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Day 406: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 2021 Paper 21 (same type asked 11 times) See all 11 of this type

    82
    Let SS be the mirror image of the point Q(1,3,4)Q(1,3,4) with respect to the plane 2x−y+z+3=02x - y + z + 3 = 0 and let R(3,5,γ)R(3,5,\gamma) be a point of this plane. Then the square of the length of the line segment SRSR is

  2. Question 2

    Three Dimensional Geometry. Asked once: 11 Apr 2023 (same type asked 10 times) See all 10 of this type

    85
    Let a line ll pass through the origin and be perpendicular to the lines
    l1:r→=(i^−11j^−7k^)+λ(i^+2j^+3k^),λ∈Rl_{1}:\overrightarrow{r}= (\widehat{i}- 11\widehat{j}- 7\widehat{k}) + \lambda(\widehat{i}+ 2\widehat{j}+ 3\widehat{k}),\lambda \in R
    and l2:r→=(−i^+k^)+μ(2i^+2j^+k^),μ∈Rl_{2}:\overrightarrow{r}= ( -\widehat{i}+\widehat{k}) + \mu(2\widehat{i}+ 2\widehat{j}+\widehat{k}),\mu \in R. If PP is the point of intersection of ll and l1l_{1}, and Q(αQ(\alpha ,β,γ),\beta,\gamma) is the foot of perpendicular from PP on l2l_{2}, then 9(α+β+γ)9(\alpha + \beta + \gamma) is equal to

  3. Question 3

    Quadratic Equations. Asked once: 2021 Paper 15 (same type asked 10 times) See all 10 of this type

    43
    The number of real solutions of x2−∣x∣−12=0x^{2}- |x| - 12 = 0 is

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  4. Question 4

    Sequences and Series. Asked once: 2021 Paper 25 (same type asked 10 times) See all 10 of this type

    66
    In an increasing, geometric series, the sum of the second and the sixth term is 252\frac{25}{2} and the product of the third and fifth term is 25. Then, the sum of 4th ,6th 4^{\text{th~}},6^{\text{th~}} and 8th 8^{\text{th~}} terms is equal to:

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  5. Question 5

    Relations and Functions. Asked once: 13 Apr 2023 (same type asked 9 times) See all 9 of this type

    172
    Let A={−4,−3,−2,0,1,3,4}\mathbf{A = \{ - 4, - 3, - 2,0,1,3,4\}} and R={(a,b)∈A\mathbf{R = \{(a,b) \in A} ×A:b=∣a∣\times A:b = |a| or  b2=a+1}\left. \ b^{2}= a + 1 \right\} be a relation on AA. Then the minimum number of elements, that must be added to the relation RR so that it becomes reflexive and symmetric, is