VITEEE Sample Paper Mathematics

VITEEE Sample Questions Note: Please select the most appropriate choice from A, B, C and D. No negative marking MATHEMATICS 1. For the system of equations 𝑥 + 𝑘𝑦 + 𝑧 = 0, 𝑘𝑥 + 3𝑦 − 𝑘𝑧 = 0, 𝑥 − 𝑦 − 3𝑧 = 0 to have only the trivial solution, k cannot be equal to A) 2 and 3 B) −2 and 3 C) 2 and −3 D) −2 and −3 2. How many positive numbers 𝒙 satisfy the equation cos (97 𝒙) = 𝒙? A) 1 B) 15 C) 31 D) 49 3. The locus of the mid-point of the focal chord of the parabola 𝑦 2 = 4𝑥 is a parabola, whose vertex is A) (0, 0) B) (1, 0) C) (0, 1) D) (1, 1) 4. If two forces of magnitude 7 and 50 units act in the directions 3𝑖̂ + 2𝑗̂ – 6𝑘̂ and 9𝑖̂ – 12𝑗̂ + 20𝑘̂ respectively on a particle moving it from the point A (1, 0, -3) to the point B (3, -2, -5), then the work done by the forces is A) 14 units B) 27 units C) 18 units D) 24 units 5. One end-point of a diameter of the sphere 𝑥 2 + 𝑦 2 + 𝑧 2 − 𝑥 − 2𝑧 = 1 is (1, 1, 0). Then the other end- point of the diameter will be A) (0, 1, 0) B) (1, 1, 2) C) (1,√2 , 1) D) (0, −1, 2) 6. is equal to A) e–1 B) 1 C) e D) e–1/2 7. The bounded area cut-off by the line 𝑦 − 𝑥 + 4 = 0 from the parabola 𝑦 2 = 2𝑥 is equal to 8 14 40 A) B) C) D) 18 3 3 3 8. The general solution of the differential equation is A) B) C) D) 9. A pair of coins is tossed a fixed number of times. If the probability of getting both heads exactly 3 times is same as the probability of getting both heads exactly 4 times, then the number of trials is A) 7 B) 15 C) 21 D) 14 10. Consider the following statements p : suman is brilliant q : suman is rich r : suman is honest The negation of the statement "suman is brilliant and dishonest if and only if suman is rich" is equivalent to A) B) C) D)