PM Yashasvi 11th Class Maths Model Paper 2 | Yashasvi Important Bits

by

PM Yashasvi Scholarship 11th Class Maths Model Paper 1 | Yashasvi Important Bits

 

Inter 1st Year(11th) Students Practice This Bits{10th class Syllabus}

101. In an Arithmetic Progression, if a = 28, d = -4, n = 7, then an is:
(a) 4 (b) 5
(c) 3 (d) 7
Answer: (a) 4

102. If a = 10 and d = 10, then first four terms will be:
(a) 10, 30, 50, 60
(b) 10, 20, 30, 40
(c) 10, 15, 20, 25
(d) 10, 18, 20, 30
Answer: (b) 10, 20, 30, 40

103. The first term and common difference for the A.P. 3, 1, -1, -3 is:
(a) 1 and 3
(b) -1 and 3
(c) 3 and -2
(d) 2 and 3
Answer: (c) 3 and -2

104. 30th term of the A.P: 10, 7, 4, …, is
(a) 97
(b) 77
(c) -77
(d) -87
Answer: (c) -77

105. 11th term of the A.P. -3, -1/2, 2 …. Is
(a) 28
(b) 22
(c) -38
(d) -48
Answer: (b) 22

106. The missing terms in AP: __, 13, __, 3 are:
(a) 11 and 9
(b) 17 and 9
(c) 18 and 8
(d) 18 and 9
Answer: (c)

107. Which term of the A.P. 3, 8, 13, 18, … is 78?
(a) 12th
(b) 13th
(c) 15th
(d) 16th
Answer: (d) (d) 16th

108. The 21st term of AP whose first two terms are -3 and 4 is:
(a) 17
(b) 137
(c) 143
(d) -143
Answer: (b) 137

109. If 17th term of an A.P. exceeds its 10th term by 7. The common difference is:
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (a) 1

All competitive exams most important Bits

110. The number of multiples of 4 between 10 and 250 is:
(a) 50
(b) 40
(c) 60
(d) 30
Answer: (c) 60

111. 20th term from the last term of the A.P. 3, 8, 13, …, 253 is:
(a) 147
(b) 151
(c) 154
(d) 158
Answer: (d) 158

112. The sum of the first five multiples of 3 is:
(a) 45
(b) 55
(c) 65
(d) 75
Answer: (a) 45

113. The 10th term of the AP: 5, 8, 11, 14, … is
(a) 32
(b) 35
(c) 38
(d) 185
Answer: (a) 32

114. In an AP, if d = -4, n = 7, an = 4, then a is
(a) 6 (b) 7
(c) 20 (d) 28
Answer: (d) 28

115. The list of numbers –10, –6, –2, 2,… is
(a) an AP with d = –16
(b) an AP with d = 4
(c) an AP with d = –4
(d) not an AP
Answer: (b) an AP with d = 4

116. If the 2nd term of an AP is 13 and the 5th term is 25, then its 7th term is
(a) 30 (b) 33
(c) 37 (d) 38
Answer: (b) 33

117. Which term of the AP: 21, 42, 63, 84,… is 210?
(a) 9th
(b) 10th
(c) 11th
(d) 12th
Answer: (b) 10th

118. What is the common difference of an AP in which a18 – a14 = 32?
(a) 8
(b) -8
(c) -4
(d) 4
Answer: (a) 8

119. The famous mathematician associated with finding the sum of the first 100 natural numbers is
(a) Pythagoras
(b) Newton
(c) Gauss
(d) Euclid
Answer: (c) Gauss

120. The sum of first 16 terms of the AP: 10, 6, 2,… is
(a) –320
(b) 320
(c) –352
(d) –400
Answer: (a) -320

121. Equation of (x+1)2-x2=0 has number of real roots equal to:
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (a) 1

122. The roots of 100×2 – 20x + 1 = 0 is:
(a) 1/20 and 1/20
(b) 1/10 and 1/20
(c) 1/10 and 1/10
(d) None of the above
Answer: (c) 1/10 and 1/10

