For Olympiads I RMS I Sainik School
- The standard form of a linear equation in one variable x is
(a) ax + b = 0
(b) ax² + bx + c = 0
(c) ax³ + bx² + cx + d = 0
(d) ax4 + bx³ + cx² + dx + e = 0. - One number is greater than the other number by 3. The sum of two numbers is 23. The two numbers are
(a) 13, 10
(b) 14, 9
(c) 12, 11
(d) 15, 8. - Twice a number is as much greater than 30 as the three times of the number less than 60. The number is
(a) 6
(b) 9
(c) 12
(d) 18. - If two angles are supplementary and one angle is double the other, then the larger angle is
(a) 60°
(b) 90°
(c) 120°
(d) 180°. - The root of the equation 32 x = – 27 is
(a) 6
(b) 12
(c) 18
(d) -18 - If two angles are complementary and one angle is 10° greater than the other, then the smaller angle of the two is
(a) 40°
(b) 50°
(c) 90°
(d) 180°. - The root of the equation 7 (x – 1) = 21 is
(a) 1
(b) 2
(c) 3
(d) 4. - The root of the equation 2/3 y = 5/12 is
(a) 8/5
(b) 5/8
(c) 5
(d) 8 - The root of the equation
11x – 5 – x + 6 = 2x + 17 is
(a) 1
(b) 2
(c) 3
(d) 4. - The root of the equation
13x – 14 = 9x + 10 is
(a) 1
(b) 2
(c) 3
(d) 6. - The root of the equation
(2x – 1) + (x – 1) = x + 2 is
(a) 1
(b) 2
(c) -1
(d) -2. - The root of the equation 2y = 5 (7 – y ) is
(a) 5
(b) -5
(c) 3
(d) -3. - The root of the equation 4x/7 – 12 = 0 is
(a) 7
(b) 14
(c) 21
(d) -21 - The root of the equation 9z – 15 = 9 – 3z is
(a) 1
(b) 2
(c) 3
(d) 4. - The root of the equation 3x + 4 = 13 is
(a) 1
(b) 2
(c) 3
(d) 4. - The root of the equation 3y + 4 = 5y – 4 is
(a) 1
(b) 2
(c) 3
(d) 4. - The root of the equation 5x/3 = 30 is
(a) 9
(b) 12
(c) 15
(d) 18 - The root of the equation 14 – x = 8 is
(a) 2
(b) 4
(c) 6
(d) 8. - The root of the equation y/3 – 7 = 11 is
(a) 54
(b) -54
(c) 18
(d) -18 - The root of the equation 2y = 5(3 + y) is
(a) 5
(b) 1/5
(c) -5
(d) –1/5The root of the equation 3x + 8 = 14 is
(a) 1
(b) 2
(c) -1
(d) 12 - The root of the equation x – 8 = 2 is
(a) 2
(b) 8
(c) 6
(d) 10. - The root of the equation x + 3 = 5 is
(a) 1
(b) 2
(0 -1
(d) -2. - The root of the equation 5x – 8 = 7 is
(a) 1
(b) 2
(c) 3
(d) -3. - The value of x in –2/3 = 2x is 3
(a) 1/3
(b) –1/3
(c) 3
(d) – 3. - 3/4 part of a number is 5 more than its 2/3 part. This statement in the form of an equation is
(a) 2/3 x – 3/4 x= 5
(5) 2/3 x – 5 =3/4 x
(c) 3/4 x = 2/3 x + 5
(d) 3/4 x – 5 = –2/3 x - The value of x in 3/4 x = 7 – x is
(a) 4
(b) 3
(c) 7/3
(d) 7. - The root of the equation –5/4x = 15 is
(a) 1/12
(b) –1/12
(c) 1/20
(d) –1/20 - When 9 are added to two times a number, we get 67. The number is
(a) 25
(b) 27
(c) 29
(d) 31. - In a two digit number, the unit’s digit is x and the ten’s digit is y. Then, the number is
(a) 10y + x
(b) 10x + y
(c) 10y – x
(d) 10x – y. - The difference of two numbers is 21. The larger number is x. The smaller number is
(a) 21 + x
(b) 21 – x
(c) x – 21
(d) -x – 21. - x is an odd number. The largest odd number preceding x is
(a) x – 1
(b) x – 2
(c) x – 3
(d) x – 4. - If x is an even number then the consecutive even number is
(a) x + 1
(b) x + 2
(c) 2x
(d) x – 1. - The largest number of the three consecutive numbers is x + 1. Then, the smallest number is
(a) x + 2
(b) x + 1
(c) x
(d) x – 1. - The solution of the equation 5/x = 2 is
(a) 10
(b) 2/5
(c) 5/2
(d) 1/10 - The root of the equation 2x + 3 = 2(x – 4) is
(a) 2
(b) 4
(c) 0
(d) does not exist. - The root of the equation 3x = 20/7 – x is
(a) 10
(b) 20/21
(c) –5/7
(d) 5/7 - The root of the equation z + 4 = -8 is
(a) 3
(b) -32
(c) 12
(d) 4. - On subtracting 30 from two times a number, we get 56. This statement in the form of an equation is
(a) 2x – 30 = 56
(b) 2x + 30 = 56
(c) 30 – 2x = 56
(d) 30/2x = 56. - If 6 is added to 3 times of a number, it becomes 15. This statement in the form of an equation is
(a) 3x + 6 = 15
(b) 3x – 6 = 15
(c) 3x + 15 = 6
(d) 3x/6 = 15 - A number when subtracted from 40 results into 15. This statement in the form of an equation is
(a) 40 – x = 15
(b) x – 40 = 15
(c) 40 + x = 15
(d) 40x = 15. - A number when divided by 5 gives 6. This statement in the form of an equation is
(a) x – 5 = 6
(b) x + 5 = 6
(c) x/5 = 6
(d) 5x = 6. - Seven times a number is 42. This statement in the form of an equation is
(a) x + 7 = 42
(b) 7x = 42
(c) x/7 = 42
(d) x – 7 = 42. - If 15 is subtracted from a number, it becomes -5. This statement in the form of an equation is
(a) x + 15 = -5
(b) x – 15 = 5
(c) x + 15 = 5
(d) x – 15 = -5. - If 9 is added to a number, it becomes 25. This statement in the form of an equation is
(a) x + 9 = 25
(b) x – 9 = 25
(c) 9x = 25
(d) x/9 = 25. - The statement ‘on adding 10 in a number, the number becomes 20’ in the form of an equation is
(a) x – 10 = 20
(b) x + 10 = 20
(c) 10x = 20
(d) x/10 = 20. - The degree of the equation x² – 2x + 1 = x² – 3 is
(a) 1
(b) 2
(c) 0
(d) 3. - Of the following, the linear equation in one variable x, is
(a) 4/x = x/4
(b) 1/x + 1/x−1 = 1
(c) x/2 + x/3 + 1/4
(d) x² + 2x + 3 = 0.