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Previous Years Questions
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MCQ (Single Correct Answer)
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The value of a for which the sum of the squares of the roots of the equation $${x^2} - (a - 2)x - a - 1 = 0$$ assumes th...
WB JEE 2022
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If a, b are odd integers, then the roots of the equation $$2a{x^2} + (2a + b)x + b = 0$$, $$a \ne 0$$ are
WB JEE 2022
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Let $$\alpha$$, $$\beta$$ be the roots of the equation x2 $$-$$ 6x $$-$$ 2 = 0 with $$\alpha$$ > $$\beta$$. If an = $$\a...
WB JEE 2021
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If P(x) = ax2 + bx + c and Q(x) = $$ - $$ax2 + dx + c, where ac $$ \ne $$ 0 [a, b, c, d are all real], then P(x).Q(x) = ...
WB JEE 2020
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Let z1 and z2 be two imaginary roots of z2 + pz + q = 0, where p and q are real. The points z1, z2 and origin form an eq...
WB JEE 2020
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The expression ax2 + bx + c (a, b and c are real) has the same sign as that of a for all x if
WB JEE 2020
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Let a, b, c be real numbers such that a + b + c < 0 and the quadratic equation ax2 + bx + c = 0 has imaginary roots. ...
WB JEE 2019
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If $${b_1}{b_2} = 2({c_1} + {c_2})$$ and b1, b2, c1, c2 are all real numbers, then at least one of the equations $${x^2}...
WB JEE 2018
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For real x, the greatest value of $${{{x^2} + 2x + 4} \over {2{x^2} + 4x + 9}}$$ is
WB JEE 2017
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Let $$\alpha$$ and $$\beta$$ be the roots of $${x^2} + x + 1 = 0$$. If n be a positive integer, then $$\alpha$$n + $$\be...
WB JEE 2017
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If p, q are odd integers, then the roots of the equation $$2p{x^2} + (2p + q)x + q = 0$$ are
WB JEE 2017
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The greatest integer which divides $$(p + 1)(p + 2)(p + 3)...(p + q)$$ for all $$p \in N$$ and fixed $$q \in N$$ is
WB JEE 2017
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If $$\alpha$$ and $$\beta$$ are the roots of the equation x2 + x + 1 = 0, then the equation whose roots ar $$\alpha$$19 ...
WB JEE 2011
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If the ratio of the roots of the equation $$p{x^2} + qx + r = 0$$ is $$a:b$$, then $${{ab} \over {{{(a + b)}^2}}}$$ =...
WB JEE 2011
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Let a, b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax2 + bx + c = 0
WB JEE 2011
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If sin $$\theta$$ and cos $$\theta$$ are the roots of equation ax2 $$-$$ bx + c = 0, then a, b and c satisfy the relatio...
WB JEE 2011
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The quadratic equation $${x^2} + 15|x| + 14 = 0$$ has
WB JEE 2010
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The roots of the quadratic equation $${x^2} - 2\sqrt 3 x - 22 = 0$$ are
WB JEE 2010
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If $$\alpha$$, $$\beta$$ be the roots of the quadratic equation x2 + x + 1 = 0 then the equation whose roots are $$\alph...
WB JEE 2010
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If a, b, c are real, then both the roots of the equation $$(x - b)(x - c) + (x - c)(x - a) + (x - a)(x - b) = 0$$ are al...
WB JEE 2009
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The quadratic equation whose roots are three times the roots of $$3a{x^2} + 3bx + c = 0$$ is
WB JEE 2009
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The sum of all real roots of the equation $$|x - 2{|^2} + |x - 2| - 2 = 0$$ is
WB JEE 2009
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If $$\alpha$$, $$\beta$$ be the roots of $${x^2} - a(x - 1) + b = 0$$, then the value of $${1 \over {{\alpha ^2} - a\alp...
WB JEE 2009
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The equation $${x^2} - 3|x| + 2 = 0$$ has
WB JEE 2008
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If one root of the equation $${x^2} + (1 - 3i)x - 2(1 + i) = 0$$ is $$-$$1 + i, then the other root is
WB JEE 2008
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MCQ (More than One Correct Answer)
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If the equation $${x^2} - cx + d = 0$$ has roots equal to the fourth powers of the roots of $${x^2} + ax + b = 0$$, wher...
WB JEE 2018
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If a, b$$ \in $$ {1, 2, 3} and the equation ax2 + bx + 1 = 0 has real roots, then
WB JEE 2017
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Subjective
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Determine the sum of imaginary roots of the equation $$(2{x^2} + x - 1)(4{x^2} + 2x - 3) = 6$$
WB JEE 2011
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Find the values of a for which the expression $${x^2} - (3a - 1)x + 2{a^2} + 2a - 11$$ is always positive.
WB JEE 2009
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