123. The sum of two numbers is 27 and product is 182. The numbers are:
(a) 12 and 13
(b) 13 and 14
(c) 12 and 15
(d) 13 and 24
Answer: (b) 13 and 14

124. If ½ is a root of the quadratic equation x2-mx-5/4=0, then value of m is:
(a) 2
(b) -2
(c) -3
(d) 3
Answer: (b) -2

125. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides of the triangle are equal to:
(a) Base=10cm and Altitude=5cm
(b) Base=12cm and Altitude=5cm
(c) Base=14cm and Altitude=10cm
(d) Base=12cm and Altitude=10cm
Answer: (b) Base=12cm and Altitude=5cm

126. The roots of quadratic equation 2×2 + x + 4 = 0 are:
(a) Positive and negative
(b) Both Positive
(c) Both Negative
(d) No real roots
Answer: (d) No real roots

127. The sum of the reciprocals of Rehman’s ages 3 years ago and 5 years from now is 1/3. The present age of Rehman is:
(a) 7
(b) 10
(c) 5
(d) 6
Answer: (a) 7

128. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
(a) 30 km/hr
(b) 40 km/hr
(c) 50 km/hr
(d) 60 km/hr
Answer: (b) 40 km/hr

129. If one root of equation 4×2-2x+k-4=0 is reciprocal of the other. The value of k is:
(a) -8
(b) 8
(c) -4
(d) 4
Answer: (b) 8

130. Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0.62. The probability of Reshma winning the match is
(a) 0.62
(b) 0.38
(c) 0.58
(d) 0.42
Answer: (b) 0.38

131. Which one of the following is not a quadratic equation?
(a) (x + 2)2 = 2(x + 3)
(b) x2 + 3x = (–1) (1 – 3x)2
(c) (x + 2) (x – 1) = x2 – 2x – 3
(d) x3 – x2 + 2x + 1 = (x + 1)3
Answer: (c) (x + 2) (x – 1) = x2 – 2x – 3

132. Which of the following equations has 2 as a root?
(a) x2 – 4x + 5 = 0
(b) x2 + 3x – 12 = 0
(c) 2×2 – 7x + 6 = 0
(d) 3×2 – 6x – 2 = 0
Answer: (c) 2×2 – 7x + 6 = 0

133. A quadratic equation ax2 + bx + c = 0 has no real roots, if
(a) b2 – 4ac > 0
(b) b2 – 4ac = 0
(c) b2 – 4ac < 0
(d) b2 – ac < 0
Answer: (c) b2 – 4ac < 0

134. The product of two consecutive positive integers is 360. To find the integers, this can be represented in the form of quadratic equation as
(a) x2 + x + 360 = 0
(b) x2 + x – 360 = 0
(c) 2×2 + x – 360
(d) x2 – 2x – 360 = 0
Answer: (b) x2 + x – 360 = 0

135. The equation which has the sum of its roots as 3 is
(a) 2×2 – 3x + 6 = 0
(b) –x2 + 3x – 3 = 0
(c) √2×2 – 3/√2x + 1 = 0
(d) 3×2 – 3x + 3 = 0
Answer: (b) –x2 + 3x – 3 = 0

136. The quadratic equation 2×2 – √5x + 1 = 0 has
(a) two distinct real roots
(b) two equal real roots
(c) no real roots
(d) more than 2 real roots
Answer: (c) no real roots

137. The equation (x + 1)2 – 2(x + 1) = 0 has
(a) two real roots
(b) no real roots
(c) one real root
(d) two equal roots
Answer: (a) two real roots

138. The quadratic formula to find the roots of a quadratic equation ax2 + bx + c = 0 is given by
(a) [-b ± √(b2-ac)]/2a
(b) [-b ± √(b2-2ac)]/a
(c) [-b ± √(b2-4ac)]/4a
(d) [-b ± √(b2-4ac)]/2a
Answer: (d) [-b ± √(b2-4ac)]/2a

