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Day 140: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 24 Jan 2023 (same type asked 7 times) See all 7 of this type

    161
    If ( 30C1)2+2( 30C2)2+3( 30C3)2+….+30( 30C30)2=α60!(30!)2\left( \ ^{30}C_{1} \right)^{2}+ 2\left( \ ^{30}C_{2} \right)^{2}+ 3\left( \ ^{30}C_{3} \right)^{2}+ \ldots. + 30\left( \ ^{30}C_{30} \right)^{2}=\frac{\alpha 60!}{(30!)^{2}} then α\alpha is equal to :

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  2. Question 2

    Application of Derivatives. Asked once: 6 Apr 2023 (same type asked 7 times) See all 7 of this type

    176
    The number of points, where the curve y=x5−20x3+50x+2y =x^{5}- 20x^{3}+ 50x + 2 crosses the xx-axis, is

  3. Question 3

    Three Dimensional Geometry. Asked once: 13 Apr 2023 (same type asked 7 times) See all 7 of this type

    65
    The distance of the point (−1,2,3)( - 1,2,3) from the plane r→⋅(i^−2j^+3k^)=10\overrightarrow{r}\cdot (\widehat{i}- 2\widehat{j}+ 3\widehat{k}) = 10 parallel to the line of the shortest distance between the lines r→=(i^−j^)+λ(2i^+k^)\overrightarrow{r}= (\widehat{i}-\widehat{j}) + \lambda(2\widehat{i}+\widehat{k}) and r→=(2i^−j^)+μ(i^−j^+k^)\overrightarrow{r}= (2\widehat{i}-\widehat{j}) + \mu(\widehat{i}-\widehat{j}+\widehat{k}) is :

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  4. Question 4

    Probability. Asked once: 27 Jun 2022 (same type asked 7 times) See all 7 of this type

    77
    Let XX be a random variable having binomial distribution B(7,p)B(7,p). If P(X=3)=5P(X=4)P(X = 3) = 5P(X = 4), then the sum of the mean and the variance of XX is:

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  5. Question 5

    Binomial Theorem. Asked once: 23 Jan 2026 S1 (same type asked 6 times) See all 6 of this type

    62
    The value of  100C5051+ 100C5152+….+ 100C100101\frac{\ ^{100}C_{50}}{51}+\frac{\ ^{100}C_{51}}{52}+ \ldots. +\frac{\ ^{100}C_{100}}{101} is :

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