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Day 565: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 2021 Paper 19

    75
    A hall has a square floor of dimension 10 m×10 m10\text{ }m \times 10\text{ }m (see the figure) and vertical walls. If the angle GPH between the diagonals AGAG and BHBH is cos⁡−115\cos^{- 1}\frac{1}{5}, then the height of the hall (in meters) is:

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  2. Question 2

    Vector Algebra. Asked once: 27 Jul 2022

    180
    Let a→,b→,c→\overrightarrow{a},\overrightarrow{b},\overrightarrow{c} be three non-coplanar vectors such that a→×b→=4c→,b→×c→=9a→ and c→×a→=αb→,α>0\overrightarrow{a}\times\overrightarrow{b}= 4\overrightarrow{c},\overrightarrow{b}\times\overrightarrow{c}= 9\overrightarrow{a}\text{~and~}\overrightarrow{c}\times\overrightarrow{a}= \alpha\overrightarrow{b},\alpha > 0If ∣a→∣+∣b→∣+∣c→∣=36|\overrightarrow{a}| + |\overrightarrow{b}| + |\overrightarrow{c}| = 36, then α\alpha is equal to

  3. Question 3

    Application of Derivatives. Asked once: 29 Jul 2022

    177
    If the tangent to the curve y=x3−x2+xy =x^{3}-x^{2}+ x at the point (a,b)(a,b) is also tangent to the curve y=5x2+y = 5x^{2}+ 2x−252x - 25 at the point (2,−1)(2, - 1), then ∣2a+9b∣|2a + 9b| is equal to

  4. Question 4

    Application of Integrals. Asked once: 1 Feb 2023

    87
    Let AA be the area bounded by the curve y=x∣x−3∣y = x|x - 3|, the xx-axis and the ordinates x=−1x = - 1 and x=2x = 2. Then 12A12A is equal to

  5. Question 5

    Binomial Theorem. Asked once: 2021 Paper 21

    88
    3×722+2×1022−443 \times7^{22}+ 2 \times10^{22}- 44 when divided by 18 leaves the remainder