139. The quadratic equation x2 + 7x – 60 has
(a) two equal roots
(b) two real and unequal roots
(b) no real roots
(c) two equal complex roots
Answer: (b) two real and unequal roots

140. The maximum number of roots for a quadratic equation is equal to
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (b) 2

Also Read This:

141. A circle has a number of tangents equal to
(a) 0
(b) 1
(c) 2
(d) Infinite
Answer: (d) Infinite

142. A tangent intersects the circle at:
(a) One point
(b) Two distinct point
(c) At the circle
(d) None of the above
Answer: (a) One point

143. A circle can have _____parallel tangents at a single time.
(a) One
(b) Two
(c) Three
(d) Four
Answer: (b) Two

144. If the angle between two radii of a circle is 110º, then the angle between the tangents at the ends of the radii is:
(a) 90º
(b) 50º
(c) 70º
(c) 40º
Answer: (c) 70º

145. The length of the tangent from an external point A on a circle with centre O is
(a) always greater than OA
(b) equal to OA
(c) always less than OA
(d) cannot be estimated
Answer: (c) always less than OA

146. AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to
(a) 65°
(b) 60°
(c) 50°
(d) 40°
Answer: (c) 50°

147. If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to
(a) 60°
(b) 70°
(c) 80°
(d) 90°
Answer: (b) 70°

148. The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is:
(a) 3 cm
(b) 5 cm
(c) 7 cm
(d) 10 cm
Answer: (a) 3 cm

149. If a parallelogram circumscribes a circle, then it is a:
(a) Square
(b) Rectangle
(c) Rhombus
(d) None of the above
Answer: (c) Rhombus

150. Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle is:
(a) 8 cm
(b) 10 cm
(c) 12 cm
(d) 18 cm
Answer: (a) 8 cm

151. If angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii is
(a) 90° (b) 50°
(c) 70° (d) 40°
Answer: (b) 50°

152. A line intersecting a circle in two points is called a _______.
(a) Secant
(b) Chord
(c) Diameter
(d) Tangent
Answer: (a) Secant

153. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7
(b) 14
(c) 21
(d) 28
Answer: (b) 14

154. If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to
(a) (3/2)√3 cm
(b) 6 cm
(c) 3 cm
(d) 3√3 cm
Answer: (d) 3√3 cm

155. The tangent to a circle is ___________ to the radius through the point of contact.
(a) parallel
(b) perpendicular
(c) perpendicular bisector
(d) bisector
Answer: (b) perpendicular

156. Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. The radius of the inner circle will be
(a) 3 cm
(b) 4 cm
(c) 2.5 cm
(d) 2 cm
Answer: (a) 3 cm

157. The distance between two parallel tangents of a circle is 18 cm, then the radius of the circle is
(a) 8 cm
(b) 10 cm
(c) 9 cm
(d) 7.5 cm
Answer: (c) 9 cm

158. The probability that a non leap year selected at random will contain 53 Sundays is
(a) 1/7 (b) 2/7
(c) 3/7 (d) 5/7
Answer: (a) 1/7

159. If the probability of an event is p, the probability of its complementary event will be
(a) p – 1
(b) p
(c) 1 – p
(d) 1 – 1/p
Answer: (c) 1 – p

160. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is
(a) 4
(b) 13
(c) 48
(d) 51
Answer: (d) 51

161. If the length of the shadow of a tree is decreasing then the angle of elevation is:
(a) Increasing
(b) Decreasing
(c) Remains the same
(d) None of the above
Answer: (a) Increasing

162. The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is:
(a) 10 m
(b) 30/√3 m
(c) √3/10 m
(d) 30 m
Answer: (b) 30/√3 m

163. If the height of the building and distance from the building foot’s to a point is increased by 20%, then the angle of elevation on the top of the building:
(a) Increases
(b) Decreases
(c) Do not change
(d) None of the above
Answer: (c) Do not change

