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Day 315: JEE Mains Maths

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

  1. Question 1

    Differentiation. Asked once: 25 Jul 2022 (same type asked 5 times) See all 5 of this type

    86
    Let f(x)={∣4x2−8x+5∣, if 8x2−6x+1≥0[4x2−8x+5], if 8x2−6x+1<0f(x) =\left\{ \begin{matrix} \left| 4x^{2}- 8x + 5 \right|,\text{~if~}8x^{2}- 6x + 1 \geq 0 \\ \left\lbrack 4x^{2}- 8x + 5 \right\rbrack,\text{~}\text{if~}8x^{2}- 6x + 1 < 0 \end{matrix} \right., where [α]\lbrack\alpha\rbrack denotes the greatest integer less than or equal to α\alpha. Then the number of points in R where ff is not differentiable is

  2. Question 2

    Probability. Asked once: 11 Apr 2023 (same type asked 5 times) See all 5 of this type

    172
    Let the probability of getting head for a biased coin be 14\frac{1}{4}. It is tossed repeatedly until a head appears. Let NN be the number of tosses required. If the probability that the equation 64x2+5Nx+1=064x^{2}+ 5Nx + 1 = 0 has no real root is pq\frac{p}{q}, where pp and qq are co-prime, then q−pq - p is equal to

  3. Question 3

    Relations and Functions. Asked once: 30 Jan 2023 (same type asked 5 times) See all 5 of this type

    62
    The minimum number of elements that must be added to the relation R={(a,b),(b,c)}\mathbf{R = \{(a,b),(b,c)\}} on the set {a,b,c}\mathbf{\{ a,b,c\}} so that is becomes symmetric and transitive is:

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  4. Question 4

    Application of Derivatives. Asked once: 2021 Paper 22 (same type asked 5 times) See all 5 of this type

    84
    If ' RR ' is the least value of ' aa ' such that the function f(x)=x2+ax+1f(x) =x^{2}+ax+ 1 is increasing on [1, 2] and 'S' is the greatest value of ' aa ' such that the function f(x)=x2+ax+1f(x) =x^{2}+ax+ 1 is decreasing on [1,2]\lbrack 1,2\rbrack, then the value of ∣R−S∣|R - S| is

  5. Question 5

    Complex Numbers. Asked once: 2021 Paper 12 (same type asked 5 times) See all 5 of this type

    45
    If the real part of the complex number (1−cos⁡θ+2isinθ)−1(1 - \cos\theta+ 2isin\theta)^{- 1} is 15\frac{1}{5} for θ∈(0,π)\theta\in (0,\pi), then the value of the integral ∫0θsin⁡xdx\int_{0}^{\theta} \sin xdx is equal to :

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