Maths Sample paper 5, Part- B for class 10th

 Maths Sample Paper

Part - B (52 marks)

20. Case Study IV (4 marks)

Similar Triangles

Two geometrical figures are said to be similar figures, if they have same shape but not necessarily the same size. Some examples of similar figures are given below:

Two triangles are said to be similar, if 

(i) their corresponding angles are equal.

(ii) their corresponding sides are proportional (i.e. the ratios of the lengths of corresponding sides are equal).

Some of the criterion used for making similarity are AAA, SSS and SAS.

Through the mid point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting  AC in L and AD produced in E.

(a) The figure formed in the given statement, AE is equal to

i) AB

ii) 2BC 

iii) 3BC

iv) 4BC

(b) Which similarity criterion is used for making  similarity of triangles ∆AEL and ∆CBL.

i. AA

ii. SSS

iii. SAS

iv. None of these

(c) Suppose ∆AEL and ∆CBL is similar, then ar(∆AEL)/ar(∆CBL) is

i. AE/CB

ii. (AE/CB)²

iii. (AE/BL)²

iv. None of these

(d) If area of two similar triangles are 25cm² and 81cm², then find the ratio of their corresponding sides.

i. 5/9

ii. 7/9

iii. 1/9

iv. 9/5

(e) If one angle of a triangle is equal to the one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. The criterion used to represent the above statement is

i. ASA

ii. SAS

iii. SSA

iv. None of these

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Part - B (48 marks)

Directions (Q.nos. 21 - 26) is of 2 marks each.

21. Solve the quadratic equation

x+3/x-2  -  1-x/x = 17/4 by factorization method.

Or

If -4 is a root of the quadratic equation

 x² +px-4 = 0 and the quadratic equation

 x² +px+ k= 0 has equal roots, find the value of k.

22. If the mean of the following distribution is 6, find the value of p.

x           2         4        6        10         p+5

f            3         2        3         1            2 

Or 

The mode of the following series is 36, then find the value of f.

Class            Frequency

Interval

0-10                    8

10-20                 10

20-30                  f

30-40                16

40-50                12

50-60                 6

60-70                7

23. If cost -sin I =√2 sinø, then prove that cost +sinø =√2 cost.

24. Divide the line segment of length 9cm internally in the ration of 4:3.

25. Write HCF and LCM of the smallest odd  composite number and the smallest odd prime number. If an odd number p divides we, then will it divide Q3 also? Explain.

26. The vertices of ∆ABC are A(4,6), B(1,5) and C(7,2). A line is drawn to intersect sides AB and AC at D and E, respectively such that

AD/AB = AE/AC =1/4. Determine the coordinates of D and E.

Directions:- (Q.nos. 27-33 are of 3 marks each)

27. In a two digit number, the ten's digit is three times the unit's digit. When the number is decreased by 54, the digits are reversed. Find the number.

28. Find the solution of the equation

x² + x -(a+1) (a+2) = 0.

29. In ∆ABC, AD is perpendicular to BC and BD = 3CD. Prove that 2AB² = 2AC² + BC²

Or

ABC is an isosceles triangle in which AB= AC =10cm and BC= 12cm. PQRS is a rectangle inside the isosceles triangle. If PQ =SR =y cm, PS= QR =2x, then prove that x= 6-3y/4.

30. A decorative block as shown in figure is made of two solids, a cube and a hemisphere.

The base of the block is the cube with edge of 5 cm and the hemisphere attached on the top has a diameter of 4.2cm. If the block is to be painted, then find the total area to be painted. (Take the =22/7)

Or

A cone of maximum size is cut out from a cube of edge 14cm. Find the surface area of the remaining solid left out after the cone is cut- out.

31. The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 15sec, the angle of elevation changes to 30°. If the jet plane is flying at a constant height of 1500√3m, then find the speed of the jet plane.

32. If  a and ẞ are the zeroes of the quadratic equation polynomial  f(x) = 3x² -4x +1, find the quadratic polynomial whose zeroes are a²/ẞ and ẞ²/a.

33. If tanø + sinø =m and tanø - sincø=n, then show that (m² - n²)1 = 16 mn or (m² - n²) =4√m√n.

Directions:- (Q.nos from 34-36 are of 5 marks each)

34. In the given figure, ABC is a right angled triangle, right angled at A. Semi - circles are drawn on AB, AC and BC as diameters.

Find the area of the shaded region.

Or

In the following figure, ABC is a right angled triangle at A. Find the area of the shaded region if AB=6cm, BC= 10cm and I is the centre of in circle of ∆ABC.

35. Out of a pack of 52 playing cards, two black kings and 4 red cards(not king) are removed. A card is drawn at random. Find the probability that the card drawn is 

i. A black jack

ii. A black queen

iii. A black card

36. If is an AP, the sum of m terms is equal to n and the sum of n terms is equal to m, then prove that the sum of (m+n) terms is -(m+n)

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Posted by :- Anuranjan Gadekar

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