MATHS ALLEN SA2 [5] UNSOLVED
SECTION-A
1. If the circumference of a circle increases from 2p to 4p then find its new area.
2. If the ratio of height of a tower and the length of its shadow on the ground is 3 : 1, then what is the angle of elevation of the sun ?
3. Find the area of the largest triangle that can be inscribed in a semi - circle of radius r units ?
4. Eight solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 6 cm and height 32 cm. What is the diameter of each sphere :
SECTION-B
5. If 2 and 1 are the two roots of the quadratic equation ax2 + bx + 2 = 0 , find a and b.
6. Two concentric circles are of radii (3x + 5) and (2x — 4) cm (x > 0). Length of the chord of the outer circle which touches the inner circle is 48 cm. Find the radii of the two circles.
7. A card is drawn from a well shuffled pack of 52 playing cards. What is the probability that the card drawn is : (i) either a red or a king (ii) a black face card OR A coin is tossed three times. Find the probability of getting exactly two tails.
8. A number is selected from the numbers 1, 2, 3, 4 and a second number is selected from the numbers 1, 5, 6, 12. Find the probability that the product of two numbers selected is less than 12?
9. If the point (1, p) lies on the line joining the points (–5, 1) and (4, –2), find the value of p.
10. Find a relation between x and y if the point p (x, y) is equidistant from the points A (3, 6) and B (–3, 4).
SECTION-C
11. Draw a triangle ABC with AB = 4 cm, BC = 5 cm and AC = 6 cm. Then construct another
triangle whose sides are 2/3 times the corresponding sides of DABC.
12. If –5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k. OR Solve, for value of x : 4x2 – 2 (a2 + b2) x + a2 b2 = 0.
13. Find the sum of first 22 terms of an A.P. in which 4th term is 15 and 8th term is one more than twice the 4th term.
14. In an A.P. the first term is –4, the last term is 29 and the sum of all its terms is 150. Find its common difference.
15. In the given figure, a circle touches side BC of a DABC at a point P and touches AB and AC
when produced at Q and R respectively. Show that AQ =
1/2(Perimeter of DABC)
16. A tree breaks due to wind and the broken part bends, so that the top of the tree touches the ground making an angle of 60° with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the total height of the tree before it was uprooted.
17. Find the area of the triangle whose vertices are (4, 3), (5, 4) and (11, 2).
OR
If A(–2, 4), B(0,0) and C(4, 2) are the vertices of a DABC, then find the length of median through the vertex A.
18. In the given figure, O is the centre of a semi-circular arc and AOB is a straight line. Find the area of the shaded region.
19. In figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of shaded region.
20. A well with 14 m inside diameter is dug 7 m deep. Earth taken out of it is spread all around to a width of 6 m to form an embankment. Find the height of embankment.
SECTION-D
21. A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
22. In a godown, parcels are stacked in rows one above the other. There are 25 parcels in the first row, 22 in the second row, 19 in the third row and so on. The last row has 4 parcels. Find the number of rows in which the parcels are stacked and the total number of parcels. OR A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.
23. A triangle PQR is drawn to circumscribe a circle of radius 4 cm such that the segments SQ and RS into which QR is divided by the point of contact S are of lengths 8 cm and 6 cm respectively (see figure). Find the lengths of sides PQ and PR.
24. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
25. In the given figure, AB and PQ are perpendicular diameters of the circle whose centre is O and radius OA = 7 cm. Find the area of the shaded region. BPQ
26. A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag. OR Two dice are thrown simultaneously. Find the probability that the sum of the numbers appearing on the dice is 7.
27. The speed of a motor boat in still water is 15 km/h. It can go 30 km upstream and return
downstream in 4 hours. Find the speed of the stream.
28. A hemispherical tank of radius 74 m is full of water. It is connected by a cylindrical pipe which empties it at 7 litres per second. Find the time it will take to empty the whole tank. OR A right circular cone is 4.1 cm high and radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and radius of its base is 2.1 cm. Both cones are melted and recast into a sphere. Find the diameter of the sphere.
29. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
30. Determine the ratio in which the straight line x – y + 2 = 0 divides the line segment joining (–1, 3) and (9, 8).
31. A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and angle of depression of the base of the hill as 30°. Find the distance of the hill from the ship and the height of the hill.
