PYQ Vault
EbooksTutor

Day 166: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 4 Apr 2025 (same type asked 4 times) See all 4 of this type

    146
    If α\alpha is a root of the equation x2+x+1=0x^{2} + x + 1 = 0 and ∑k=1n(αk+1αk)2=20\sum_{k = 1}^{n} \left( \alpha^{k} + \frac{1}{\alpha^{k}} \right)^{2} = 20, then nn is equal to .

  2. Question 2

    Conic Sections. Asked once: 27 Jan 2024 (same type asked 4 times) See all 4 of this type

    168
    Let e1e_{1} be the eccentricity of the hyperbola x216−y29=1\frac{x^{2}}{16}-\frac{y^{2}}{9}= 1 and e2e_{2} be the eccentricity of the ellipse x2a2+y2b2=1,a>b\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1,a > b, which passes through the foci of the hyperbola. If e1e2=1e_{1}e_{2}= 1, then the length of the chord of the ellipse parallel to the xx-axis and passing through (0,2)(0,2) is:

    Tap an option to check your answer.

  3. Question 3

    Conic Sections. Asked once: 4 Apr 2025 (same type asked 4 times) See all 4 of this type

    135
    Let the sum of the focal distances of the point P(4,3)P\left( 4,3 \right) on the hyperbola H:x2a2−y2 b2=H:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{{\text{ }b}^{2}}= 11 be 8538\sqrt{\frac{5}{3}}. If for H , the length of the latus rectum is ll and the product of the focal distances of the point P is m , then 9l2+6 m9l^{2}+ 6\text{ }m is equal to :-

    Tap an option to check your answer.

  4. Question 4

    Conic Sections. Asked once: 8 Apr 2024 (same type asked 4 times) See all 4 of this type

    63
    Let the circles C1:(x−α)2+(y−β)2=r12C_{1}:(x - \alpha)^{2}+ (y - \beta)^{2}=r_{1}^{2} and C2:(x−8)2+(y−152)2=r22C_{2}:(x - 8)^{2}+\left( y -\frac{15}{2} \right)^{2}=r_{2}^{2} touch each other externally at the point (6,6)(6,6). If the point (6,6)(6,6) divides the line segment joining the centres of the circles C1C_{1} and C2C_{2} internally in the ratio 2:12:1, then (α+β)+4(r12+r22)(\alpha + \beta) + 4\left( r_{1}^{2}+r_{2}^{2} \right) equals

    Tap an option to check your answer.

  5. Question 5

    Application of Integrals. Asked once: 30 Jan 2024 (same type asked 4 times) See all 4 of this type

    179
    The area of the region enclosed by the parabola (y−2)2=x−1(y- 2)^{2}=x- 1, the line x−2y+4=0x- 2y+ 4 = 0 and the positive coordinate axes is