164. If a tower 6m high casts a shadow of 2√3 m long on the ground, then the sun’s elevation is:
(a) 60° (b) 45°
(c) 30° (d) 90°
Answer: (a) 60°

165. The angle of elevation of the top of a building 30 m high from the foot of another building in the same plane is 60°, and also the angle of elevation of the top of the second tower from the foot of the first tower is 30°, then the distance between the two buildings is:
(a) 10√3 m
(b) 15√3 m
(c) 12√3 m
(d) 36 m
Answer: (a) 10√3 m

166. The angle formed by the line of sight with the horizontal when the point is below the horizontal level is called:
(a) Angle of elevation
(b) Angle of depression
(c) No such angle is formed
(d) None of the above
Answer: (b) Angle of depression

167. The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called:
(a) Angle of elevation
(b) Angle of depression
(c) No such angle is formed
(d) None of the above
Answer: (a) Angle of elevation

168. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. The height of the tower (in m) standing straight is:
(a) 15√3
(b) 10√3
(c) 12√3
(d) 20√3
Answer: (a) 15√3

169. The line drawn from the eye of an observer to the point in the object viewed by the observer is said to be
(a) Angle of elevation
(b) Angle of depression
(c) Line of sight
(d) None of the above
Answer: (c) Line of sight

170. The height or length of an object or the distance between two distant objects can be determined with the help of:
(a) Trigonometry angles
(b) Trigonometry ratios
(c) Trigonometry identities
(d) None of the above
Answer: (b) Trigonometry ratios

171. When the shadow of a pole h metres high is √3h metres long, the angle of elevation of the Sun is
(a) 30° (b) 60°
(c) 45° (d) 15°
Answer: (a) 30°

172. A ladder makes an angle of 60° with the ground, when placed along a wall. If the foot of ladder is 8 m away from the wall, the length of ladder is
(a) 4 m (b) 8 m
(c) 8√3 m (d) 16 m
Answer: (d) 16 m

173. If the height and length of a shadow of a tower are the same, then the angle of elevation of Sun is
(a) 30°
(b) 60°
(c) 45°
(d) 15°
Answer: (c) 45°

174. The angle of depression of an object on the ground, from the top of a 25 m high tower is 30°. The distance of the object from the base of tower is
(a) 25√3 m
(b) 50√3 m
(c) 75√3 m
(d) 50 m
Answer: (a) 25√3

175. The shadow of a tower standing on level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it was 60°. The height of the tower is
(a) 40√3 m
(b) 20√3
(c) 20 m
(d) 15√3 m
Answer: (b) 20√3 m

All competitive exams most important Bits

176. If the angles of elevation of the top of a tower from two points at the distance of a m and b m from the base of tower and in the same straight line with it are complementary, then the height of the tower (in m) is
(a) √(a/b)
(b) √ab
(c) √(a + b)
(d) √(a – b)
Answer: (b) √ab

177. From a point on a bridge across a river the angle of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at the height of 30 m from the banks, the width of the river is
(a) 30(1 + √3) m
(b) 30(√3 – 1) m
(c) 30√3 m
(d) 60√3 m
Answer: (a) 30(1 + √3) m

178. The ratio of the height of a tower and the length of its shadow on the ground is √3 : 1. The angle of elevation of the Sun is
(a) 30°
(b) 45°
(c) 60°
(d) 75°
Answer: (c) 60°

179. A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the foot of the tree to the point where the top touches the ground is 8 m. The height of the tree is
(a) 4√3 m
(b) 8√3 m
(c) 6√3 m
(d) 16√3 m
Answer: (b) 8√3 m

180. The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will be
(a) Greater than 60°
(b) Equal to 30°
(c) Less than 60°
(d) Equal to 60°
Answer: (c) Less than 60°

181. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is:
(a) 12/7 (b) 24/7
(c) 20/7 (d) 7/24
Answer: (b) 24/7

