Quadratic Equations PYQs - Last 10 Years
WB JEE / Mathematics / Algebra / 26 recent questions
MathematicsAlgebra2017-2026
Practice 26 WB JEE Mathematics questions from Quadratic Equations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
26
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Mathematics / Algebra
2017-2026
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Based on indexed question metadata
14
Last 5 Years
2022-2026
26
Last 10 Years
2017-2026
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26PYQs
MCQ84.6%
MCQM15.4%
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#1 Unknown26
14 in last 5 years26 in last 10 years
Last 10 Years Quadratic Equations Questions
Showing 26 of 26 filtered questions.
1Quadratic Equations
If $\alpha, \beta$ are the roots of the equation $x^2-p x+q=0$ and $\alpha>0, \beta>0$, then $\alpha^{\frac{1}{4}}+\beta^{\frac{1}{4}}=\left(p+6 \sqrt{p}+4 q^{\frac{1}{4}} \sqrt{p+2 \sqrt{q}}\right)^k$, where $K$ is
MCQ+1 / -0.252026
2Quadratic Equations
If $0<\alpha<\beta<\gamma<\frac{\pi}{2}$, then the equation $\frac{1}{x-\sin \alpha}+\frac{1}{x-\sin \beta}+\frac{1}{x-\sin \gamma}=0$ has
MCQ+1 / -0.252026
3Quadratic Equations
If $\left(4^{\sec ^2 \alpha}\right) x^2+2 x+\left(\beta^2-\beta+\frac{1}{2}\right)=0$ has real roots，then the value／values of $\left(\cos \alpha+\cos ^{-1} \beta\right)$ is／are
MCQM+2 / -02026
4Quadratic Equations
The equation $x^3+5 x^2+p x+q=0$ and $x^3+7 x^2+p x+r=0$ have two roots in common. If the third root of each equation is represented by $x_1$ and $x_2$ respectively, the GCD of $x_1, x_2$ will be
MCQ+2 / -0.52026
5Quadratic Equations
Let 1 lies between the roots of the equation $y^2-m y+1=0$ and $[x]$ denotes the greatest integer function. Then the value of $\left[\left(\frac{4|x|}{x^2+16}\right)^m\right]$ is
MCQ+2 / -0.52026
6Quadratic Equations
For what value of ' $a$ ', the sum of the squares of the roots of the equation $x^2-(a-2) x-a+1=0$ will have the least value?
MCQ+1 / -0.252025
7Quadratic Equations
If the sum of the squares of the roots of the equation $x^2-(a-2) x-(a+1)=0$ is least for an appropriate value of the variable parameter $a$, then that value of ' $a$ ' will be
MCQ+1 / -0.252025
8Quadratic Equations
If the quadratic equation \(a x^2+b x+c=0(a>0)\) has two roots \(\alpha\) and \(\beta\) such that \(\alpha<-2\) and \(\beta>2\), then
MCQM+2 / -02024
9Quadratic Equations
If \(a, b, c\) are distinct odd natural numbers, then the number of rational roots of the equation \(a x^2+b x+c=0\)
MCQ+1 / -0.252024
10Quadratic Equations
Let \(\mathrm{N}\) be the number of quadratic equations with coefficients from \(\{0,1,2, \ldots, 9\}\) such that 0 is a solution of each equation. Then the value of \(\mathrm{N}\) is
MCQ+1 / -0.252024
11Quadratic Equations
If \(\mathrm{P}(x)=\mathrm{a} x^2+\mathrm{b} x+\mathrm{c}\) and \(\mathrm{Q}(x)=-\mathrm{a} x^2+\mathrm{d} x+\mathrm{c}\) where \(\mathrm{ac} \neq 0\), then \(\mathrm{P}(x) \cdot \mathrm{Q}(x)=0\) has (a, b, c, d are real)
MCQ+1 / -0.252024
12Quadratic Equations
If one root of \({x^2} + px - {q^2} = 0,p\) and \(q\) are real, be less than 2 and other be greater than 2, then
MCQ+1 / -0.252023
13Quadratic Equations
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 the least value is
MCQ+2 / -0.52022
14Quadratic Equations
If a, b are odd integers, then the roots of the equation \(2a{x^2} + (2a + b)x + b = 0\), \(a \ne 0\) are
MCQ+1 / -0.252022
15Quadratic Equations
Let \(\alpha\), \(\beta\) be the roots of the equation x2 \(-\) 6x \(-\) 2 = 0 with \(\alpha\) > \(\beta\). If an = \(\alpha\)n \(-\) \(\beta\)n for n \(\ge\) 1, then the value of \({{{a_{10}} - 2{a_8}} \over {2{a_9}}}\) is
MCQ+1 / -0.252021
16Quadratic Equations
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) = 0 has
MCQ+2 / -0.52020
17Quadratic Equations
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 equilateral triangle if
MCQ+2 / -0.52020
18Quadratic Equations
The expression ax2 + bx + c (a, b and c are real) has the same sign as that of a for all x if
MCQ+1 / -0.252020
19Quadratic Equations
Let a, b, c be real numbers such that a + b + c < 0 and the quadratic equation ax2 + bx + c = 0 has imaginary roots. Then,
MCQ+1 / -0.252019
20Quadratic Equations
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 \({x^2} + {b_1}x + {c_1} = 0\) and \({x^2} + {b_2}x + {c_2} = 0\) has
MCQ+1 / -0.252018
21Quadratic Equations
If the equation \({x^2} - cx + d = 0\) has roots equal to the fourth powers of the roots of \({x^2} + ax + b = 0\), where \({a^2} > 4b\), then the roots of \({x^2} - 4bx + 2{b^2} - c = 0\) will be
MCQM+2 / -02018
22Quadratic Equations
If a, b\(\in\) {1, 2, 3} and the equation ax2 + bx + 1 = 0 has real roots, then
MCQM+2 / -02017
23Quadratic Equations
If p, q are odd integers, then the roots of the equation \(2p{x^2} + (2p + q)x + q = 0\) are
MCQ+1 / -0.252017
24Quadratic Equations
Let \(\alpha\) and \(\beta\) be the roots of \({x^2} + x + 1 = 0\). If n be a positive integer, then \(\alpha\)n + \(\beta\)n is
MCQ+2 / -0.52017
25Quadratic Equations
The greatest integer which divides \((p + 1)(p + 2)(p + 3)...(p + q)\) for all \(p \in N\) and fixed \(q \in N\) is
MCQ+1 / -0.252017
26Quadratic Equations
For real x, the greatest value of \({{{x^2} + 2x + 4} \over {2{x^2} + 4x + 9}}\) is
MCQ+2 / -0.52017