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Math Chapter Wise Theory Of Equation And Inequations English EMRS PGT-2023

Q01.The value of 'a' for which one root of the quadratic equation (a² – 5a + 3)x² + (3a – 1)x + 2 = 0 is twice as large as the other, is:

A2/3 B−2/3 C1/3 D−1/3

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Math Chapter Wise Theory Of Equation And Inequations English EMRS PGT-2023

Q02.Let p and q be the roots of the equation x² – 2x + A = 0 and let r and s be the roots of the equation x² – 10x + B = 0. If p < q < r < s are in A.P., then the values of A and B are:

AA = 77, B = −3 BA = −7, B = 33 CA = 33, B = −7 DA = −3, B = 77

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Math Chapter Wise Theory Of Equation And Inequations English EMRS PGT-2023

Q03.α and β are the roots of the equation px² + qx + r = 0 (p ≠ 0). If p, q, r are in A.P. and 1/α + 1/β = 4, then the value of |α − β| is:

A2√17/9 B√34/9 C2√13/9 D√61/9

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Math Chapter Wise Theory Of Equation And Inequations English Bihar (TRE 2.0)-2023

Q04.The pair of equations 3x − 5y = 7 and −6x + 10y = 7 has:

Aa unique solution Binfinitely many solutions Cno solution DMore than one of the above ENone of the above

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Math Chapter Wise Theory Of Equation And Inequations English Bihar (TRE 2.0)-2023

Q05.n² < 2ⁿ is true for all natural numbers, if:

An ≥ 5 Bn < 5 Cn ≤ 3 DMore than one of the above ENone of the above

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Math Chapter Wise Theory Of Equation And Inequations English Bihar (TRE 1.0)-2023

Q06.The maximum number of positive real roots of the equation 2x⁷ − x⁴ + 4x³ − 5 = 0 is:

A2 B3 C6 DMore than one of the above ENone of the above

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Math Chapter Wise Theory Of Equation And Inequations English EMRS TGT-2023

Q07.If x and a are real numbers and a > 0, |x| > a, then:

Ax ∈ [−∞, a) Bx ∈ (−a, a) Cx ∈ (−∞, −a) ∪ (a, ∞) Dx ∈ (−a, ∞)

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Math Chapter Wise Theory Of Equation And Inequations English EMRS TGT-2023

Q08.The solution set of |3 − 4x| ≥ 9 is:

Ax ∈ (−∞, 3] ∪ [3, ∞) Bx ∈ (−∞, −3/2] ∪ [−3/2, ∞) Cx ∈ (−∞, 3] ∪ (3, ∞) Dx ∈ (−∞, −3/2] ∪ [3, ∞)

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Math Chapter Wise Theory Of Equation And Inequations English EMRS TGT-2023

Q09.Solution of (x − 2)/(x + 5) > 2 is:

Ax ∈ (5, 12) Bx ∈ [−12, −5] Cx ∈ (−12, −5) Dx ∈ (−12, 5)

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Math Chapter Wise Theory Of Equation And Inequations English KVS PGT 2023

Q10.Which of the following quadratic equations has two distinct real roots?

A2x² + 3√2x + 9/4 = 0 Bx² + x − 5 = 0 Cx² + 3x + 2√2 = 0 D2x² − √5x + 1 = 0

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Math Chapter Wise Theory Of Equation And Inequations English KVS PGT 2023

Q11.If |x − 2| > 6, then:

Ax ∈ (−4, 8) Bx ∈ (−∞, −4) ∪ (8, ∞) Cx ∈ (−∞, 4] ∪ [8, ∞) Dx ∈ [−4, 8]

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Math Chapter Wise Theory Of Equation And Inequations English KVS PGT 2023

Q12.The number of real roots of the equation (x − 1)² + (x − 3)² + (x − 5)² = 0 is:

A0 B1 C2 D3

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Math Chapter Wise Theory Of Equation And Inequations English NVS PGT 2022

Q13.The values of 'x' satisfying the inequalities 3x − 7 < 5 + x and 11 − 5x ≤ 1, are:

A2 ≤ x ≤ 8 B2 ≤ x < 6 C2 < x ≤ 6 D2 < x < 8

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Math Chapter Wise Theory Of Equation And Inequations English NVS PGT 2022

Q14.The roots of the equation |x²| + |x| − 6 = 0 are:

AOne and only one real number BReal with sum one CReal with sum zero DReal with product zero

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Math Chapter Wise Theory Of Equation And Inequations English NVS PGT 2022

Q15.Three numbers are in G.P. If we double the middle term, we get an A.P. The common ratio of the G.P. is:

A2 ± √3 B3 ± √2 C√2 ± 3 D√3 ± 2

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Math Chapter Wise Theory Of Equation And Inequations English NVS PGT 2022

Q16.If x, 3x + 2, 6x + 4 are first three terms of a G.P., then the fifth term of the G.P. is:

A−16 B+16 C−32 D+32

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Math Chapter Wise Theory Of Equation And Inequations English NVS PGT 2022

Q17.If one root of the equation (x − 4)(x − 6) = p is four times the other, then p equals to:

A6 B8 C−6 D−8

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Math Chapter Wise Theory Of Equation And Inequations English KVS PGT 2022

Q18.Which of the following equations has no real roots?

Ax² − 4x + 3√2 = 0 Bx² − 4x − 3√2 = 0 Cx² + 4x − 3√2 = 0 D3x² + 4√3x + 4 = 0

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Math Chapter Wise Theory Of Equation And Inequations English KVS PGT 2022

Q19.The value of k for which the quadratic equation kx² + 8kx + 32 = 0 has equal roots is:

A1 B2 C4 D8

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Math Chapter Wise Theory Of Equation And Inequations English KVS PGT 2022

Q20.If −2x + 15 < −13, then:

Ax ∈ (−∞, 14] Bx ∈ (14, ∞) Cx ∈ [14, ∞) Dx ∈ [−14, 14)

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