182. (Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to:
(a) 0
(b) 1+2√3
(c) 1-√3
(d) 1+√3
Answer: (c) 1-√3

183. The value of tan 60°/cot 30° is equal to:
(a) 0 (b) 1
(c) 2 (d) 3
Answer: (b) 1

184. 1 – cos2A is equal to:
(a) sin2A
(b) tan2A
(c) 1 – sin2A
(d) sec2A
Answer: (a) sin2A

185. sin (90° – A) and cos A are:
(a) Different
(b) Same
(c) Not related
(d) None of the above
Answer: (b) Same

186. If cos X = ⅔ then tan X is equal to:
(a) 5/2
(b) √(5/2)
(c) √5/2
(d) 2/√5
Answer: (c) √5/2

187. If cos X = a/b, then sin X is equal to:
(a) (b2-a2)/b
(b) (b-a)/b
(c) √(b2-a2)/b
(d) √(b-a)/b
Answer: (c) √(b2-a2)/b

188. The value of sin 60° cos 30° + sin 30° cos 60° is:
(a) 0
(b) 1
(c) 2
(d) 4
Answer: (b) 1

189. 2 tan 30°/(1 + tan230°) =
(a) sin 60°
(b) cos 60°
(c) tan 60°
(d) sin 30°
Answer: (a) sin 60°

190. sin 2A = 2 sin A is true when A =
(a) 30°
(b) 45°
(c) 0°
(d) 60°
Answer: (c) 0°

191. The value of (sin 45° + cos 45°) is
(a) 1/√2
(b) √2
(c) √3/2
(d) 1
Answer: (b) √2

192. If sin A = 1/2 , then the value of cot A is
(a) √3
(b) 1/√3
(c) √3/2
(d) 1
Answer: (a) √3

193. If ∆ABC is right angled at C, then the value of cos(A+B) is
(a) 0
(b) 1
(c) 1/2
(d) √3/2
Answer: (a) 0

194. The value of (tan 1° tan 2° tan 3° … tan 89°) is
(a) 0
(b) 1
(c) 2
(d) 1/2
Answer: (b) 1

195. The value of the expression [cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)] is
(a) -1
(b) 0
(c) 1
(d) 3/2
Answer: (b) 0

196. If cos(α + β) = 0, then sin(α – β) can be reduced to
(a) cos β
(b) cos 2β
(c) sin α
(d) sin 2α
Answer: (b) cos 2β

197. If sin A + sin2A = 1, then the value of the expression (cos2A + cos4A) is
(a) 1
(b) 1/2
(c) 2
(d) 3
Answer: (a) 1

198. If cos 9α = sinα and 9α < 90°, then the value of tan 5α is
(a) 1/√3
(b) √3
(c) 1
(d) 0
Answer: (c) 1

199. If P(A) denotes the probability of an event A, then
(a) P(A) < 0
(b) P(A) > 1
(c) 0 ≤ P(A) ≤ 1
(d) –1 ≤ P(A) ≤ 1
Answer: (c) 0 ≤ P(A) ≤ 1

200. The value of the expression sin6θ + cos6θ + 3 sin2θ cos2θ is
(a) 0
(b) 3
(c) 2
(d) 1
Answer: (d) 1

201. To divide a line segment AB in the ratio 3:4, first, a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is:
(a) 5
(b) 7
(c) 9
(d) 11
Answer: (b) 7

202. To divide a line segment AB of length 7.6 cm in the ratio 5 : 8, a ray AX is drawn first such that ∠BAX forms an acute angle and then points A1, A2, A3, ….are located at equal distances on the ray AX and the point B is joined to:
(a) A5
(b) A6
(c) A10
(d) A13
Answer: (d) A13

203. To construct a triangle similar to a given ΔPQR with its sides 5/8 of the similar sides of ΔPQR, draw a ray QX such that ∠QRX is an acute angle and X lies on the opposite side of P with respect to QR. Then locate points Q1, Q2, Q3, … on QX at equal distances, and the next step is to join:
(a) Q10 to C
(b) Q3 to C
(c) Q8 to C
(d) Q4 to C
Answer: (c) Q8 to C

