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Day 172: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 2021 Paper 19 (same type asked 4 times) See all 4 of this type

    79
    A circle CC touches the line x=2yx = 2y at the point (2,1)(2,1) and intersects the circle C1:x2+y2+2y−5=0C_{1}:x^{2}+y^{2}+ 2y- 5 = 0 at two points PP and QQ such that PQPQ is a diameter of C1C_{1}. Then the diameter of CC is:

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  2. Question 2

    Differential Equations. Asked once: 27 Jan 2024 (same type asked 4 times) See all 4 of this type

    63
    Let x=x(t)x = x(t) and y=y(t)y = y(t) be solutions of the differential equations  dxdt+ax=0\ \frac{dx}{dt}+ ax = 0 and dydt+by=0\frac{dy}{dt}+ by = 0 respectively, a,b∈Ra,b \in R. Given that x(0)=2;y(0)=1x(0) = 2;y(0) = 1 and 3y(1)=2x(1)3y(1) = 2x(1), the value of tt, for which x(t)=y(t)x(t) = y(t), is :

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  3. Question 3

    Inverse Trigonometric Functions. Asked once: 31 Jan 2023 (same type asked 4 times) See all 4 of this type

    79
    If sin⁡−1α17+cos⁡−145−tan⁡−17736=0,0<α<13\sin^{- 1}\frac{\alpha}{17}+\cos^{- 1}\frac{4}{5}-\tan^{- 1}\frac{77}{36}= 0,0 < \alpha < 13, then sin⁡−1(sin⁡α)+cos⁡−1(cos⁡α)\sin^{- 1}(\sin\alpha) +\cos^{- 1}(\cos\alpha) is equal to

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  4. Question 4

    Application of Derivatives. Asked once: 28 Jul 2022 (same type asked 4 times) See all 4 of this type

    83
    Let f:[0,1]→Rf:\lbrack 0,1\rbrack \rightarrow R be a twice differentiable function in (0,1)(0,1) such that f(0)=3f(0) = 3 and f(1)=5f(1) = 5. If the line y=2x+3y = 2x + 3 intersects the graph of ff at only two distinct points in (0,1)(0,1), then the least number of points x∈(0,1)x \in (0,1), at which f′′(x)=0f^{''}(x) = 0, is

  5. Question 5

    Differential Equations. Asked once: 6 Apr 2023 (same type asked 4 times) See all 4 of this type

    178
    Let a curve y=f(x),x∈(0,∞)y = f(x),x \in (0,\infty) pass through the points P(1,32)P\left( 1,\frac{3}{2} \right) and Q(a,12)Q\left( a,\frac{1}{2} \right). If the tangent at any point R(b,f(b))R(b,f(b)) to the given curve cuts the yy-axis at the point S(0,c)S(0,c) such that bc=3bc = 3, then (PQ)2(PQ)^{2} is equal to