Maths Sample paper 6, Part - B for class 10th
Maths Sample Paper
Part -B
20. Case Study IV
Tree plantation to control pollution
The class X students of a secondary school in Krishna nagar have been alloted a rectangular plot of land for this gardening activity.
The students sowing seeds of flowering plants on the remaining area of the plot.
a) Find the coordinates of point Q and S are
i. (2,3), (6,6)
ii. (3,2), (6,6)
iii. (2,3), (5,5)
iv. None of the above
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b) Find the distance between the vertices of diagonal Q and S
i. 3
ii. 5
iii. 6
iv. 7
c) Find the width of rectangle PQRS.
i. 3
ii. 4
iii. 2
iv. 5
d) If the point G divides the line QR in the ratio 1:2, then the coordinates of G is
i. (10,3)
ii. (10/3,3)
iii. 3,10/3
iv. None of these
e) Find the area of the rectangle field PQRS.
i) 8 sq. units
ii. 10 sq units
iii. 12 sq units
iv. 14 sq units
Part- B
Directions (Q.nos 21-26 are of 2 marks each)
21. Find the HCF and LCM of 10224 and 1608 using prime factorization method.
22. Check whether the given quadratic equation 2x² +5√3x +6= 0 has real roots and if so, find the roots.
23. A boy noted the number of cars passing through a spot on a road for 100 periods each of 3 min and summarized it in the table given below. Find the mode of the data.
The Arithmetic Mean of the following frequency distribution is 50. Find the value of p.
Class Frequency
Interval
0-20 17
20-40 p
40-60 32
60-80 24
80-100 19
24. Prove that
(tan² A - tan² B) = (sin² A - sin²B)/cos²A cos²B
= cos²B- cos²A/cos²B cos²A
Or
If √3 tan2∅-3= 0, then find the value of cos∅.
25. In the following figure, CM and RN are respectively the medians of ∆ABC and ∆PQR.
If ∆ABC ~ ∆PQR, then prove that ∆AMC~∆PNR.
26. Two opposite angular points of a square ABCD are A(-1,2) and C(3, -2). Find the coordinates of the remaining angular points of the square.
Directions (Q.nos. 27-33 are of 3 marks each)
27. The angles of a triangle are in AP. If the greatest angle equals to the sum of the other two, then find the angles. Also, conclude that find these angles are multiple of which angle.
Or
A sum of Rs 1000 is invested at 8% simple interest per annum. Calculate the interest at the end of 1, 2, 3. . . . . .years. Is the sequence of interests an AP? Find the interest at the end of 30 yrs.
28. In a violent storm, a tree got bent by the wind. The top of the tree meets the ground at an angle of 30°, whose distance of 30 m from the root. At what height from the bottom did the tree get bent? What was the original height of the tree?
[Take,√3=1.73]
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29. A car has wheels which are 80cm in diameter. How many complete revolutions does each wheel make in 10 min when the car is travelling at a speed of 66km/hr?
30. Prove that, if a, b, c and d are positive rationals such that, a + √b =c + √d, then either a = c and b = d or b and d are squares of rationals.
31. Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is
i. 8
ii. 13
iii. Less than or equal to 12.
Or
From a pack of 52 playing cards jacks, queens, kings, and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability othat the card drawn is
i. A black queen
ii. A red card
iii. A ten
32. Draw the graphs of the equations
5x - y = 5 and 3x - y = 3. Determine the coordinates of the vertices of the triangle formed by these lines and Y- axis.
33. Prove that
(1+cotA + tanA)(sinA- cosA)/(sec³A - cosec³A)= sin²A cos²A.
Directions (Q.nos. 34-36 are of 5 marks each)
34. Ram and Shyam together have 55 marbles. Both of them lost 5 marbles they row have is 164. Find out how many marbles they had to start with?
35. Construct a tangent to a circle of radius 5cm from a point on the concentric circle of radius 7cm and measure it's length. Also, verify the measurements of actual calculation.
36. From a solid cylinder whose height is 12cm and diameter is 10cm, a conical cavity of same height and same diameter is hollowed out. Find the volume and total surface area of the remaining solid.
Or
A right angled triangle whose sides are 3cm and 4cm (other than hypotenuse) is made to revolve about it's hypotenuse. Find the volume and surface area of the double cone so formed. [Choose the value of the as found appropriate.]
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