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Day 377: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 24 Jan 2023 (same type asked 13 times) See all 13 of this type

    61
    Let u→=ı^−ȷ^−2k^,v→=2ı^+ȷ^−k^,v→⋅w→=2\overrightarrow{u}=\widehat{\imath}-\widehat{\jmath}- 2\widehat{k},\overrightarrow{v}= 2\widehat{\imath}+\widehat{\jmath}-\widehat{k},\overrightarrow{v}\cdot\overrightarrow{w}= 2 and v→×w→=u→+λv→\overrightarrow{v}\times\overrightarrow{w}=\overrightarrow{u}+ \lambda\overrightarrow{v}. Then u→⋅w→\overrightarrow{u}\cdot\overrightarrow{w} is equal to

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  2. Question 2

    Differential Equations. Asked once: 4 Apr 2024 (same type asked 13 times) See all 13 of this type

    64
    If the solution y=y(x)y = y(x) of the differential equation (x4+2x3+3x2+2x+2)dy−(2x2+2x+3)dx=0\left( x^{4}+ 2x^{3}+ 3x^{2}+ 2x + 2 \right)dy -\left( 2x^{2}+ 2x + 3 \right)dx = 0 satisfies y(−1)=−π4y( - 1) = -\frac{\pi}{4}, then y(0)y(0) is equal to :

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  3. Question 3

    Statistics. Asked once: 13 Apr 2023 (same type asked 13 times) See all 13 of this type

    171
    The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is

  4. Question 4

    Relations and Functions. Asked once: 29 Jan 2023 (same type asked 13 times) See all 13 of this type

    154
    Let RR be a relation defined on NN as aRbaRb if 2a+3 b2a + 3\text{ }b is a multiple of 5,a,b∈N5,a,b \in N. Then RR is

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  5. Question 5

    Probability. Asked once: 4 Apr 2024 (same type asked 12 times) See all 12 of this type

    62
    Three urns A, B and CC contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn AA is:

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