Practice Questions PDF

# Practice Questions 1. Using truth table, Prove the following logical equivalence P→(q^r)=(pq)^(pr) 2. Find inverse of a matrix by adjoint method $\begin{bmatrix} 2 & -3 & 3 \\ 3 & -2 & 2 \\ 1 & 3 & -2 \\ \end{bmatrix}$ 3. The cost of 4 pencils, 3 pens and 2 books is Rs. 150. The cost of 1...

# Practice Questions 1. Using truth table, Prove the following logical equivalence P→(q^r)=(pq)^(pr) 2. Find inverse of a matrix by adjoint method $\begin{bmatrix} 2 & -3 & 3 \\ 3 & -2 & 2 \\ 1 & 3 & -2 \\ \end{bmatrix}$ 3. The cost of 4 pencils, 3 pens and 2 books is Rs. 150. The cost of 1 pencil, 2 pens and 3 books is Rs. 125. The cost of 6 pencils, 2 pens and 3 books is Rs. 175. Find the cost of each item by using matrices. 4. In AABC, if a = 13, b = 14 and c = 15 then find the values of i) cos A ii) sin (A/2) iii) cos (A/2) iv) A(ΔABC) v) sin A 5. Find the volume of tetrahedron whose vertices are A(-1,2,3), B(3,-2,1), C(2,1,3) and D(-1,-2,4) 6. Minimize, z = 7x + y, Subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0 7. Maximize,z = 11x + 8y, Subject to x ≤ 4, y ≤ 6, x + y ≤ 6,x ≥ 0, y ≥ 0 8. If ū=î – 2ĵ + k, v = 3î + k and w=î - k are given vectors then find (ū + w). [(ū x v) × (v x w)] 9. Find the equation of tangents and normal to the curve y = x² + 2ex + 2 at the point (0, 4) 10. Find the area of the circle x² + y² = 9, using integration. 11. A random variable X has the probability distribution: | X=x | P(X=x) | |---|---| | 0 | k | | 1 | 3k | | 2 | 5k | | 3 | 7k | | 4 | 9k | | 5 | 11k | | 6 | 13k | Find i) k ii) P(X < 3) iii P(X≥ 2) iv) P(0 < X < 4) v) P(2 ≤ X ≤ 5) 12]Given, X~B(n,p), i) If n=10 and p=0.4, find E(X) and Var(X) ii) If n=25 and E(X)= 10, find p and SD(X) 13] Evaluate ∫-3^3 (x^3)/(9-x^2)dx 14] Find the approximate value of (3.97)4 15] Find the maximum and minimum value of f(x) = 2x3 - 21x2 + 36x - 20 16] A die is thrown 6 times. If 'getting an odd number', is a success, find the probability of i) 5 Successes ii) At most 5 successes