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Day 179: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 1 Feb 2024 (same type asked 3 times) See all 3 of this type

    61
    A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is:

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  2. Question 2

    Quadratic Equations. Asked once: 22 Jan 2026 S2 (same type asked 3 times) See all 3 of this type

    63
    Let α,β\alpha,\beta be the roots of the quadratic equation 12x2−20x+3λ=0,λ∈Z12x^{2}- 20x + 3\lambda = 0,\lambda \in Z. If 12≤∣β−α∣≤32\frac{1}{2}\leq |\beta - \alpha| \leq\frac{3}{2}, then the sum of all possible values of λ\lambda is :

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  3. Question 3

    Conic Sections. Asked once: 28 Jan 2025 (same type asked 3 times) See all 3 of this type

    149
    Let AA and BB be the two points of intersection of the line y+5=0y + 5 = 0 and the mirror image of the parabola y2=4xy^{2}= 4x with respect to the line x+y+4=0x + y + 4 = 0. If dd denotes the distance between AA and BB, and a denotes the area of △SAB\bigtriangleup SAB, where SS is the focus of the parabola y2=4xy^{2}= 4x, then the value of (a+d)(a + d) is ______\_\_\_\_\_\_ .

  4. Question 4

    Differential Equations. Asked once: 29 Jan 2024 (same type asked 3 times) See all 3 of this type

    177
    Let f(x)=lim⁡r→x{2r2[(f(r))2−f(x)f(r)]r2−x2−r3ef(r)r}f(x) =\sqrt{\lim_{r\rightarrow x} \left\{ \frac{2r^{2}\left\lbrack (f(r))^{2}-f(x)f(r) \right\rbrack}{r^{2}-x^{2}}-r^{3}e^{\frac{f(r)}{r}} \right\}} be differentiable in (−∞,0)∪(0,∞)( - \infty,0) \cup (0,\infty) and f(1)=1f(1) = 1. Then the value of ea, such that f(a)=0f(a) = 0, is equal to

  5. Question 5

    Definite Integration. Asked once: 29 Jan 2025 (same type asked 3 times) See all 3 of this type

    71
    Let f:(0,∞)→Rf:(0,\infty) \rightarrow R be a twice differentiable function. If for some a≠0,∫01f(λx)dλ=af(x)a \neq 0,\int_{0}^{1} f(\lambda x)d\lambda = af(x), f(1)=1f(1) = 1 and f(16)=18f(16) =\frac{1}{8}, then 16−f′(116)16 -f^{'}\left( \frac{1}{16} \right) is equal to ____\_\_\_\_ ,