204. To construct a triangle similar to a given ΔPQR with its sides, 9/5 of the corresponding sides of ΔPQR draw a ray QX such that ∠QRX is an acute angle and X is on the opposite side of P with respect to QR. The minimum number of points to be located at equal distances on ray QX is:
(a) 5
(b) 9
(c) 10
(d) 14
Answer: (b) 9

205. To construct a pair of tangents to a circle at an angle of 60° to each other, it is needed to draw tangents at endpoints of those two radii of the circle, the angle between them should be:
(a) 100°
(b) 90°
(c) 180°
(d) 120°
Answer: (d) 120°

206. To divide a line segment PQ in the ratio m : n, where m and n are two positive integers, draw a ray PX so that ∠PQX is an acute angle and then mark points on ray PX at equal distances such that the minimum number of these points is:
(a) m + n
(b) m – n
(c) m + n – 1
(d) Greater of m and n
Answer: (a) m + n

207. To draw a pair of tangents to a circle which are inclined to each other at an angle of 45°, it is required to draw tangents at the endpoints of those two radii of the circle, the angle between which is:
(a) 135°
(b) 155°
(c) 160°
(d) 120°
Answer: (a) 135°

208. A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of ___________ from the centre.
(a) 3.5 cm
(b) 2.5 cm
(c) 5 cm
(d) 2 cm
Answer: (c) 5 cm

209. To construct a triangle ABC and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle. A ray AX is drawn where multiple points at equal distances are located. The last point to which point B will meet the ray AX will be:
(a) A1
(b) A2
(c) A3
(d) A4
Answer: (c) A3

210. To construct a triangle similar to a given ΔPQR with its sides 3/7 of the similar sides of ΔPQR, draw a ray QX such that ∠QRX is an acute angle and X lies on the opposite side of P with respect to QR. Then locate points Q1, Q2, Q3, … on QX at equal distances, and the next step is to join:
(a) Q10 to C
(b) Q3 to C
(c) Q7 to C
(d) Q4 to C
Answer: (c) Q7 to C

211. If the scale factor is 3/5, then the new triangle constructed is _____ the given triangle.
(a) smaller the
(b) greater than
(c) overlaps
(d) congruent to
Answer: (a) smaller than

212. To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A1, A2, A3, … and B1, B2, B3, … are located at equal distances on ray AX and BY, respectively. Then the points joined are
(a) A5 and B6
(b) A6 and B5
(c) A4 and B5
(d) A5 and B4
Answer: (a) A5 and B6

213. By geometrical construction, which one of the following ratios is not possible to divide a line segment?
(a) 1 : 10 (b) √9 : √4
(c) 10 : 1 (d) 4 + √3 : 4 – √3
Answer: (d) 4 + √3 : 4 – √3

214. By geometrical construction, is it possible to divide a line segment in the ratio 1/√3 : √3?
(a) Yes
(b) No
(c) Cannot be determined
(d) None of these
Answer: (a) Yes

215. In constructions, the scale factor is used to construct ______ triangles.
(a) right (b) equilateral
(c) similar (d) congruent
Answer: (c) similar

216. In the division of a line segment AB, any ray AX making angle with AB is _______.
(a) an acute angle
(b) a right angle
(c) an obtuse angle
(d) reflex angle
Answer: (a) an acute angle.

