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Day 409: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 14 Jun 2022 (same type asked 14 times) See all 14 of this type

    66
    The number of values of α\alpha for which the system of equations:
    x+y+z=αx + y + z =\alpha
    αx+2αy+3z=−1\alpha x+ 2\alpha y+ 3z= - 1
    x+3αy+5z=4x+ 3\alpha y+ 5z= 4
    is inconsistent, is

    Tap an option to check your answer.

  2. Question 2

    Statistics. Asked once: 2021 Paper 16 (same type asked 13 times) See all 13 of this type

    51
    For the data 6,10,7,13,a,12,b,126,10,7,13,a,12,b,12. If mean is 9 , variance is 374\frac{37}{4} find (a−b)2(a-b)^{2}.

  3. Question 3

    Vector Algebra. Asked once: 25 Jun 2022 (same type asked 13 times) See all 13 of this type

    176
    Let b→=i^+j^+λk^,λ∈R\overrightarrow{b}=\widehat{i}+\widehat{j}+ \lambda\widehat{k},\lambda \in R. If a→\overrightarrow{a} is a vector such that a→×b→=13i^−j^−4k^\overrightarrow{a}\times\overrightarrow{b}= 13\widehat{i}-\widehat{j}- 4\widehat{k} and  a→⋅b→+21=0,\ \overrightarrow{a}\cdot\overrightarrow{b}+ 21 = 0, then (b→−a→)⋅(k^−j^)+(b→+a→)⋅(i^−k^)(\overrightarrow{b}-\overrightarrow{a}) \cdot (\widehat{k}-\widehat{j}) + (\overrightarrow{b}+\overrightarrow{a}) \cdot (\widehat{i}-\widehat{k}) is equal to

  4. Question 4

    Differential Equations. Asked once: 2021 Paper 17 (same type asked 13 times) See all 13 of this type

    87
    Let y=y(x)y=y(x) be the solution of the differential equation dy=eαx+ydx;α∈Ndy =e^{\alpha x+y}dx;\alpha\in N. If y(log⁡e2)=log⁡e2y\left( \log_{e}2 \right)=\log_{e}2 and y(0)=log⁡e(12)y(0) =\log_{e}\left( \frac{1}{2} \right), then the value of α\alpha is equal to

  5. Question 5

    Statistics. Asked once: 28 Jun 2022 (same type asked 13 times) See all 13 of this type

    83
    The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5 . Then, the correct variance is equal to