PYQ Vault
EbooksTutor

Day 123: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Trigonometric Identities. Asked once: NDA 2 2022 (same type asked 3 times)

    51
    What is cos⁡36°−cos⁡72°\cos36° - \cos72° equal to?

    Tap an option to check your answer.

  2. Question 2

    Vectors. Asked once: NDA 2 2022 (same type asked 3 times)

    67
    Let a⃗\vec{a} and b⃗\vec{b} are two unit vectors such that a⃗+2b⃗\vec{a}+2\vec{b} and 5a⃗−4b⃗5\vec{a}-4\vec{b} are perpendicular. What is the angle between a⃗\vec{a} and b⃗\vec{b}?

    Tap an option to check your answer.

  3. Question 3

    Applications of Integration. Asked once: NDA 2 2022 (same type asked 3 times)

    97
    What is the area of the region enclosed in the first quadrant by x2+y2=π2x^2+y^2=\pi^2, y−sin⁡xy-\sin x and x=0x=0?

    Tap an option to check your answer.

  4. Question 4

    Binomial Theorem. Asked once: NDA 1 2023 (same type asked 3 times)

    24
    If the sixth term in the binomial expansion of (x−83+x2log⁡10x)8\left(x^{-\frac{8}{3}}+x^{2}\log_{10}x\right)^{8} is 5600, then what is the value of xx?

    Tap an option to check your answer.

  5. Question 5 (case study, 2 parts)

    Definite Integration. Asked once: NDA 2 2023 (same type asked 3 times)

    Let I=∫−2π2πsin⁡4x+cos⁡4x1+3x dxI=\int_{-2\pi}^{2\pi}\frac{\sin^4x+\cos^4x}{1+3^x}\,dx.
    61
    What is ∫0π(sin⁡4x+cos⁡4x) dx\int_0^\pi(\sin^4x+\cos^4x)\,dx equal to?

    Tap an option to check your answer.

    62
    What is II equal to?

    Tap an option to check your answer.