Write 156 as a product of its prime factors.
2. If 120 = 2a ×3b ×5c then write the value of a, b and c.
Related : Jharkhand Academic Council X Science Question Paper Model : www.pdfquestion.in/7640.html
3. If 3825 = 3x ×5y ×17z , then write the value of x.
4. Write 150 as a factor tree of its prime factors.
5. Find the missing numbers a, b and c in the given factor tree
6. Fill in the blank – A ×B = HCF(A, B) ×…………(A, B)
7. If L.C.M. (306, 657) = 22338, find H.C.F. (306, 657).
8. Find the H.C.F. of 26 and 91 by prime factorization method.
9. Find the L.C.M. of 12, 15 and 18 by prime factorization method.
10. H.C.F of 24 and 42 is 6, then find the L.C.M. of 24 and 42.
11. State whether the decimal of17/8 is terminating of non- terminating.
12. From which place the decimal of the decimal form of the rational no.1/250 will be terminated.
13. State whether 2 + 3 is rational or irrational no.?
14. Express 0.23 in the form p/q, where p and q are co-prime and q is of the form 2n ×5m .
15. Which of the following is an irrational number.
(a) 3
(b) 1.5
(c) 0
(d) 4
16. Which of the following is a prime number?
(a) 2
(b) 5
(c) 3
(d) (none of these)
Three Marks :
1. Show that every positive even integer is of the form 2q and that every positive odd integer is of the form 2q+1, where q is some integer.
2. Show that any positive odd integer is of the form 4q+1 or 4q+3, where q is come integer.
3. Show that any positive odd integer is of form 6q+1, 6q+3 or 6q+5, where q is some integer
4. Use Euclid’s division lemma to show that the square of any positive is either of the form 3m or 3m+1 for some integer m .
5. Show that any positive even integer is of the form 4q or 4q+2, where q is some integer.
6. Show that any positive even integer is of the form 6q, 6q+2 or 6q+4 where q is some integer.
7. Show that any positive even integer is of the form 8q, 8q+2 or 8q+6 where q is some integer.
8. Use Euclid’s algorithm to find the H.C.F. of 4052 and 12576.
9. Use Euclid’s algorithm to find the H.C.F. of 135 and 135
10. An army contingent of 616 members is to march behind an army band of 32 members in parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march.
11. A sweet seller has 420 Kaju barfis and 130 Badam barfis. She wants to stack them in such a way that each stack has the same number and they take up the least area of the tray. What is the number of that can be placed in each stack for this pupose?
12. Three containers contain 27 liters, 36 liters and 72 liters of milk. What biggest measure can measure exactly the milk is the three containers.
13. There is circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose the both start at the same point and at the same time and go in the same direction. After how many minutes will they meet again at the starting point.
14. Find the H.C.F. and L.C.M. of 6, 72 and 120 using prime factorization method.
15. Find the H.C.F. and L.C.M. of 16 and 60 by the prime factorization method and verify that HCF × LCM = product of the two numbers.
16. Find the H.C.F. of 96 and 404 by the prime factorization method. Hence, find their L.C.M.
17. Check whether 6n can end with the digit 0 for any natural number n.
18. 5×7×11+11 is a composite number of prime number. Give reasons.
19. Prove that 5 is irrational.
20. Prove that 5 – 3 is irrational.
21. Prove that 3 2 is irrational.
22. Prove that 3+ 2 5 is irrational.
Polynomial – 1 One mark :
1. Which of the following is a polynomial in x ?
2. The sum of zeros of the quadratic polynomial 4×2 + 4x +1will be
3. Write the standard form of a polynomial 5 + 2×2 -5x
4. Write the zero of polynomial x2 -3
5. If x + 2 be a factor of the polynomial p(x) then what will be zero of p(x) ?
Quadratic Equation :
1. Which of the following is a not of x2-3x+2=0 ?
2. ax2+bx+c=0 will have two real and distinct roots if
3. Write the discriminate of the quadratic equation 2×2-4x+3=0
4. Write the nature of root of the quadratic equation 2×2-4x+3=0
5. Write the root of the quadratic equation y2-5=0
6. Check whether the following is quadratic equation or not :
(i) x(x+1)+8 = (x+2)(x-2) (ii) x2-2x = (-2)(3-x) (iii) (2x-1)(x-3) = (x+5)(x-1)
Arithmetic Progression :
1. Which of the following are A.P?
(a) 2, 4, 8, 16, …………….
(b) 1, 3, 9, 27, …………….
(c) a, a2, a3, a4, …………………
(d) -10, -6, -2, 2, ………
2. The famous mathematician associated with finding the sum of the first 100 natural numbers is
3. Write the first term and common difference of a A.P: 3, 1, -1 -3, …………..
4. A.P: 1, -1 -3,-5, ………….. then write the next two terms.
5. Write the first two terms of the A.P. whose first terms (a) = 4 and common difference (d) = -3
6. If the first terms (a) = 3.5, common difference (d) = 0 and nth term of an A.P = 10.5 then find an.
7. If the first term (a) = -8, nth term (an) = 0 and number of term (n) = 10 then find common difference (d).
Two Marks :
1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and reminder in each of the following :
(i) p(x) = x3-3×2+5x-3, g(x)= x2-2
(ii) p(x) = x4-3×2+4x+5, g(x)= x2+1-x
(iii) p(x) = x4-5x+6, g(x)= 2- x2
2. On dividing x3-3×2+x+2 by a polynomial g(x), the quotient and remainder were x-2 and -2x+4, respectively. Find g(x)
3. g(x) = x2+3x+1, p(x) = 3×4+5×3-7×2+2x+2 Check whether the g(x) is a factor of p(x) by dividing p(x) by g(x)
4. Find the zeroes of the quadratic polynomial x2+7x+10, and verify the relationship between the zeroes.