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Day 252: JEE Mains Maths

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

  1. Question 1

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

    72
    Let the system of linear equations
    x+y+kz=2x + y + kz = 2
    2x+3y−z=12x + 3y - z = 1
    3x+4y+2z=k3x + 4y + 2z = k
    have infinitely many solutions. Then the system
    (k+1)x+(2k−1)y=7(k + 1)x + (2k - 1)y = 7
    (2k+1)x+(k+5)y=10(2k + 1)x + (k + 5)y = 10
    has:

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  2. Question 2

    Quadratic Equations. Asked once: 2021 Paper 21 (same type asked 5 times) See all 5 of this type

    71
    The set of all values of k>−1k> - 1, for which the equation (3x2+4x+3)2−(k+1)(3x2+4x+3)\left( 3x^{2}+ 4x + 3 \right)^{2}- (k + 1)\left( 3x^{2}+ 4x + 3 \right) (3x2+4x+2)+k(3x2+4x+2)2=0\left( 3x^{2}+ 4x+ 2 \right)+k\left( 3x^{2}+ 4x+ 2 \right)^{2}= 0 has real roots, is:

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  3. Question 3

    Complex Numbers. Asked once: 26 Jul 2022 (same type asked 5 times) See all 5 of this type

    62
    Let OO be the origin and AA be the point z1=1+2iz_{1}= 1 + 2i. If BB is the point z2,Re(z2)<0z_{2},Re\left( z_{2} \right)< 0, such that OABOAB is a right- angled isosceles triangle with OBOB as hypotenuse, then which of the following is NOT true?

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  4. Question 4

    Relations and Functions. Asked once: 24 Jan 2023 (same type asked 5 times) See all 5 of this type

    153
    If f(x)=22x22x+2, x∈Rf(x)=\frac{2^{2x}}{2^{2x}+2},\ x\in R, then f(12023)+f(22023)+⋯+f(20222023)f\left(\frac{1}{2023}\right)+f\left(\frac{2}{2023}\right)+\cdots+f\left(\frac{2022}{2023}\right) is equal to

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  5. Question 5

    Differentiation. Asked once: 29 Jul 2022 (same type asked 5 times) See all 5 of this type

    176
    If [t]\lbrack t\rbrack denotes the greatest integer ≤t\leq t, then number of points, at which the function f(x)=4∣2x+3∣+f(x) = 4|2x + 3| + 9[x+12]−12[x+20]9\left\lbrack x +\frac{1}{2} \right\rbrack- 12\lbrack x + 20\rbrack is not differentiable in the open interval (−20,20)( - 20,20), is