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Day 551: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 6 Apr 2024

    158
    A software company sets up mm number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of mm is equal to :

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  2. Question 2

    Straight Lines. Asked once: 27 Jan 2024

    174
    If the sum of squares of all real values of α\alpha, for which the lines 2x−y+3=0,6x+3y+1=02x - y + 3 = 0,6x + 3y + 1 = 0 and αx+2y−2=0\alpha x + 2y - 2 = 0 do not form a triangle is pp, then the greatest integer less than or equal to pp is ......

  3. Question 3

    Three Dimensional Geometry. Asked once: 29 Jun 2022

    89
    Let P1:r→⋅(2i^+j^−3k^)=4P_{1}:\overrightarrow{r}\cdot (2\widehat{i}+\widehat{j}- 3\widehat{k}) = 4 be a plane. Let P2P_{2} be another plane which passes through the points (2,−3,2)(2,-3,2), (2,−2,−3)(2,-2,-3) and (1,−4,2)(1, - 4,2). If the direction ratios of the line of intersection of P1P_{1} and P2P_{2} be 16 , α,β\alpha,\beta, then the value of α+β\alpha + \beta is equal to

  4. Question 4

    Vector Algebra. Asked once: 31 Jan 2023

    69
    Let a→=2ı^+ȷ^+k^\overrightarrow{a}= 2\widehat{\imath}+\widehat{\jmath}+\widehat{k}, and b→\overrightarrow{b} and c→\overrightarrow{c} be two nonzero vectors such that ∣a→+b→+c→∣=∣a→+b→−c→∣|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}| = |\overrightarrow{a}+\overrightarrow{b}-\overrightarrow{c}| and b→⋅c→=0\overrightarrow{b}\cdot\overrightarrow{c}= 0. Consider the following two statements: (A) ∣a→+λc→∣≥∣a→∣|\overrightarrow{a}+ \lambda\overrightarrow{c}| \geq |\overrightarrow{a}| for all λ∈R\lambda \in R. (B) a→\overrightarrow{a} and c→\overrightarrow{c} are always parallel. Then.

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  5. Question 5

    Application of Derivatives. Asked once: 25 Jan 2023

    75
    Let f:(0,1)→Rf:(0,1) \rightarrow R be a function defined by f(x)=11−e−xf(x) =\frac{1}{1 -e^{- x}}, and g(x)=(f(−x)−f(x))g(x) = (f( - x) - f(x)). Consider two statements (I) gg is an increasing function in (0,1)(0,1) (II) gg is one-one in (0,1)(0,1) Then,

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