Function and Sq. Cm
Presidency University Admission Test, 2013 ECONOMICS MAJOR Model Questions Group A : English(30 Marks) Write an essay on any one of the following topics:
a) Our sweetest songs are those that tell of saddest thought. b) A good film I have seen and enjoyed.
Group B : Mathematics (70 Marks) Answer all questions. You will get 2 marks for a correct answer and -0.5 for an incorrect answer. 1. The radius of a circle is 2.5 cm. The error in the calculated area due to an error of 0.01 cm in the radius is A. 0.154 sq. cm B. 0.157 sq. cm C. 0.161 sq. cm D. 0.169 sq. cm 2. A. ½ 3. Lim { x -> 0 B. -1/2 C. 1 D. none of these
log e (1 x ) x 1 + } is equal to x2 x
Let f(x) = x for 0 < x ≤ 2 = 1 for x = 0 Then at x = 0, f(x) has A. a local maximum B. no local maximum
C. a local minimum
D. no extremum
4. Find out the points of contact on the curve y = x2 + 3x + 4 of the two tangents which pass through the origin are A. (2,14), (-2,2) B. (2,14), (-2,-2) C. (2,14), (2,2) D. none of these 5. There are 10 lamps in Vivekananda sporting club. Each lamp can be switched on independently. The number of ways in which the club can be lightened to different amounts of illumination is A. 102 B. 1023 C. 210 D. 10! 6. units The area bounded by the curves y = x - 1 and y = - x + 1 is B. 4 sq. units C. 6 sq. units D. 2 sq. units A. 3 sq.
7. Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is A. 11 B. 12 C. 13 D. 14 8. If a, b, c are in G. P. and a, b, c are positive, then the following relation holds A. a +c > 2b B. a + c > b C. a + b > 2c D. none of these 9. The number of odd numbers between 60 and 360 is A. 120 B. 125 C. 150 D. none of these 10. A. 11. A. If x y = e x - y, then the value of
dy is dx
C.
1 log x log x
B.
(1 log x) 2 log x
log x (1 log x) 2
D.
1 log x 1 log x y 1 y
If y = x + x2 + x3 + ……………to ∞, then x equals
y y 1
B.
y 1 y
a) Our sweetest songs are those that tell of saddest thought. b) A good film I have seen and enjoyed.
Group B : Mathematics (70 Marks) Answer all questions. You will get 2 marks for a correct answer and -0.5 for an incorrect answer. 1. The radius of a circle is 2.5 cm. The error in the calculated area due to an error of 0.01 cm in the radius is A. 0.154 sq. cm B. 0.157 sq. cm C. 0.161 sq. cm D. 0.169 sq. cm 2. A. ½ 3. Lim { x -> 0 B. -1/2 C. 1 D. none of these
log e (1 x ) x 1 + } is equal to x2 x
Let f(x) = x for 0 < x ≤ 2 = 1 for x = 0 Then at x = 0, f(x) has A. a local maximum B. no local maximum
C. a local minimum
D. no extremum
4. Find out the points of contact on the curve y = x2 + 3x + 4 of the two tangents which pass through the origin are A. (2,14), (-2,2) B. (2,14), (-2,-2) C. (2,14), (2,2) D. none of these 5. There are 10 lamps in Vivekananda sporting club. Each lamp can be switched on independently. The number of ways in which the club can be lightened to different amounts of illumination is A. 102 B. 1023 C. 210 D. 10! 6. units The area bounded by the curves y = x - 1 and y = - x + 1 is B. 4 sq. units C. 6 sq. units D. 2 sq. units A. 3 sq.
7. Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is A. 11 B. 12 C. 13 D. 14 8. If a, b, c are in G. P. and a, b, c are positive, then the following relation holds A. a +c > 2b B. a + c > b C. a + b > 2c D. none of these 9. The number of odd numbers between 60 and 360 is A. 120 B. 125 C. 150 D. none of these 10. A. 11. A. If x y = e x - y, then the value of
dy is dx
C.
1 log x log x
B.
(1 log x) 2 log x
log x (1 log x) 2
D.
1 log x 1 log x y 1 y
If y = x + x2 + x3 + ……………to ∞, then x equals
y y 1
B.
y 1 y