1. Equation x2 + 5x – 7 = 0 has roots a and b. Equation 2x2 + px + q = 0 has roots a + 1 and b + 1. Find p + q. 1.6 2.0 3.-16 4.2 Show Answer
Answer: Option A Explanation: Given, x2 + 5x – 7 = 0 has roots a and b. We know that, Sum of roots in a quadratic equation = a+b = (−5)1 = -5. Product of the roots = ab = (−7)1 = -7. Now, The second equation 2x2 + px + q = 0 has roots a + 1 and b + 1. Sum of the roots = a+1+b+1 = a+b+2 = (−p)2 = -5 +2 = -3 = (−p)2 => -p = -6 => p =6. Product of the roots = (a+1)(b+1) = ab+a+b+1 = q2. We know the values of ab and a+b. Substituting this, we get, -7+(-5)+1 = q2 => -11 = q2 => q =-22. Hence, p = 6 and q = -22. => p+q = 6 +(-22) = -16.
Answer: Option B Explanation: There are 19% students who have specialization in IB and 22% students have specialization in Marketing. So, the required percentage =(19/22) x 100 = 86.36%
Answer: Option D Explanation: Answer 1: (c) There are 2 such symbols * and $ Correct option is (c) Answer 2: (b) HA% is the required series. Correct option is (b) Answer 3: (a) I@L should be following the trend. Correct option is (a) Answer 4: (a) The required element is Q. Correct option is (a) Answer 5: (d) ? =FK. The elements are neighbors and there are 2 spaces between two groups of neighbors. Correct option is (d)
Answer: Option D Explanation: Option 4 is the correct choice as it forms a valid syllogism. The premises state that the increase in carbon monoxide is hazardous to health and traffic congestion increases carbon monoxide in the environment. Hence, it can be interpreted that traffic congestion is hazardous to health.
Answer: Option A Explanation: The Maharashtra government has decided to form ‘Good Morning’ squads to curb open defecation in all villages and districts across the State. These squads will comprise representatives of local bodies, self-help groups, NGOs, students and social workers working in the area of sanitation and cleanliness. The squads will also check whether residents have access to toilets. They also have the right to take up issues, such as the pending construction of toilets, with the local civic bodies and help speed up the work.