PYQ Vault
EbooksTutor

Day 625: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 29 Jan 2024

    81
    Equation of two diameters of a circle are 2x−3y=52x- 3y= 5 and 3x−4y=73x- 4y= 7. The line joining the points (−227,−4)\left( -\frac{22}{7}, - 4 \right) and (−17,3)\left( -\frac{1}{7},3 \right) intersects the circle at only one point P(α,β)P(\alpha,\beta). Then 17β−α17\beta-\alpha is equal to

  2. Question 2

    Definite Integration. Asked once: 27 Jul 2022

    67
    Let f:R→Rf:R \rightarrow R be a function defined as f(x)=asin(π[x]2)+[2−x],a∈Rf(x) = asin\left( \frac{\pi\lbrack x\rbrack}{2} \right)+ \lbrack 2 - x\rbrack,a \in R, where [t]\lbrack t\rbrack is the greatest integer less than or equal to tt. If lim⁡x→−1f(x)\lim_{x \rightarrow - 1} f(x) exists, then the value of ∫04f(x)dx\int_{0}^{4} f(x)dx is equal to:

    Tap an option to check your answer.

  3. Question 3

    Sequences and Series. Asked once: 26 Jun 2022

    153
    If A=∑n=1∞1(3+(−1)n)nA =\sum_{n = 1}^{\infty} \frac{1}{\left( 3 + ( - 1)^{n} \right)^{n}} and B=∑n=1∞(−1)n(3+(−1)n)nB =\sum_{n = 1}^{\infty} \frac{( - 1)^{n}}{\left( 3 + ( - 1)^{n} \right)^{n}}, then AB\frac{A}{B} is equal to :

    Tap an option to check your answer.

  4. Question 4

    Conic Sections. Asked once: 15 Apr 2023

    84
    Let an ellipse with centre (1,0)(1,0) and latus rectum of length 12\frac{1}{2} have its major axis along xx-axis. If its minor axis subtends an angle 60∘60^{\circ} at the foci, then the square of the sum of the lengths of its minor and major axes is equal to

  5. Question 5

    Definite Integration. Asked once: 27 Jul 2022

    177
    Let f(x)=min{[x−1],[x−2],…,[x−10]}f\left( x \right)= min\left\{ \left\lbrack x - 1 \right\rbrack,\left\lbrack x - 2 \right\rbrack,\ldots,\left\lbrack x - 10 \right\rbrack \right\}where [t]\lbrack t\rbrack denotes the greatest integer ≤t\leq t. Then ∫010f(x)dx+∫010(f(x))2dx+∫010∣f(x)∣dx\int_{0}^{10} f(x)dx +\int_{0}^{10} (f(x))^{2}dx +\int_{0}^{10} |f(x)|dx is equal to