Q.10549·Miscellaneous·2015·EasyConsider the following functions: 1.f(x) = x³, x ∈ R 2.f(x) = sin x, 0 < x < 2π 3.f(x) = e^x, x ∈ R Which of the above functions have inverse defined on their ranges?View question
Q.10550·Miscellaneous·2015·Easyf(x) = -1 if x ≤ 0 f(x) = ax + b if 0 < x < 1 f(x) = 1 if x ≥ 1 where a, b are constants. The function is continuous everywhere. What is the value of b?View question
Q.10551·Miscellaneous·2015·EasyWhich one among the following happens when a swing rises to a certain height from its rest position?View question
Q.10552·Miscellaneous·2015·EasyLook at the underlined part of each sentence. Below each sentence are given three possible substitutions for the underlined part. If one of them, (a), (b) or (c), is better than the underlined part, indicate your response on the Answer Sheet against the corresponding letter (a), (b) or (c). If none of the substitutions improve the sentence, indicate (d) as your response on the Answer Sheet. Thus a ‘No improvement’ response will be signified by the letter (d). The old man felled some trees in the garden with hardly no effort at all.View question
Q.10553·Miscellaneous·2015·EasyLet X be the set of all persons living in a city. Persons x, y in X are said to be related as x < y if y is at least 5 years older than x. Which one of the following is correct?View question
Q.10554·Miscellaneous·2015·EasyWhich one of the following matrices is an elementary matrix?View question
Q.10555·Miscellaneous·2015·EasyConsider the following statements in respect of the given equation : (x² + 2)² + 8x² − 6x(x² + 2) 1.All the roots of the equation are complex. 2.The sum of all the roots of the equation is 6. Which of the above statements is/are correct?View question
Q.10556·Miscellaneous·2015·EasyIn solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains 8 and 2 for roots. Another student makes a mistake only in the coefficient of first-degree term and finds −9 and −1 for roots. The correct equation isView question
Q.10557·Miscellaneous·2015·EasyIn a class of 60 students, 45 students like music, 50 students like dancing, 5 students like neither. Then the number of students in the class who like both music and dancing isView question
Q.10558·Miscellaneous·2015·EasyWhat is the sum of the series 0.5 + 0.55 + 0.555 + … to n terms?View question
Q.10559·Miscellaneous·2015·EasyLet A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then the number of subsets of A containing exactly two elements isView question
Q.10560·Miscellaneous·2015·EasyConsider the following in respect of two non-singular matrices A and B of same order : 1.det(A + B) = detA + detB 2.(A + B)⁻¹ = A⁻¹ + B⁻¹ Which of the above is/are correct?View question
Q.10561·Miscellaneous·2015·EasyHow many words can be formed using all the letters of the word "NATION" so that all the three vowels should never come together?View question
Q.10563·Miscellaneous·2015·EasyIf A = {x : x is a multiple of 3} and B = {x : x is a multiple of 4} and C = {x : x is a multiple of 12}, then which one of the following is a null set?View question
Q.10564·Miscellaneous·2015·EasyLet A = {x, y, z} and B = {p, q, r, s}. What is the number of distinct relations from B to A?View question
Q.10565·Miscellaneous·2015·EasyThe angle of elevation of the top of a tower from a point 20 m away from its base is 45°. What is the height of the tower?View question
Q.10566·Miscellaneous·2015·EasyThe angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are 43° and 47° respectively. What is the height of the tower?View question