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Day 117: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. This type asked 2 times: 26 Jun 2022, 12 Apr 2023. This one: 26 Jun 2022 See all 2 of this type

    75
    Let the plane 2x+3y+z+20=02x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x−3y+5z=8x - 3y + 5z = 8. If the mirror image of the point (2,−12,2)\left( 2, -\frac{1}{2},2 \right) in the rotated plane is B(a,b,c)B(a,b,c), then :

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  2. Question 2

    Matrices. This type asked 2 times: 30 Jan 2023, 11 Apr 2023. This one: 11 Apr 2023 See all 2 of this type

    76
    Let AA be a 2×22 \times 2 matrix with real entries such that A′=αA+IA^{'}= \alpha A + I, where α∈R−{−1,1}\mathbf{\alpha \in R - \{ - 1,1\}}. If det⁡\det (A2−A)=4\left( A^{2}- A \right)= 4, then the sum of all possible values of α\alpha is equal to

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  3. Question 3

    Sequences and Series. This type asked 2 times: 14 Jun 2022, 11 Apr 2023. This one: 11 Apr 2023 See all 2 of this type

    163
    Let a,b,ca,b,c and dd be positive real numbers such that a+b+c+d=11a + b + c + d = 11. If the maximum value of a5b3c2da^{5}b^{3}c^{2}d is 3750β3750\beta, then the value of β\beta is

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  4. Question 4

    Application of Derivatives. This type asked 2 times: 2021 Paper 21, 10 Apr 2023. This one: 10 Apr 2023 See all 2 of this type

    64
    A square piece of tin of side 30 cm30\text{ }cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the volume of the box is maximum, then its surface area (in cm2cm^{2} ) is equal to

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  5. Question 5

    Limits and Continuity. This type asked 2 times: 14 Jun 2022, 10 Apr 2023. This one: 10 Apr 2023 See all 2 of this type

    82
    Let f:(−2,2)→f:( - 2,2) \rightarrow IR be defined by
    f(x)={x[x],−2<x<0(x−1)[x],0≤x<2f(x) =\left\{ \begin{matrix} x\lbrack x\rbrack & , - 2 < x < 0 \\ (x - 1)\lbrack x\rbrack & ,0 \leq x < 2 \end{matrix} \right.
    Where [x]\lbrack x\rbrack denotes the greatest integer function. If mm and nn respectively are the number of points in (−2,2)( - 2,2) at which y=∣f(x)∣y = |f(x)| is not continuous and not differentiable, then m+nm + n is equal to