Math Chapter Wise

EnglishEMRS 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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EnglishEMRS 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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EnglishEMRS 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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EnglishBihar (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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EnglishBihar (TRE 2.0)-2023

Q05.Which of the following statements is correct?

AA polynomial equation has at least one root. BA polynomial equation of degree n has n roots. CA polynomial equation may have no real roots. DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q06.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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EnglishBihar (TRE 1.0)-2023

Q07.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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EnglishEMRS TGT-2023

Q08.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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EnglishEMRS TGT-2023

Q09.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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EnglishEMRS TGT-2023

Q10.Solution of (x − 2)/(x + 5) > 2 is:

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

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EnglishKVS PGT 2023

Q11.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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EnglishKVS PGT 2023

Q12.If |x − 2| > 6, then:

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

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EnglishKVS PGT 2023

Q13.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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EnglishNVS PGT 2022

Q14.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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EnglishNVS PGT 2022

Q15.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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EnglishNVS PGT 2022

Q16.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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EnglishNVS PGT 2022

Q17.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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EnglishNVS PGT 2022

Q18.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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EnglishKVS PGT 2022

Q19.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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EnglishKVS PGT 2022

Q20.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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