Refer to JEE Mathematics Quadratic Equations MCQs provided below. JEE (Main) Full Syllabus Mathematics MCQs with answers available in Pdf for free download. The MCQ Questions for Full Syllabus Mathematics with answers have been prepared as per the latest syllabus, JEE (Main) books and examination pattern suggested in Full Syllabus by JEE (Main), NCERT and KVS. Multiple Choice Questions for Quadratic Equations are an important part of exams for Full Syllabus Mathematics and if practiced properly can help you to get higher marks. Refer to more Chapter-wise MCQs for JEE (Main) Full Syllabus Mathematics and also download more latest study material for all subjects
MCQ for Full Syllabus Mathematics Quadratic Equations
Full Syllabus Mathematics students should refer to the following multiple-choice questions with answers for Quadratic Equations in Full Syllabus. These MCQ questions with answers for Full Syllabus Mathematics will come in exams and help you to score good marks
Quadratic Equations MCQ Questions Full Syllabus Mathematics with Answers
Question: The roots of the quadratic equation 2x2 – 7x + 4 = 0 are -
- a) Irrational and different
- b) Rational and equal
- c) Imaginary and different
- d) Rational and different
Answer: Irrational and different
Question: The roots of the quadratic equation
x2 – 2 (a + b) x + 2 (a2 + b2) = 0 are -
- a) Imaginary and different
- b) Irrational and different
- c) Rational and equal
- d) Rational and different
Answer: Imaginary and different
Question: The roots of the equation x2 – 2 √2 x + 1 = 0 are –
- a) Real and different
- b) Real and equal
- c) Imaginary and different
- d) Rational and different
Answer: Real and different
Question: The roots of the equation x2 –3x – 4 = 0 are–
- a) Opposite and greater root in magnitude is positive
- b) Opposite and greater root in magnitude is negative
- c) Reciprocal to each other
- d) None of these
Answer: Opposite and greater root in magnitude is positive
Question: The roots of the equation 2x2 – 3x + 2 = 0 are -
- a) Reciprocal to each other
- b) Both roots are zero
- c) None of these
- d) Negative of each other
Answer: Reciprocal to each other
Question: If equation x2-bx/ax-c = k-1/k+1 has equal and opposite roots then the value of k is -
- a) a-b/a+b
- b) a-b/a-b
- c) a+b/a-b
- d) None of these
Answer: a-b/a+b
Question:
- a) Rational and different
- b) Imaginary and different
- c) Real and equal
- d) Real and different
Answer: Rational and different
Question: If the roots of the equation x2 + 2x + P = 0 are real then the value of P is -
- a) P≤1
- b) P≤2
- c) P≤3
- d) P≤4
Answer: P≤1
Question: If the product of the roots of the quadratic equation mx2 – 2x + (2m – 1) = 0 is 3 then the value of m is -
- a) –1
- b) 1
- c) 2
- d) 3
Answer: –1
Question:
- a) 35
- b) 45
- c) 40
- d) None of these
Answer: 35
Question: If the equation (k – 2)x2 – (k – 4) x – 2 = 0 has difference of roots as 3 then the value of k is-
- a) 3,3/2
- b) 3/2, 1
- c) 1,3
- d) 2, 3/2
Answer: 3,3/2
Question:
- a) b2-2ac/a2c2
- b) b2-2ac/ac
- c) b2-2ac/ac2
- d) None of these
Answer: b2-2ac/a2c2
Question: The roots of the equation x2 – 2x – 8 = 0 are -
- a) 4, – 2
- b) – 4,– 2
- c) – 4, 2
- d) 4, 2
Answer: 4, – 2
Question: The roots of the equation x2 – 4x + 1 = 0 are –
- a) 2 ± √3
- b) -2 ± 3
- c) 2, 4
- d) None of these
Answer: 2 ± √3
Question: The roots of the quadratic equation 7x2 – 9x + 2 = 0 are -
- a) Rational and different
- b) Irrational and different
- c) Rational and equal
- d) Imaginary and different
Answer: Rational and different
More Questions................................
