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Day 307: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 1 Feb 2024 (same type asked 6 times) See all 6 of this type

    164
    Consider the relations R1R_{1} and R2R_{2} defined as aR1baR_{1}b ⇔a2+b2=1\Leftrightarrow a^{2}+b^{2}= 1 for all a,b,∈Ra,b, \in R and (a,b)R2(c,d)(a,b)R_{2}(c,d) ⇔a+d=b+c\Leftrightarrow a + d = b + c for all (a,b),(c,d)∈N×N(a,b),(c,d) \in N \times N. Then

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  2. Question 2

    Differential Equations. Asked once: 14 Jun 2022 (same type asked 6 times) See all 6 of this type

    74
    If x=x(y)x = x(y) is the solution of the differential equation ydxdy=2x+y3(y+1)ey,x(1)=0y\frac{dx}{dy}= 2x +y^{3}(y + 1)e^{y},x(1) = 0; then x(e)x(e) is equal to :

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  3. Question 3

    Definite Integration. Asked once: 26 Jul 2022 (same type asked 6 times) See all 6 of this type

    70
    If a=lim⁡n→∞∑k=1n2nn2+k2a =\lim_{n \rightarrow \infty} \sum_{k = 1}^{n} \frac{2n}{n^{2}+k^{2}} and f(x)=1−cos⁡x1+cos⁡x,x∈(0,1)f\left( x \right)=\sqrt{\frac{1 - \cos x}{1 + \cos x}},x \in (0,1), then:

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  4. Question 4

    Differential Equations. Asked once: 26 Jul 2022 (same type asked 6 times) See all 6 of this type

    178
    Suppose y=y(x)y = y(x) be the solution curve to the differential equation dydx−y=2−e−x\frac{dy}{dx}- y = 2 -e^{- x} such that lim⁡x→∞y(x)\lim_{x \rightarrow \infty} y(x) is finite. If aa and bb are respectively the x−x - and yy-intercepts of the tangent to the curve at x=0x = 0, then the value of a−4ba - 4b is equal to

  5. Question 5

    Vector Algebra. Asked once: 30 Jan 2024 (same type asked 6 times) See all 6 of this type

    78
    Let A(2,3,5)A(2,3,5) and C(−3,4,−2)C( - 3,4, - 2) be opposite vertices of a parallelogram ABCDABCD if the diagonal BD→=i^+2j^+3k^\overrightarrow{BD}=\widehat{i}+ 2\widehat{j}+ 3\widehat{k} then the area of the parallelogram is equal to

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