CA Foundation Maths Practice Set
1. If 𝑎, 𝖰, are the roots of equation x3 – 4x2 + x + 6 then the equation
𝟏 𝟏
roots are 𝟏 , 𝒂𝒏𝒅 is
𝑎 𝖰
(a) X3 – 4x2 + x + 6 = 0
(b) 4x3 – 6x2 + x – 1 = 0
(c) 6x3 + x2 – 4x + 1 = 0
(d) 6x3 + x2 - 4x +1 = 0
2. A cottage industry produces a certain number of pottery articles in
a day. It was observed on a particular day that the cost of each
article (in Rs.) was 2 more than thrice the number of articles
produced on that day. If the total cost of production on that day was
Rs. 800, the number of articles was
(a) 14
(b) 16
(c) 12
(d) 18
3. If 𝑎, 𝖰 are the roots of the equation 2x2 – 5x + 7 = 0, the equation
whose roots are (𝟐𝑎 + 𝟑𝖰) and (𝟑𝑎 + 𝟐𝖰) is
(a) 2x2 + 25x – 82 = 0
(b) 2x2 - 25x + 82 = 0
(c) 2x2 + 25x + 82 = 0
(d) none
4. positive value of ‘k’ for which the roots of equation 12x2 + kx + 5 =
0 are in the ratio 3:2 is:
(a) 5/12
(b) 12/5
5√10
(c)
2
(d) 5√10
5. Equation : x2 + x + 1 = 0 roots are
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, (a) Real and equal
(b) Real and unequal
(c) Imaginary
(d) Real and rational
6. If the roots of the equation λ2+8λ+μ2+6μ=0 are real, then μ lies
between
(a) -2 and 8
(b) -3 and 6
(c) -8 and 2
(d) -6 and 3
7. If α,β are roots of the equation x2−5x+6=0, then the equation whose
roots are (α+3) and (β+3) is
(a) 2x2 – 30x + 30 = 0
(b) -x2 + 11x = 30
(c) X2 – 11x + 30 = 0
(d) None of these
8. Sum of cubes of the roots of the equation x3 – px2 – qx – 4 = 0 is
given by
(a) p3 + 3pq – 3r
(b) p3 – 3pq + 3r
(c) p2 – 3pq – 3r
(d) p2 + 3pq + 3r
9. On solving , we get one value of x as:
(a) 4/13
(b) 1/13
(c) 2/13
(d) 3/13
10. If 𝑎, 𝖰 are the roots of the equation ax2 + bx + c = 0, then the
𝟏 𝟏
equations whose roots are (𝑎 + ) and (𝖰 + ) is
𝖰 𝑎
(a) abx2 + b(c + a)x + (c + a)2 = 0
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1. If 𝑎, 𝖰, are the roots of equation x3 – 4x2 + x + 6 then the equation
𝟏 𝟏
roots are 𝟏 , 𝒂𝒏𝒅 is
𝑎 𝖰
(a) X3 – 4x2 + x + 6 = 0
(b) 4x3 – 6x2 + x – 1 = 0
(c) 6x3 + x2 – 4x + 1 = 0
(d) 6x3 + x2 - 4x +1 = 0
2. A cottage industry produces a certain number of pottery articles in
a day. It was observed on a particular day that the cost of each
article (in Rs.) was 2 more than thrice the number of articles
produced on that day. If the total cost of production on that day was
Rs. 800, the number of articles was
(a) 14
(b) 16
(c) 12
(d) 18
3. If 𝑎, 𝖰 are the roots of the equation 2x2 – 5x + 7 = 0, the equation
whose roots are (𝟐𝑎 + 𝟑𝖰) and (𝟑𝑎 + 𝟐𝖰) is
(a) 2x2 + 25x – 82 = 0
(b) 2x2 - 25x + 82 = 0
(c) 2x2 + 25x + 82 = 0
(d) none
4. positive value of ‘k’ for which the roots of equation 12x2 + kx + 5 =
0 are in the ratio 3:2 is:
(a) 5/12
(b) 12/5
5√10
(c)
2
(d) 5√10
5. Equation : x2 + x + 1 = 0 roots are
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, (a) Real and equal
(b) Real and unequal
(c) Imaginary
(d) Real and rational
6. If the roots of the equation λ2+8λ+μ2+6μ=0 are real, then μ lies
between
(a) -2 and 8
(b) -3 and 6
(c) -8 and 2
(d) -6 and 3
7. If α,β are roots of the equation x2−5x+6=0, then the equation whose
roots are (α+3) and (β+3) is
(a) 2x2 – 30x + 30 = 0
(b) -x2 + 11x = 30
(c) X2 – 11x + 30 = 0
(d) None of these
8. Sum of cubes of the roots of the equation x3 – px2 – qx – 4 = 0 is
given by
(a) p3 + 3pq – 3r
(b) p3 – 3pq + 3r
(c) p2 – 3pq – 3r
(d) p2 + 3pq + 3r
9. On solving , we get one value of x as:
(a) 4/13
(b) 1/13
(c) 2/13
(d) 3/13
10. If 𝑎, 𝖰 are the roots of the equation ax2 + bx + c = 0, then the
𝟏 𝟏
equations whose roots are (𝑎 + ) and (𝖰 + ) is
𝖰 𝑎
(a) abx2 + b(c + a)x + (c + a)2 = 0
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