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Day 335: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 8 Apr 2023 (same type asked 11 times) See all 11 of this type

    153
    Let PP be the plane passing through the line x−11=y−2−3=z+57\frac{x - 1}{1}=\frac{y - 2}{- 3}=\frac{z + 5}{7} and the point (2,4,−3)(2,4, - 3). If the image of the point (−1,3,4)( - 1,3,4) in the plane PP is (α,β,γ)(\alpha,\beta,\gamma), then α+β+γ\alpha + \beta + \gamma is equal to

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  2. Question 2

    Three Dimensional Geometry. Asked once: 7 Apr 2025 (same type asked 10 times) See all 10 of this type

    139
    If the equation of the line passing through the point (0,−12,0)\left( 0, -\frac{1}{2},0 \right) and perpendicular to the lines r→=λ(i^+aj^+bk^)\overrightarrow{r}=\lambda(\widehat{i}+ a\widehat{j}+ b\widehat{k}) and r→=(i^−j^−6k^)+μ(−bi^+aj^+5k^)\overrightarrow{r}= (\widehat{i}-\widehat{j}- 6\widehat{k}) +\mu( - b\widehat{i}+ a\widehat{j}+ 5\widehat{k}) is x−1−2=y+4 d=z−c−4\frac{x - 1}{- 2}=\frac{y + 4}{\text{ }d}=\frac{z - c}{- 4}, then a+b+c+da + b + c + d is equal to:

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  3. Question 3

    Quadratic Equations. Asked once: 8 Apr 2024 (same type asked 10 times) See all 10 of this type

    176
    The number of distinct real roots of the equation ∣x+1∣∣x+3∣−4∣x+2∣+5=0|x + 1||x + 3| - 4|x + 2| + 5 = 0, is

  4. Question 4

    Vector Algebra. Asked once: 29 Jul 2022 (same type asked 10 times) See all 10 of this type

    70
    Let a→=3i^+j^\overrightarrow{a}= 3\widehat{i}+\widehat{j} and b→=i^+2j^+k^\overrightarrow{b}=\widehat{i}+ 2\widehat{j}+\widehat{k}. Let c→\overrightarrow{c} be a vector satisfying a→×(b→×c→)=b→+λc→\overrightarrow{a}\times (\overrightarrow{b}\times\overrightarrow{c}) =\overrightarrow{b}+ \lambda\overrightarrow{c}. If b→\overrightarrow{b} and c→\overrightarrow{c} are non-parallel, then the value of λ\lambda is:

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  5. Question 5

    Sequences and Series. Asked once: 8 Apr 2024 (same type asked 10 times) See all 10 of this type

    154
    In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 703\frac{70}{3} and the product of the third and fifth terms is 49. Then the sum of the 4th ,6th 4^{\text{th~}},6^{\text{th~}} and 8th 8^{\text{th~}} terms is: -

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