PYQ Vault
EbooksTutor

Day 133: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 30 Jan 2024 (same type asked 9 times) See all 9 of this type

    151
    Consider the system of linear equations x+y+z=5,x+2y+λ2z=9x + y + z = 5,x + 2y +\lambda^{2}z = 9, x+3y+λz=μx + 3y + \lambda z = \mu, where λ,μ∈R\lambda,\mu \in R. Then, which of the following statement is NOT correct?

    Tap an option to check your answer.

  2. Question 2

    Statistics. Asked once: 11 Apr 2023 (same type asked 8 times) See all 8 of this type

    64
    Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of AA and adding 2 to each element of B. Then the sum of the mean and variance of the elements of CC is

    Tap an option to check your answer.

  3. Question 3

    Determinants. Asked once: 5 Apr 2026 S1 (same type asked 8 times) See all 8 of this type

    54
    Consider the system of linear equations in x,y,zx,y,z : x+2y+tz=0x + 2y + tz = 0, 6x+y+5tz=06x + y + 5tz = 0, 3x+t2y+f(t)z=03x +t^{2}y + f(t)z = 0, Where f:R→Rf:R \rightarrow R is a differentiable function. If this system has infinitely many solutions for all t∈Rt\in R, then ff

    Tap an option to check your answer.

  4. Question 4

    Differential Equations. Asked once: 5 Apr 2026 S2 (same type asked 8 times) See all 8 of this type

    69
    Let f:[1,∞)→Rf:\lbrack 1,\infty) \rightarrow R be a differentiable function defined as f(x)=∫1xf(t)dt+(1−x)(log⁡ex−1)+ef(x) =\int_{1}^{x} f(t)dt+ (1 -x)\left( \log_{e}x- 1 \right)+e. Then the value of f(f(1))f(f(1)) is :

    Tap an option to check your answer.

  5. Question 5

    Sequences and Series. Asked once: 4 Apr 2025 (same type asked 8 times) See all 8 of this type

    137
    If the sum of the first 20 terms of the series
    4.14+3.12+14+4.24+3.22+24+\frac{4.1}{4 +3.1^{2}+1^{4}}+\frac{4.2}{4 +3.2^{2}+2^{4}}+
    4.34+3.32+34+4.44+3.42+44+….\frac{4.3}{4 +3.3^{2}+3^{4}}+\frac{4.4}{4 +3.4^{2}+4^{4}}+ \ldots.
    is mn\frac{m}{n}, where m and n are coprime, then m+nm + n is equal to :-

    Tap an option to check your answer.