Section-1
1) If sinA = 1 and cot B = 1, prove that sin(A+B) = 1, where A
√2
and B both are acute angles.
2) The length of the minute hand of a clock is 3.5 cm. Find the area swept by minute hand in 30 minutes. (Use 𝞹 = 22/7)
3) Express cos𝞱 in terms of tan𝞱 .
4) From the first 50 natural numbers, find the probability of randomly selected number is a multiple of 3.
5) Write the formula to find curved surface area of a cone and explain each term in it.
6) " The median of observations, -2,5,3,-1,4,6 is 3.5". Is it correct?Justify your answer.
7) If cos𝞱 = 1 , then find the value of 4 + cot 𝞱
√2
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Section-2
8) The diameter of a solid sphere is 6 cm. It is melted and recast into a solid cylinder of height 4 cm. Find the radius of a cylinder.
9) Write the formula of mode for grouped data, and explain each term in it.
10) A person 25 mts away from the cell-tower observes the top of cell-tower at an elevation of 30 deg. Draw the suitable diagram for this situation.
11) Find the area of shaded region in the given figure. ABCD is a square of side 10.5 cm.
12) One card is selected from a well-shuffled deck of 52 cards. Find the probability of getting a red card with a prime numbers.
13) In a △ABC , AD_|_BC and AD^2 = BD * CD. Prove that △ABC is a right angled triangle .
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Section-3
14). The length of cuboid is 12 cm, breadth and height are equal in measurements, and its volume is 432 cm^3. The cuboid is cut into 2 cubes. Find the lateral surface of each cube.
OR
Two poles are standing opposite to each other on the either side of the road which is 90 feet wide. The angle of elevation from the bottom of first pole to the top of second pole is 45 deg, the angle of elevation from the bottom of second pole to the top of first pole is 30 deg. Find the heights of poles.(Use √3 = 1.732)
15) A bag contains some square cards. A prime number between 1 and 100 has been written on each card. Find the probability of getting a card that the sum of the digits of prime number written on it is 8.
OR
The daily wages of 80 workers of a factory.
Find the mean daily wages of the workers of the factory by using an appropriate method.
16) Draw a circle of diameter of 6 cm from a point 5 cm away from its center. Construct the pair of tangents to the circle and measure their length.
OR
The following data gives the information on the observed life span(in hours) of 90 electrical components.
Draw both Ogives for the above data.
17) ABCD is a trapezium with AB//DC, the diagonals AC and BD are intersecting at E. If △AED is similar to △BEC, then prove that AD=BC
OR
Prove that (1 + tan^2𝝷) + ( 1 + 1 ) = 1
tan^2𝝷 sin^2𝝷 - sin^4𝝷
1) If sinA = 1 and cot B = 1, prove that sin(A+B) = 1, where A
√2
and B both are acute angles.
2) The length of the minute hand of a clock is 3.5 cm. Find the area swept by minute hand in 30 minutes. (Use 𝞹 = 22/7)
3) Express cos𝞱 in terms of tan𝞱 .
4) From the first 50 natural numbers, find the probability of randomly selected number is a multiple of 3.
5) Write the formula to find curved surface area of a cone and explain each term in it.
6) " The median of observations, -2,5,3,-1,4,6 is 3.5". Is it correct?Justify your answer.
7) If cos𝞱 = 1 , then find the value of 4 + cot 𝞱
√2
*****************************************
Section-2
8) The diameter of a solid sphere is 6 cm. It is melted and recast into a solid cylinder of height 4 cm. Find the radius of a cylinder.
9) Write the formula of mode for grouped data, and explain each term in it.
10) A person 25 mts away from the cell-tower observes the top of cell-tower at an elevation of 30 deg. Draw the suitable diagram for this situation.
11) Find the area of shaded region in the given figure. ABCD is a square of side 10.5 cm.
12) One card is selected from a well-shuffled deck of 52 cards. Find the probability of getting a red card with a prime numbers.
13) In a △ABC , AD_|_BC and AD^2 = BD * CD. Prove that △ABC is a right angled triangle .
******************************************************
Section-3
14). The length of cuboid is 12 cm, breadth and height are equal in measurements, and its volume is 432 cm^3. The cuboid is cut into 2 cubes. Find the lateral surface of each cube.
OR
Two poles are standing opposite to each other on the either side of the road which is 90 feet wide. The angle of elevation from the bottom of first pole to the top of second pole is 45 deg, the angle of elevation from the bottom of second pole to the top of first pole is 30 deg. Find the heights of poles.(Use √3 = 1.732)
15) A bag contains some square cards. A prime number between 1 and 100 has been written on each card. Find the probability of getting a card that the sum of the digits of prime number written on it is 8.
OR
The daily wages of 80 workers of a factory.
Find the mean daily wages of the workers of the factory by using an appropriate method.
16) Draw a circle of diameter of 6 cm from a point 5 cm away from its center. Construct the pair of tangents to the circle and measure their length.
OR
The following data gives the information on the observed life span(in hours) of 90 electrical components.
Draw both Ogives for the above data.
17) ABCD is a trapezium with AB//DC, the diagonals AC and BD are intersecting at E. If △AED is similar to △BEC, then prove that AD=BC
OR
Prove that (1 + tan^2𝝷) + ( 1 + 1 ) = 1
tan^2𝝷 sin^2𝝷 - sin^4𝝷
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