DCE (Delhi College of Engineering) Entrance Examination Sample Paper - Maths

121. Which of the following is not true in linear programming problem?

122. The equation of the circle whose diameter lies on 2x + 3y = 3 and 16x - y = 4 and which passes through (4, 6) is

123. Let n(A) = 4 and n(B) = 5. The number of all possible injections from A to B is

124. If aN = {ax : x Î N} and bN Ç cN = dN, where b, c Î N are relatively prime, then

125. A square root of 3 + 4i is

126. Which of the following is not applicable for a complex number?

127. | maximum amp (z) - minimum amp (z) | is equal to

128. If e, e' be the eccentricities of two conics S and S' and if e² + e'² = 3, then both S and S' can be

129. A stick of length 'l' rests against the floor and a wall of a room. If the stick begins to slide on the floor, then the locus of its middle point is

130. The eccentricity of the ellipse which meets the straight line x/y + y/2 = 1 on the axis of x and the straight line x/3 - y/5 =1 on the axis of y and whose axes lie along the axes of co-ordinates is

131. A and B are positive acute angles satisfying the equations 3 cos² A + 2 cos² B = 4 and 3 sin A/sin B = 2 cos B/cos A, then A + 2B is equal to

132. At a point 15 metres away from the base of a 15 metres high house, the angle of elevation of the top is

133. If tan(p cos q) = cot(p sin q), 0 < q < 3p/4, then sin(q + p/4) equals

134. In a triangle ABC, Ð B = p/3, Ð B = p/4, and D divides BC internally in the ratio1 : 3. Then (sin Ð BAD)/(sin Ð CAD) equals

135. The straight line 5x + 4y = 0 passes through the point of intersection of the lines

136. The number of common tangents of the circles x² + y² - 2x - 1 = 0 and x² + y² - 2y - 7 = 0 is

137. If the product of the roots of the equation ax² + 6x + a² + 1 = 0 is -2, then a equals

138. If the roots of a₁x² + b₁x + c₁ = 0 and a₂x² + b₂x + c₂ = 0 are same, then

139. The roots of the equation (3 - x)⁴ + (2 - x)⁴ = (5 - 2x)⁴ are

141. If the 10th term of a G.P. is 9 and 4th term is 4, then its 7 th term is

142. 1 - 1/2 + 1/3 - 1/4 + ....... to ¥ equals

143. 9/1! + 19/2! + 35/3! + 57/4! + 85/5! + ....... =

144. How many different arrangements can be made out of the letters in the expansion A²B³C⁴, when written in full?

145. The numbner of straight lines that can be drawn out of 10 points of which 7 are collinear is

146. 1/n! + 1/[2! (n - 2)!] + 1/[4! (n - 4)!] + ..... is

147. The term independent of x in (x² - 1/x)⁹ is

148. The 9th term of an A.P. is 499 and 499th term is 9. The term which is equal to zero is

150. If AB = A and BA = B, then B² is equal to

152. The value of K so that (x - 1)/-3 = (y - 2)/2K = (z - 3)/2 and (x - 1)/3K = (y - 1)/1 = (z - 6)/-5 may be perpendicular is given by

156. If a, b, c, d are constants such that a and c are both negative and r is the correlation coefficient between x and y, then the correlation coefficient between (ax + b) and (cy + d) is equal to

157. A person draws a card from a pack of 52 playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade, the chance that he will fail in the first two draws is

158. In tossing 10 coins, the probability of getting exactly 5 heads is

159. Four tickets marked 00, 01, 10, 11 respectively are placed in a bag. A ticket is drawn at random five times, being replaced each time, the probability that the sum of the numbers on tickets thus drawn is 23, is

161. Let f[x + (1/x)] = [x² + (1/x²)](x ¹ 0), then f(x) is equal to

162. Let f(x) = [tan(p/4 - x)]/cot2x, x ¹ p/4. The value which should be assigned to f at x = p/4, so that it is continous everywhere is

163. If f₁(x) and f₂(x) are defined on domains D₁ and D₂ respectively, then domain of f₁(x) + f₂(x) is

164. The derivative of sin x³ with respect to cos x³ is equal to

165. If y = f(x) is an odd differentiable function defined on (¥, ¥) such that f'(3) = -2, then f'(-3) equals

166. The line (x/a) + (y/b) = 1 touches the curve y = be^-x/a at the point

167. The least value of 'a' for which the equation (4/sin x) + [1/(1 - sin x)] = a has atleast one solution on the interval (0, p/2) is

168. The area bounded by the curve y² = 8x and x² = 8y is

169. The integrating factor of the differential equation [(dy/dx)(x log x)] + y = 2 log x is given by

170. If y = tan ^-1[(sin x + cos x)/(cos x - sin x)], then dy/dx is equal to

171. The length of tangent from (5, 1) to the circle x² + y² + 6x - 4y - 3 = 0 is

172. The equation of the straight line which is perpendicular to y = x and passes through (3, 2) will be given by

173. If the imaginary part of (2z + 1)/(iz + 1) is - 2, then the locus of the point representing z in the complex plane is

174. The sum of 40 terms of an A.P. whose first term is 2 and common difference 4, will be

175. If a, b, c are in A.P., then a/bc, 1/c, 2/b are in

176. The term independent of x in [x² + (1/x²)] is

177. The equation of a line through (2, -3) parallel to y-axis is

179. The range of the function f(x) = (1 + x²)/x² is equal to

180. Two vectors are said to be equal if