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Coordinate Geometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry4 Marks
Question

A round clock is traced on a graph paper as shown below The boundary intersect the
coordinate axis at a distance of 4/3 units from origin.

Based on the above information, answer the following questions.
(i) Circle intersect the positive y-axis at
(ii)The radius of the circle is
(iii)The area of the circle is
OR
If (1,√7/3)is one of the ends of a diameter, then its other end is
✓

Answer

(i) (0,4/3)
(ii) 4/3 units
(iii) 16/9π sq. cm OR (-1,-√7/3)

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Rahul goes to a fete in Mussoorie. There he saw a game having prizes - wall clocks, power banks, puppets and water bottles. The game consists of a box having cards inside it, bearing the numbers I to 200, one on each card. A person has to select a card at random. Now, the winning of prizes has the following conditions:
  • Wall clock- If the number on the selected card is a perfect square.
  • Power bank - If the number on the selected card is multiple of 3.
  • Puppet - If the number on selected card is divisible by 10.
  • Water bottle - If the number on the selected card is a prime number more than 100 but less than 150.
  • Better luck next time - If the number on the selected card is a perfect cube.

On the basis of above information, answer the following questions.
  1. Find the probability of winning a puppet.
  2. What is the probability of winning a water bottle?
  3. What is the probability of winning a Power bank?
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    What is the probability of winning a wall clock?
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Observe the factor tree below and answer the questions:
Image
(i) The value of $x$ is
(a) 8325 $\qquad$ (b) 3825 $\qquad$ (c) 835 $\qquad$ (d) 3325
(ii) The value of $y$ is
(a) 5 $\qquad$ (b) 25 $\qquad$ (c) 17 $\qquad$ (d) 3
(iii) The value of $z$ is
(a) 3 $\qquad$ (b) 17 $\qquad$ (c) 5 $\qquad$ (d) 13
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From the top of a tower h meter high, the angles of depression of two objects, which are in the line with the foot of the tower are $\alpha$ and $\beta(\beta>\alpha).$ Find the distance between the two objects.
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A helicopter lifts up 1000 feet over an island and spots a swimmer that need to be rescued. Using a distant land mark, the helicopter pilot determines the angle of depression.
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(i) As the angle of depression increases what will be the effect?
(a) The helicopter gets further from the island.
(b) The helicopter gets closer to the island.
(c) The swimmer gets closer to the island.
(d) The swimmer gets further from the island.
(ii) How does the swimmer's distance from island changes as the angle of depression is halved from $60^{\circ}$ to $30^{\circ}$ ?
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(b) The swimmer's distance from the island doubles
(c) The swimmer's distance from the island increases three times.
(d) The swimmer's distance from the island is halved.
(iii) For which angle of depression both the helicopter and swimmer's will be at same distance?
(a) $30^{\circ}$ $\qquad$ (b) $45^{\circ}$ $\qquad$ (c) $60^{\circ}$ $\qquad$ (d) $90^{\circ}$
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Read the following text carefully and answer the questions that follow:
Aashish and his family went for a vacation to Manali. There they had a stay in tent for a night. Aashish found that the tent in which they stayed is in the form of a cone surmounted on a cylinder. The total height of the tent is $42 m,$ diameter of the base is $42 m$ and height of the cylinder is $22 m$.
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$i$. What is curved surface area of cone? $(1)$
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$iii$. What is the curved surface area of cylinder? $(2)$
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How much canvas required to make a tent? $(2)$
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Teewan, Arun and Pankaj were celebrating the festival of Diwali in open ground with
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(i) If the position of Pankaj is 25 m away from the base of pedestal and Zr = 30°, then
find the height of pedestal.
(ii) If the height of pedestal is 30 m, t = 45° and z = 30°, then the horizontal distance
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(iii) If the vertical height of sky lantern from the top of pedestal is 12 m and ∠y =
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OR
If ∠q=60° and position of Arun is 15 m away from the base of pedestal, then find the
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Amit was playing a number card game. In the game, some number cards (having both + ve or -ve numbers) are arranged in a row such that they are following an arithmetic progression. On his first turn, Amit picks up $6^{\text {th }}$ and $14^{\text {th }}$ card and finds their sum to be -76 . On the second turn he picks up $8^{\text {th }}$ and $16^{\text {th }}$ card and finds their sum to be -96 . Based on the above information, answer the following questions:
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  1. 7
  2. -5
  3. 11
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  1. The number on first card is,
  1. 12
  2. 3
  3. 5
  4. 7
  1. What is the number on the $19^{th}$ card?
  1. -88
  2. -83
  3. -92
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  1. What is the number on the $23^{rd}$ card?
  1. -103
  2. -122
  3. -108
  4. -117
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(i) What will be the value of $x$ ?
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(ii) What will be the value of $y$ ?
(a) 23 $\qquad$ (b) 22 $\qquad$ (c) 11 $\qquad$ (d) 19
(iii) What will be the value of $z$ ?
(a) 22 $\qquad$ (b) 23 $\qquad$ (c) 17 $\qquad$ (d) 19
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(b) prime number
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(d) even numbe>
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leaves green and fruit to grow. A rural Indian school Gardner planted some
trees on his school at certain distances from the water body following a sequence.
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distance of the well from the nearest tree being 10 meters. A gardener waters
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