SECTION-A
1. If the circumference of a circle increases from 2p to 4p then find its new area.
2. If the ratio of height of a tower and the length of its shadow on the ground is 3 : 1, then what is the angle of elevation of the sun ?
3. Find the area of the largest triangle that can be inscribed in a semi - circle of radius r units ?
4. Eight solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 6 cm and height 32 cm. What is the diameter of each sphere :
SECTION-B
5. If 2 and 1 are the two roots of the quadratic equation ax2 + bx + 2 = 0 , find a and b.
6. Two concentric circles are of radii (3x + 5) and (2x — 4) cm (x > 0). Length of the chord of the outer circle which touches the inner circle is 48 cm. Find the radii of the two circles.
7. A card is drawn from a well shuffled pack of 52 playing cards. What is the probability that the card drawn is : (i) either a red or a king (ii) a black face card OR A coin is tossed three times. Find the probability of getting exactly two tails.
8. A number is selected from the numbers 1, 2, 3, 4 and a second number is selected from the numbers 1, 5, 6, 12. Find the probability that the product of two numbers selected is less than 12?
9. If the point (1, p) lies on the line joining the points (–5, 1) and (4, –2), find the value of p.
10. Find a relation between x and y if the point p (x, y) is equidistant from the points A (3, 6) and B (–3, 4).
SECTION-C
11. Draw a triangle ABC with AB = 4 cm, BC = 5 cm and AC = 6 cm. Then construct another
triangle whose sides are 2/3 times the corresponding sides of DABC.
12. If –5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k. OR Solve, for value of x : 4x2 – 2 (a2 + b2) x + a2 b2 = 0.
13. Find the sum of first 22 terms of an A.P. in which 4th term is 15 and 8th term is one more than twice the 4th term.
14. In an A.P. the first term is –4, the last term is 29 and the sum of all its terms is 150. Find its common difference.
15. In the given figure, a circle touches side BC of a DABC at a point P and touches AB and AC
when produced at Q and R respectively. Show that AQ =
1/2(Perimeter of DABC)
16. A tree breaks due to wind and the broken part bends, so that the top of the tree touches the ground making an angle of 60° with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the total height of the tree before it was uprooted.
17. Find the area of the triangle whose vertices are (4, 3), (5, 4) and (11, 2).
OR
If A(–2, 4), B(0,0) and C(4, 2) are the vertices of a DABC, then find the length of median through the vertex A.
18. In the given figure, O is the centre of a semi-circular arc and AOB is a straight line. Find the area of the shaded region.
19. In figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of shaded region.
20. A well with 14 m inside diameter is dug 7 m deep. Earth taken out of it is spread all around to a width of 6 m to form an embankment. Find the height of embankment.
SECTION-D
21. A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
22. In a godown, parcels are stacked in rows one above the other. There are 25 parcels in the first row, 22 in the second row, 19 in the third row and so on. The last row has 4 parcels. Find the number of rows in which the parcels are stacked and the total number of parcels. OR A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.
23. A triangle PQR is drawn to circumscribe a circle of radius 4 cm such that the segments SQ and RS into which QR is divided by the point of contact S are of lengths 8 cm and 6 cm respectively (see figure). Find the lengths of sides PQ and PR.
24. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
25. In the given figure, AB and PQ are perpendicular diameters of the circle whose centre is O and radius OA = 7 cm. Find the area of the shaded region. BPQ
26. A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag. OR Two dice are thrown simultaneously. Find the probability that the sum of the numbers appearing on the dice is 7.
27. The speed of a motor boat in still water is 15 km/h. It can go 30 km upstream and return
downstream in 4 hours. Find the speed of the stream.
28. A hemispherical tank of radius 74 m is full of water. It is connected by a cylindrical pipe which empties it at 7 litres per second. Find the time it will take to empty the whole tank. OR A right circular cone is 4.1 cm high and radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and radius of its base is 2.1 cm. Both cones are melted and recast into a sphere. Find the diameter of the sphere.
29. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
30. Determine the ratio in which the straight line x – y + 2 = 0 divides the line segment joining (–1, 3) and (9, 8).
31. A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and angle of depression of the base of the hill as 30°. Find the distance of the hill from the ship and the height of the hill.
No comments:
Post a Comment