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Day 227: JEE Mains Maths

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

  1. Question 1

    Statistics. Asked once: 3 Apr 2025 (same type asked 13 times) See all 13 of this type

    129
    Let the Mean and Variance of five observations x1=1,x2=3,x3=a,x4=7x_{1}= 1,x_{2}= 3,x_{3}= a,x_{4}= 7 and x5=b,a>bx_{5}=b,a>b, be 5 and 10 respectively. Then the Variance of the observations n+xn, n=1,2,…,5n +x_{n},\ n = 1,2,\ldots,5 is

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  2. Question 2

    Vector Algebra. Asked once: 2 Apr 2025 (same type asked 13 times) See all 13 of this type

    143
    Let a→=2i^−3j^+k^,b→=3i^+2j^+5k^\overrightarrow{a}= 2\widehat{i}- 3\widehat{j}+\widehat{k},\overrightarrow{b}= 3\widehat{i}+ 2\widehat{j}+ 5\widehat{k} and a vector c→\overrightarrow{c} be such that (a→−c→)×b→=−18i^−3j^+12k^(\overrightarrow{a}-\overrightarrow{c}) \times\overrightarrow{b}= - 18\widehat{i}- 3\widehat{j}+ 12\widehat{k} and a→⋅c→=3\overrightarrow{a}\cdot\overrightarrow{c}= 3. If b→×c→=d→\overrightarrow{b}\times\overrightarrow{c}=\overrightarrow{d}, then ∣a→⋅d→∣|\overrightarrow{a}\cdot\overrightarrow{d}| is equal to :

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  3. Question 3

    Differential Equations. Asked once: 22 Jan 2026 S2 (same type asked 13 times) See all 13 of this type

    56
    If y=y(x)y = y(x) satisfies the differential equation 16x 9+x (4+9+x)cos⁡ydy=(1+216\sqrt{x}\,\sqrt{9 + \sqrt{x}}\,(4 +\sqrt{9 +\sqrt{x}})\cos ydy = (1 + 2 siny)dx, x>0x > 0 and y(256)=π2,y(49)=αy(256) =\frac{\pi}{2},y(49) = \alpha, then 2 sin⁡α\sin\alpha is equal to :

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  4. Question 4

    Statistics. Asked once: 24 Jan 2025 (same type asked 13 times) See all 13 of this type

    64
    For a statistical data x1,x2,…,x10x_{1},x_{2},\ldots,x_{10} of 10 values, a student obtained the mean as 5.5 and ∑i=110xi2=371\sum_{i = 1}^{10} x_{i}^{2}= 371. He later found that he had noted two values in the data incorrectly as 4 and 5 , instead of the correct values 6 and 8 , respectively. The variance of the corrected data is

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  5. Question 5

    Relations and Functions. Asked once: 28 Jan 2025 (same type asked 13 times) See all 13 of this type

    57
    The relation R={(x,y):x,y∈z\mathbf{R = \{(x,y):x,y \in z} and x+yx + y is even }\} is :

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