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Day 158: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Application of Derivatives. Asked once: 31 Jan 2023 (same type asked 5 times) See all 5 of this type

    160
    The absolute minimum value, of the function f(x)=∣x2−x+1∣+[x2−x+1]f(x) =\left| x^{2}- x + 1 \right|+\left\lbrack x^{2}- x + 1 \right\rbrack, where [t]\lbrack t\rbrack denotes the greatest integer function, in the interval [−1,2]\lbrack - 1,2\rbrack, is:

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  2. Question 2

    Three Dimensional Geometry. Asked once: 31 Jan 2023 (same type asked 5 times) See all 5 of this type

    166
    Let PP be the plane, passing through the point (1,−1,−5)(1, - 1, - 5) and perpendicular to the line joining the points (4,1,−3)(4,1, - 3) and (2,4,3)(2,4,3). Then the distance of PP from the point (3,−2,2)(3, - 2,2) is

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  3. Question 3

    Quadratic Equations. Asked once: 29 Jan 2023 (same type asked 5 times) See all 5 of this type

    76
    Let λ≠0\lambda \neq 0 be a real number. Let α,β\alpha,\beta be the roots of the equation 14x2−31x+3λ=014x^{2}- 31x + 3\lambda = 0 and α,γ\alpha,\gamma be the roots of the equation 35x2−53x+4λ=035x^{2}- 53x + 4\lambda = 0. Then 3αβ\frac{3\alpha}{\beta} and 4αγ\frac{4\alpha}{\gamma} are the roots of the equation

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  4. Question 4

    Permutations and Combinations. Asked once: 2 Apr 2026 S1 (same type asked 4 times) See all 4 of this type

    56
    The number of seven-digit numbers, that can be formed by using the digits 1,2,3,51,2,3,5 and 7 such that each digit is used at least once, is ;

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  5. Question 5

    Complex Numbers. Asked once: 29 Jan 2024 (same type asked 4 times) See all 4 of this type

    171
    Let α,β\alpha,\beta be the roots of the equation x2−6x+3=0x^{2}-\sqrt{6}x+ 3 = 0 such that Im(α)>Im(β)Im(\alpha) > Im(\beta). Let a,ba,b be integers not divisible by 3 and nn be a natural number such that α99β+α98=3n(a+ib),i=−1\frac{\alpha^{99}}{\beta}+\alpha^{98}=3^{n}(a+ib),i=\sqrt{- 1}. Then n+a+bn + a + b is equal to