Question: The equation whose roots are 3 and 4 will be-
- a) x2 – 7x + 12 = 0
- b) x2 + 7x – 12=0
- c) x2 – x + 12 = 0
- d) x2 + 7x + 12 = 0
Answer: x2 – 7x + 12 = 0
Question: The quadratic equation whose one root is 2 – i √3 is -
- a) x2 – 4x + 7 = 0
- b) x2 – 4x – 7=0
- c) x2 + 4x – 7 = 0
- d) None of these
Answer: x2 – 4x + 7 = 0
Question:
- a) x2 – 4x + 4 = 0
- b) x2 + 2x + 3 = 0
- c) x2 + 4x + 1= 0
- d) x2– 4x –1= 0
Answer: x2 – 4x + 4 = 0
Question:
- a) Both
- b) x2 – 11x + 30 = 0
- c) (x – 3)2 – 5 (x – 3) + 6 = 0
- d) None
Answer: Both
Question:
- a) x2 – x – 2 = 0
- b) x2 + x – 2 = 0
- c) x2 + 2x – 8 = 0
- d) None of these
Answer: x2 – x – 2 = 0
Question: If r and s are positive, then roots of the equation x2 – rx – s = 0 are -
(1) real (2) imaginary
(3) opposite signs (4) both negative
- a) 1 and 3 are correct
- b) 1 and 2 are correct
- c) 1, 2 and 3 are correct
- d) 2 and 4 are correct
Answer: 1 and 3 are correct
Question: If a < b < c < d, then roots of equation (x – a)(x – c) + 2 (x – b) (x – d) = 0 are
(1) real (2) unequal
(3) imaginary (4) equal
- a) 1 and 2 are correct
- b) 1 and 3 are correct
- c) 1, 2 and 3 are correct
- d) 2 and 4 are correct
Answer: 1 and 2 are correct
Question: If p and q are roots of the equation x2 – 2x + A = 0 and r and s be roots of the equation x2 – 18 x + B = 0 if p < q < r < s be in A.P., then choose the correct options –
- a) 2 and 4 are correct
- b) 1, 2 and 3 are correct
- c) 1 and 2 are correct
- d) 1 and 3 are correct
Answer: 2 and 4 are correct
Question:
- a) Statement -1 is False, Statement-2 is True.
- b) Statement -1 is True, Statement-2 is False.
- c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Answer: Statement -1 is False, Statement-2 is True.
Question: Let a, b, c be real such that ax2 + bx + c = 0 and x2 + x + 1= 0 have a common root
Statement–1 : a = b = c
Statement–2 : Two quadratic equations with real coefficients can not have only one imaginary root common.
- a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
- b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- c) Statement -1 is False, Statement-2 is True.
- d) Statement -1 is True, Statement-2 is False.
Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Question:
Statement-1 : If one roots is √5 - √2 then the equation of lowest degree with rational coefficient is x4–14x2+ 9 = 0
Statement-2 : For a polynomial equation with rational coefficient irrational roots occurs in pairs.
- a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
- b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- c) Statement -1 is False, Statement-2 is True.
- d) Statement -1 is True, Statement-2 is False.
Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Question: If f (x) is a quadratic expression which is positive for all real values of x and g(x) = f (x) + f '(x) + f "(x) , then for any real value of x-
- a) g (x) > 0
- b) g (x) < 0
- c) g (x) = 0
- d) None of these
Answer: g (x) > 0
Question: For real values of x, 2x2 + 5x – 3 > 0, if-
- a) x > 1
- b) x < – 2
- c) x > 0
- d) None of these
Answer: x > 1
Question: For what value of m the expression y2 + 4xy + 4x + my – 2 can be resolved into two rational factors-
- a) –1
- b) –2
- c) 1
- d) 2
Answer: –1
Question: The quadratic equation whose one root is 1/2 + √5 will be-
- a) x2 + 4x – 1 = 0
- b) x2 + 4x + 1= 0
- c) x2 – 4x – 1 = 0
- d) None of these
Answer: x2 + 4x – 1 = 0
Question:
- a) c,a,b
- b) a,b,c
- c) b,c,a
- d) None of these
Answer: c,a,b
Question: If the expression x2–11x + a and x2 – 14x + 2a must have a common factor and a ≠ 0, then, the common factor is –
- a) (x – 8)
- b) (x – 3)
- c) (x – 6)
- d) None of these
Answer: (x – 8)
Question: If x is real then the value of the expression x2+14x+9/ x2+2x+3 between –
- a) –5 and 4
- b) – 4 and 5
- c) –3 and 3
- d) – 4 and 4
Answer: –5 and 4
Question:
- a) All these true
- b) –3 < x < 3/2
- c) x < –4
- d) x > 5/2
Answer: All these true
Question: The real values of a for which the quadratic equation 2x2 – (a3 + 8a – 1) x + a2– 4a = 0 possesses roots of opposite signs are given by-
- a) 0 < a < 4
- b) a > 7
- c) a > 5
- d) a > 0
Answer: 0 < a < 4
Question: The value of the expression x2 + 2bx + c will be positive, if-
- a) b2 < c
- b) b2–4c < 0
- c) b2–4c > 0
- d) c2 < b
Answer: b2 < c
Question: If roots of the equation x2 + ax + 25 = 0 are in the ratio of 2 : 3 then the value of a is -
- a) ±25/√6
- b) ±5/√6
- c) ±6/√6
- d) None of these
Answer: ±25/√6
Question: If the roots of the equations x2 + 3x + 2 = 0 and x2 –x +λ=0 are in the same ratio then the value of λ is given by-
- a) 2/9
- b) 7/2
- c) 2/7
- d) 9/2
Answer: 2/9
Question:
- a) a2/ p2
- b) a2/ b2
- c) c2/ r2
- d) None of these
Answer: a2/ p2
Question:
- a) b2 pr = q2 ac
- b) p2 br = a2 qc
- c) r2 pb = c2 ar
- d) None of these
Answer: b2 pr = q2 ac
Question: The sum of all real roots of the equation |x – 2|2 + | x – 2 | – 2 = 0, is -
- a) 4
- b) 0
- c) 8
- d) None of these
Answer: 4
Question:
- a) None of these
- b)
- c)
- d)
Answer: None of these
Question: If p, q, r are in H.P. and p and r be different having same sign, then the root of the equation px2 + 2qx + r = 0 will be
- a) Imaginary
- b) Equal
- c) Real
- d) None of these
Answer: Imaginary
Question: If x = 2 + √3 then the value of x3 – 7x2 + 13 x – 12 is –
- a) –9
- b) 9
- c) 6
- d) 3
Answer: –9
Question: If every pair from among the equations x2 + px + qr = 0, x2 + qx + rp= 0 and x2 + rx + pq = 0 has a common root, then the sum of the three common roots is-
- a) p + q + r
- b) pqr
- c) 2 (p + q+ r)
- d) – (p + q + r)
Answer: p + q + r
Question: If the quadratic equations ax2 + 2cx + b = 0 and ax2 + 2bx + c = 0 (b≠c) have a common root, then a + 4b + 4c is equal to-
- a) 0
- b) –2
- c) –1
- d) 1
Answer: 0
Question: The value of m for which one of the roots of x2 – 3x + 2m = 0 is double of one of the roots of x2 – x + m = 0 is-
- a) 0, 2
- b) 2, –2
- c) 0, –2
- d) None of these
Answer: 0, 2
Question:
- a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
- b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- c) Statement -1 is False, Statement-2 is True.
- d) Statement -1 is True, Statement-2 is False.
Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Question:
- a) Statement -1 is False, Statement-2 is True.
- b) Statement -1 is True, Statement-2 is False
- c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
Answer: Statement -1 is False, Statement-2 is True.
Question:
- a) Statement -1 is True, Statement-2 is False.
- b) Statement -1 is False, Statement-2 is True.
- c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Answer: Statement -1 is True, Statement-2 is False.
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