PYQ Vault
EbooksTutor

Derivative of a determinant function at a point

This type of question, asked 4 times: 27 Jun 2022, 30 Jan 2024, 31 Jan 2024, 3 Apr 2025. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    27 Jun 2022

    152
    Let f(x)=∣a−10axa−1ax2axa∣,a∈Rf(x) =\left| \begin{matrix} a & - 1 & 0 \\ ax & a & - 1 \\ ax^{2} & ax & a \end{matrix} \right|,a\in R. Then the sum of the squares of all the values of a for which 2f′(10)−f′(5)+100=02f^{'}(10) -f^{'}(5) + 100 = 0 is:

    Tap an option to check your answer.

  2. Question 2

    30 Jan 2024

    77
    If f(x)=∣2cos⁡4x2sin⁡4x3+sin⁡22x3+2cos⁡4x2sin⁡4xsin⁡22x2cos⁡4x3+2sin⁡4xsin⁡22x∣f(x) =\left| \begin{matrix} 2\cos^{4}x & 2\sin^{4}x & 3 +\sin^{2}2x \\ 3 + 2\cos^{4}x & 2\sin^{4}x & \sin^{2}2x \\ 2\cos^{4}x & 3 + 2\sin^{4}x & \sin^{2}2x \end{matrix} \right| then 15f′(0)\frac{1}{5}f^{'}(0) is equal to

    Tap an option to check your answer.

  3. Question 3

    31 Jan 2024

    78
    If f(x)=∣x32x2+11+3x3x2+22xx3+6x3−x4x2−2∣f(x) =\left| \begin{matrix} x^{3} & 2x^{2}+ 1 & 1 + 3x \\ 3x^{2}+ 2 & 2x & x^{3}+ 6 \\ x^{3}- x & 4 & x^{2}- 2 \end{matrix} \right| for all x∈Rx \in R, then 2f(0)+f′(0)2f(0) +f^{'}(0) is equal to

    Tap an option to check your answer.

  4. Question 4

    3 Apr 2025

    61
    If y(x)=∣sin⁡xcos⁡xsin⁡x+cos⁡x+1272827111∣,x∈Ry(x) =\left| \begin{matrix} \sin x & \cos x & \sin x+ \cos x+ 1 \\ 27 & 28 & 27 \\ 1 & 1 & 1 \end{matrix} \right|,x\in\mathbb{R}, then d2ydx2+y\frac{d^{2}y}{dx^{2}}+ y is equal to.

    Tap an option to check your answer.