# Important Questions Maths for Class 10 Board Exams The best way to escape the exam fear is “Practice“. Practice all the questions given below for Maths and this will help you solve all the questions that will appear in CBSE Board Exam of Maths.

### Real Numbers

1. Use Euclid’s division algorithm to find the HCF of :
(i) 56 and 814 (ii) 6265 and 76254
2. Find the HCF and LCM of following using Fundamental Theorem of Arithmetic method. (i) 426 and 576 (ii) 625, 1125 and 2125
3. Prove that 3 is an irrational number.
4. Prove that 5 is irrational number.
1. Prove that 5 + 2 is irrational.
2. Prove that 2 + 3 is irrational.
3. Can we have any n∈ N , where 7n ends with the digit zero.
4. Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non – terminating decimal expansion :(i) 77
(ii) 15 210 1600
5. An army contingent of 616 members is to march behind and army band of 32 members in a 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?
6. There is a 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 they 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 ?
7. Write a rational number between 2 and 3 . [CBSE – 2008]
8. Use Euclid’s’ Division Lemma to show that the square of any positive integer is either of the form 3m of 3m + 1 for some integer m.

### Linear Equation in two variables

1. The equations 3x-5y+2=0, and 6x+4=10y have:
(A) No solution (B) A single solution
(C) Two solutions (D) An infinite number of solution
2. If p+q=1 and the ordered pair (p,q) satisfy 3x+2y=1 then is also satisfies:
(A) 3x + 4y = 5
(B) 5x + 4y = 4
(C) 5x + 5y = 4
(D) None of these.
1. If x=y, 3x-y=4 and x+y+z=6 then the value of z is:(A) 1 (B) 2 (C) 3 (D) 4
2. The system of linear equation ax+by=0,  cx+dy=0has no solution if:
(A) ad – bc > 0 (B) ad – bc < 0 (C) ad + bc = 0 (D) ad – bc = 0
3. The value of k for which the system kx+3y=7and 2x-5y=3 has no solution is:
(A) 7 & k = − 3/14 (B) 4 & k = 3/14 (C) 6/5 & k ≠ 14/3 (D) − 6/5 & k ≠ 14/3
1. If 29x+37y=103, 37x+29y=95 then:
(A) x = 1, y = 2 (B) x = 2, y = 1 (C) x = 2, y = 3 (D) x = 3, y = 2
2. On solving 25/x+y − 3/x-y =1, 40/x+y + 2/x-y =5 we get:(A) x = 8, y = 6 (B) x = 4, y = 6 (C) x = 6, y = 4 (D) None of these
3. If the system 2x+3y-5=0, 4x+ky-10=0 has an infinite number of solutions then:
( A ) k = 3/2 ( B ) k ≠ 3/2 ( C ) k ≠ 6 ( D ) k = 6
1. The equation x+2y=4 and 2x+y=5
(A) Are consistent and have a unique solution
(B) Are consistent and have infinitely many solution
(C) are inconsistent
(D) Are homogeneous linear equations
2. If  1/x − 1/y = 1/z then z will be:
(A)y-x (B)x-y (C) y−x /xy (D) y−x/xy
3. The denominator of a fraction is greater than its numerator by 7. If 4 is added to both its numerator and denominator, then it becomes 21 . Find the fraction.
4. In a certain number is divided by the sum of its two digits, the quotient is 6 and remainder is 3. If the digits are interchanged and the resulting number is divided by the sum of the digits, then the quotient is 4 and the remainder is 9. Find the number.
5. 2 men and 3 boys together can do a piece of work is 8 days. The same work is done in 6 days by 3 men and 2 boys together. How long would 1 boy alone or 1 man alone take to complete the work
6. The Sum of two nos is 18. The sum of their reciprocal is 14 . Find the numbers.
7. A farmer wishes to purchase a number of sheep found the if they cost him Rs 42 a head, he would not have money enough by Rs 25; But if they cost him Rs 40 a head, he would them have Rs 40 more than he required; find the number of sheeps, and the money which he had.

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