217. A point P is at a distance of 8 cm from the centre of a circle of radius 5 cm. How many tangents can be drawn from point P to the circle?
(a) 0
(b) 1
(c) 2
(d) Infinite
Answer: (c) 2

218. To divide a line segment AB in the ratio p : q, first, a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is 9. Here, the possible ratio of p : q is
(a) 3 : 5
(b) 4 : 7
(c) 2 : 9
(d) 5 : 4
Answer: (d) 5 : 4

219. A line segment drawn perpendicular from the vertex of a triangle to the opposite side is known as
(a) altitude
(b) median
(c) bisector of side
(d) radius of incircle of the triangle
Answer: (a) altitude

220. If the line segment is divided in the ratio 3 : 7, then how many parts does it contain while constructing the point of division?
(a) 3 (b) 7
(c) 4 (d) 10
Answer: (d) 10

221. The perimeter of a circle having radius 5cm is equal to:
(a) 30 cm
(b) 3.14 cm
(c) 31.4 cm
(d) 40 cm
Answer: (c) 31.4 cm

222. Area of the circle with radius 5cm is equal to:
(a) 60 sq.cm
(b) 75.5 sq.cm
(c) 78.5 sq.cm
(d) 10.5 sq.cm
Answer: (c) 78.5 sq.cm

223. The largest triangle inscribed in a semi-circle of radius r, then the area of that triangle is;
(a) r2
(b) 1/2r2
(c) 2r2
(d) √2r2
Answer: (a) r2

224. If the perimeter of the circle and square are equal, then the ratio of their areas will be equal to:
(a) 14:11
(b) 22:7
(c) 7:22
(c) 11:14
Answer: (a) 14:11

225. The area of the circle that can be inscribed in a square of side 8 cm is
(a) 36 π cm2
(b) 16 π cm2
(c) 12 π cm2
(d) 9 π cm2
Answer: (b) 16 π cm2

226. The area of the square that can be inscribed in a circle of radius 8 cm is
(a) 256 cm2
(b) 128 cm2
(c) 642 cm2
(d) 64 cm2
Answer: (b) 128 cm2

227. The area of a sector of a circle with radius 6 cm if the angle of the sector is 60°.
(a) 142/7
(b) 152/7
(c) 132/7
(d) 122/7
Answer: (c) 132/7

228. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is;
(a) 20cm
(b) 21cm
(c) 22cm
(d) 25cm
Answer: (c) 22cm

229. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The area of the sector formed by the arc is:
(a) 200 cm2
(b) 220 cm2
(c) 231 cm2
(d) 250 cm2
Answer: (c) 231 cm2

230. Area of a sector of angle p (in degrees) of a circle with radius R is
(a) p/180 × 2πR
(b) p/180 × π R2
(c) p/360 × 2πR
(d) p/720 × 2πR2
Answer: (d) p/720 × 2πR2

231. If the area of a circle is 154 cm2, then its perimeter is
(a) 11 cm
(b) 22 cm
(c) 44 cm
(d) 55 cm
Answer: (c) 44 cm

232. If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then
(a) R1 + R2 = R
(b) R12 + R22 = R2
(c) R1 + R2 < R
(d) R12 + R22 < R2
Answer: (b) R12 + R22 = R2

233. If θ is the angle (in degrees) of a sector of a circle of radius r, then the length of arc is
(a) (πr2θ)/360
(b) (πr2θ)/180
(c) (2πrθ)/360
(d) (2πrθ)/180
Answer: (a) (2πrθ)/360

234. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be
(a) 10 m
(b) 15 m
(c) 20 m
(d) 24 m
Answer: (a) 10 m

235. The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is
(a) 56 cm
(b) 42 cm
(c) 28 cm
(d) 16 cm
Answer: (c) 28 cm

236. Find the area of a sector of circle of radius 21 cm and central angle 120°.
(a) 441 cm2
(b) 462 cm2
(c) 386 cm2
(d) 512 cm2
Answer: (b) 462 cm2

237. The wheel of a motorcycle is of radius 35 cm. The number of revolutions per minute must the wheel make so as to keep a speed of 66 km/hr will be
(a) 50
(b) 100
(c) 500
(d) 1000
Answer: (c) 500

238. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(a) 2 units (b) π units
(c) 4 units (d) 7 units
Answer: (a) 2 units

