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Day 388: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 31 Jan 2024 (same type asked 16 times) See all 16 of this type

    77
    Let g(x)g(x) be a linear function and f(x)={g(x),x≤0(1+x2+x)1x,x>0f(x) =\left\{ \begin{matrix} g(x) & ,x\leq 0 \\ \left( \frac{1 +x}{2 +x} \right)^{\frac{1}{x}} & ,x> 0 \end{matrix} \right., is continuous at x=0x= 0. If f′(1)=f(−1)f^{'}(1) =f( - 1), then the value of g(3)g(3) is

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  2. Question 2

    Three Dimensional Geometry. Asked once: 28 Jun 2022 (same type asked 15 times) See all 15 of this type

    77
    Let the plane P:r→⋅a→=dP:\overrightarrow{r}\cdot\overrightarrow{a}= d contain the line of intersection of the planes r→⋅(i^+3j^−k^)=6\overrightarrow{r}\cdot (\widehat{i}+ 3\widehat{j}-\widehat{k}) = 6 and r→⋅(−6i^+5j^−k^)=7\overrightarrow{r}\cdot ( - 6\widehat{i}+ 5\widehat{j}-\widehat{k}) = 7. If the plane PP passes through the point (2,3,12)\left( 2,3,\frac{1}{2} \right), then the value of ∣13a→∣2d2\frac{|13\overrightarrow{a}|^{2}}{d^{2}} is equal to

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  3. Question 3

    Determinants. Asked once: 27 Jun 2022 (same type asked 14 times) See all 14 of this type

    62
    Let the system of linear equations x+2y+z=2x+ 2y+z= 2, αx+3y−z=α,−αx+y+2z=−α\alpha x+ 3y-z=\alpha, -\alpha x+y+ 2z= -\alpha be inconsistent. Then α\alpha is equal to:

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  4. Question 4

    Statistics. Asked once: 1 Feb 2023 (same type asked 13 times) See all 13 of this type

    70
    The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3,5 then the sum of cubes of the remaining two observations is

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  5. Question 5

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

    167
    Let a→=i^−j^+2k^\overrightarrow{a}=\widehat{i}-\widehat{j}+ 2\widehat{k} and b→\overrightarrow{b} be a vector such that a→×b→=2i^−k^\overrightarrow{a}\times\overrightarrow{b}= 2\widehat{i}-\widehat{k} and a→⋅b→=3\overrightarrow{a}\cdot\overrightarrow{b}= 3. Then the projection of b→\overrightarrow{b} on the vector a→−b→\overrightarrow{a}-\overrightarrow{b} is:-

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