PYQ Vault
EbooksTutor

Day 195: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2021 Paper 4 (same type asked 3 times) See all 3 of this type

    73
    The minimum value of f(x)=aax+a1−axf(x) =a^{a^{x}}+a^{1 -a^{x}}, where a,x∈Ra,x\in R and a>0a> 0, is equal to:

    Tap an option to check your answer.

  2. Question 2

    Application of Derivatives. Asked once: 2021 Paper 4 (same type asked 3 times) See all 3 of this type

    77
    The shortest distance between the line x−y=1x-y= 1 and the curve x2=2yx^{2}= 2y is:

    Tap an option to check your answer.

  3. Question 3

    Inverse Trigonometric Functions. Asked once: 2021 Paper 25 (same type asked 3 times) See all 3 of this type

    70
    If sin⁡−1xa=cos⁡−1xb=tan⁡−1yc;0<x<1\frac{\sin^{- 1}x}{a}=\frac{\cos^{- 1}x}{b}=\frac{\tan^{- 1}y}{c};0 <x< 1, then the value of cos⁡(πca+b)\cos\left( \frac{\pi c}{a+b} \right) is:

    Tap an option to check your answer.

  4. Question 4

    Three Dimensional Geometry. Asked once: 26 Jun 2022 (same type asked 3 times) See all 3 of this type

    165
    If the lines r→=(i^−j^+k^)+λ(3j^−k^)\overrightarrow{r}= (\widehat{i}-\widehat{j}+\widehat{k}) + \lambda(3\widehat{j}-\widehat{k}) and r→=(αi^−j^)+μ(2i^−3k^)\overrightarrow{r}= (\alpha\widehat{i}-\widehat{j}) + \mu(2\widehat{i}- 3\widehat{k}) are co-planar, then distance of the plane containing these two lines from the point (α,0,0)(\alpha,0,0) is :

    Tap an option to check your answer.

  5. Question 5

    Matrices. Asked once: 28 Jun 2022 (same type asked 3 times) See all 3 of this type

    177
    Let A=(1+i1−i0)A =\begin{pmatrix} 1 + i & 1 \\ - i & 0 \end{pmatrix} where i=−1i =\sqrt{- 1}. Then, the number of elements in the set {n∈{1,2,…,100}:An=A}\left\{ \mathbf{n \in \{ 1,2,\ldots,100\}:}A^{n}= A \right\} is