239. The area of a quadrant of a circle with circumference of 22 cm is
(a) 77 cm2
(b) 77/8 cm2
(b) 35.5 cm2
(c) 77/2 cm2
Answer: (b) 77/8 cm2

240. In a circle of radius 14 cm, an arc subtends an angle of 30° at the centre, the length of the arc is
(a) 44 cm
(b) 28 cm
(c) 11 cm
(d) 22/3 cm
Answer: (d) 22/3 cm

241. The shape of an ice-cream cone is a combination of:
(a) Sphere + cylinder
(b) Sphere + cone
(c) Hemisphere + cylinder
(d) Hemisphere + cone
Answer: (d) Hemisphere + cone

242. If a cone is cut parallel to the base of it by a plane in two parts, then the shape of the top of the cone will be a:
(a) Sphere
(b) Cube
(c) Cone itself
(d) Cylinder
Answer: (c) Cone itself

243. If we cut a cone in two parts by a plane parallel to the base, then the bottom part left over is the:
(a) Cone
(b) Frustum of cone
(c) Sphere
(d) Cylinder
Answer: (b) Frustum of cone

244. If r is the radius of the sphere, then the surface area of the sphere is given by;
(a) 4 π r2 (b) 2 π r2
(c) π r2 (d) 4/3 π r2
Answer: (a) 4 π r2

245. If we change the shape of an object from a sphere to a cylinder, then the volume of cylinder will
(a) Increase
(b) Decrease
(c) Remains unchanged
(d) Doubles
Answer: (c) Remains unchanged

246. Fifteen solid spheres are made by melting a solid metallic cone of base diameter 2cm and height 15cm. The radius of each sphere is:
(a) ½ (b) ¼
(c) 1/3√2 (d) 1/3√4
Answer: (d) 1/3√4

247. The radius of the top and bottom of a bucket of slant height 35 cm are 25 cm and 8 cm. The curved surface of the bucket is:

(a) 4000 sq.cm
(b) 3500 sq.cm
(c) 3630 sq.cm
(d) 3750 sq.cm
Answer: (c) 3630 sq.cm

248. If a cylinder is covered by two hemispheres shaped lid of equal shape, then the total curved surface area of the new object will be
(a) 4πrh + 2πr2
(b) 4πrh – 2πr2
(c) 2πrh + 4πr2
(d) 2πrh + 4πr
Answer: (c) 2πrh + 4πr2

249. A tank is made of the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and radius is 30 cm. The total surface area of the tank is:
(a) 30 m
(b) 3.3 m
(c) 30.3 m
(d) 3300 m
Answer: (b) 3.3 m

250. If we join two hemispheres of same radius along their bases, then we get a;
(a) Cone (b) Cylinder
(c) Sphere (d) Cuboid
Answer: (c) Sphere

Previous Paper

Also Read This:

 

Tags:

pm yashasvi scholarship model paper 2023, pm scholarship 2023,#pm yashasvi entrance test 2023 gk model paper, pm yashasvi scholarship 2023 model paper, pm yasasvi model paper,#pm yashasvi, pm yashasvi model paper 2023,yasasvi model paper, pm yasasvi model paper 2023, pm yashasvi scholarship, pm yashasvi scholarship 2023, pm yasasvi model paper class 9, pm yashasvi solved paper,#pm yashasvi entrance test 2023 maths model paper, pm yashasvi model paper, pm yashasvi, pm yashasvi scholarship, pm yashasvi,yashasvi scholarship important bits, pm yashasvi scholarship 2023, pm yashasvi yojana, pm yashasvi scholarship 2023 syllabus,#pm yashasvi, pm yashasvi scholarship online form 2023, pm yashasvi scholarship 2023 eligibility, how to apply for pm yashasvi scholarship, pm yashasvi scholarship 2023 last date, pm yashasvi scholarship 2023 model paper, pm yashasvi scholarship previous year bits pdf

Home | About us | Sitemap | Contact Us

© BharatBadi | All rights reserved