PYQ Vault
EbooksTutor

Day 178: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 24 Jan 2026 S1 (same type asked 3 times) See all 3 of this type

    63
    Let A(1,0),B(2,−1)A(1,0),B(2, - 1) and C(73,43)C\left( \frac{7}{3},\frac{4}{3} \right) be three points. If the equation of the bisector of the angle ABC is αx+βy=5\alpha x + \beta y = 5, then the value of α2+β2\alpha^{2}+\beta^{2} is

    Tap an option to check your answer.

  2. Question 2

    Permutations and Combinations. Asked once: 7 Apr 2025 (same type asked 3 times) See all 3 of this type

    140
    Let pp be the number of all triangles that can be formed by joining the vertices of a regular polygon PP of nn sides and qq be the number of all quadrilaterals that can be formed by joining the vertices of P. If p+q=126p+q= 126, then the eccentricity of the ellipse x216+y2n=1\frac{x^{2}}{16}+\frac{y^{2}}{n}= 1 is

    Tap an option to check your answer.

  3. Question 3

    Probability. Asked once: 25 Jul 2022 (same type asked 3 times) See all 3 of this type

    77
    If the numbers appeared on the two throws of a fair six faced die are α\alpha and β\beta, then the probability that x2+αx+β>0x^{2}+ \alpha x + \beta > 0, for all x∈Rx \in R, is:

    Tap an option to check your answer.

  4. Question 4

    Application of Integrals. Asked once: 27 Jun 2022 (same type asked 3 times) See all 3 of this type

    86
    Let A1={(x,y):∣x∣≤y2,∣x∣+2y≤8}A_{1}=\left\{ (x,y):|x| \leq y^{2},|x| + 2y\leq 8 \right\} and A2={(x,y):∣x∣+∣y∣≤k}A_{2}= \{(x,y):|x| + |y| \leq k\}. If 27(27\left( \right. Area  A1)=5\left. \ A_{1} \right)= 5 (Area A2A_{2} ), then kk is equal to:

  5. Question 5

    Sequences and Series. Asked once: 25 Jun 2022 (same type asked 3 times) See all 3 of this type

    68
    If 12⋅310+122⋅39+…1210⋅3=K210⋅310\frac{1}{2 \cdot3^{10}}+\frac{1}{2^{2}\cdot3^{9}}+ \ldots\frac{1}{2^{10}\cdot 3}=\frac{K}{2^{10}\cdot3^{10}}, then the remainder when KK is divided by 6 is

    Tap an option to check your answer.