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Day 170: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 8 Apr 2023 (same type asked 4 times) See all 4 of this type

    156
    If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which CC and SS do not come together, is (6!) kk, then kk is equal to

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  2. Question 2

    Probability. Asked once: 25 Jun 2022 (same type asked 4 times) See all 4 of this type

    166
    A biased die is marked with numbers 2,4,8,162,4,8,16, 32,32 on its faces and the probability of getting a face with mark nn is 1n\frac{1}{n}. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48 , is

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  3. Question 3

    Differentiation. Asked once: 29 Jan 2023 (same type asked 4 times) See all 4 of this type

    82
    Let f:R→Rf:R \rightarrow R be a differentiable function that satisfies the relation f(x+y)=f(x)+f(y)−f(x + y) = f(x) + f(y) - 1,∀x,y∈R1,\forall x,y \in R If f′(0)=2f^{'}(0) = 2, then ∣f(−2)∣|f( - 2)| is equal to

  4. Question 4

    Three Dimensional Geometry. Asked once: 1 Feb 2024 (same type asked 4 times) See all 4 of this type

    89
    Let the line of the shortest distance between the lines L1:r→=(i^+2j^+3k^)+λ(i^−j^+k^)L_{1}:\overrightarrow{r}= (\widehat{i}+ 2\widehat{j}+ 3\widehat{k}) + \lambda(\widehat{i}-\widehat{j}+\widehat{k}) and
    L2:r→=(4i^+5j^+6k^)+μ(i^+j^−k^)L_{2}:\overrightarrow{r}= (4\widehat{i}+ 5\widehat{j}+ 6\widehat{k}) + \mu(\widehat{i}+\widehat{j}-\widehat{k})
    intersect L1L_{1} and L2L_{2} at PP and QQ respectively. If (α,β,γ)(\alpha,\beta,\gamma) is the midpoint of the line segment PQPQ, then 2(α+β+γ)2(\alpha + \beta + \gamma) is equal to

  5. Question 5

    Straight Lines. Asked once: 8 Apr 2024 (same type asked 4 times) See all 4 of this type

    177
    Let a ray of light passing through the point (3,10)(3,10) reflects on the line 2x+y=62x+y= 6 and the reflected ray passes through the point (7,2)(7,2). If the equation of the incident ray is ax+by+1=0ax + by + 1 = 0, then a2+b2+3aba^{2}+b^{2}+ 3ab is equal to