PYQ Vault
EbooksTutor

A number lies between the roots, or both roots lie in an interval: range of the parameter

This type of question, asked 3 times: 1 Feb 2023, 21 Jan 2026 S2, 6 Apr 2026 S2. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    1 Feb 2023

    162
    The number of integral values of kk, for which one root of the equation 2x2−8x+k=02x^{2}- 8x + k = 0 lies in the interval (1,2)(1,2) and its other root lies in the interval (2,3)(2,3), is :

    Tap an option to check your answer.

  2. Question 2

    21 Jan 2026 S2

    59
    Let α\alpha and β\beta be the roots of equation x2+2ax+(3a+10)=0x^{2}+ 2ax + (3a + 10) = 0 such that α<1<β\alpha < 1 < \beta. Then the set of all possible values of aa is :

    Tap an option to check your answer.

  3. Question 3

    6 Apr 2026 S2

    66
    Let lim⁡x→2(tan⁡(x−2))(rx2+(p−2)x−2p)(x−2)2=5\lim_{x \rightarrow 2} \frac{(\tan(x - 2))\left( rx^{2}+ (p - 2)x - 2p \right)}{(x - 2)^{2}}= 5 for some r,p∈Rr,p \in R. If the set of all possible values of q , such that the roots of the equation rx2−px+q=0rx^{2}- px + q = 0 lie in (0,2)(0,2), be the interval (α,β](\alpha,\beta\rbrack, then 4(α+β)4(\alpha+\beta) equals.

    Tap an option to check your answer.