An infographic on Applied Mathematics for CUET featuring: Key Topics: Probability, Calculus, Linear Algebra with formulas (e.g., ∫f(x)dx) Problem-Solving: Step-by-step solutions for typical CUET questions Real-World Applications: Finance (compound interest), Engineering (optimization), Data Science (statistics)

applied maths cuet 2024

Grade XII Applied Mathematics Worksheet

1. The determinant of a 3×3 matrix (A) is 5. What is the determinant of (3A)?

  1. 15
  2. 45
  3. 135
  4. None of the above

2. Find the inverse of the matrix ( begin{bmatrix} 2 & 3 \ 1 & 4 end{bmatrix} ).

  1. ( begin{bmatrix} 4 & -3 \ -1 & 2 end{bmatrix} )
  2. ( begin{bmatrix} 4 & -1 \ -3 & 2 end{bmatrix} )
  3. ( begin{bmatrix} 2 & -1 \ 1 & 4 end{bmatrix} )
  4. Non-invertible

3. What is the principal value of ( arcsin(-1) )?

  1. (-pi)
  2. (-frac{pi}{2})
  3. 0
  4. (frac{pi}{2})

4. Solve the differential equation ( frac{dy}{dx} + 2y = e^{-x} ).

  1. (y = Ce^{-2x} + frac{1}{2}e^{-x})
  2. (y = Ce^{-2x} – e^{-x})
  3. (y = Ce^{2x} + e^{-x})
  4. (y = Ce^{2x} – frac{1}{2}e^{-x})

5. Evaluate the integral ( int frac{dx}{x^2 + 1} ).

  1. (arctan(x) + C)
  2. (arcsin(x) + C)
  3. (ln|x| + C)
  4. (frac{1}{x} + C)

6. Which is the equation of a parabola with focus at (2,3) and directrix y=1?

  1. ((x-2)^2 = 4(y-2))
  2. ((y-3)^2 = 8(x-2))
  3. ((y-2)^2 = 4(x-2))
  4. ((x-2)^2 = 8(y-3))

7. Calculate the area enclosed by the curve (y=x^3) and the x-axis from x=0 to x=2.

  1. 4 square units
  2. 6 square units
  3. 8 square units
  4. None of the above

8. What is the volume of the solid obtained by rotating the area between (y=x^2) and (y=x) around the x-axis from x=0 to x=1?

  1. (frac{pi}{10}) cubic units
  2. (frac{pi}{30}) cubic units
  3. (pi) cubic units
  4. (frac{pi}{15}) cubic units

9. A linear programming problem has an objective function (F = 2x + 3y) to maximize, with constraints (x geq 0), (y geq 0), (x + y leq 10), and (2x + 3y leq 18). The maximum value of (F) is:

  1. 36
  2. 30
  3. 48
  4. 54

10. The solution set for the inequality (3x – 7 leq 2x + 8) is:

  1. (x leq 15)
  2. (x geq 15)
  3. (x leq -15)
  4. (x geq -15)

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top