.Simplify .Strategize .
Succeed
s- cube cl asses
(204-206, Aagam orchid , Vesu , 9601832536)
MM:- 50
SECTION – A
Questions 1 to 10 carry 1 mark each.
1. In the ∆ABC, DE ∥ BC and AD = 3x − 2, AE = 5x − 4, BD = 7x − 5, CE = 5x − 3, then find the
value of x
(a) 1 (b) 7/10 (c) both (a) & (b) (d) none of these
2. ABCD is a trapezium with AD ∥ BC and AD = 4cm. If the diagonals AC and BD intersect each
other at O such that AO/OC = DO/OB =1/2, then BC =
(a) 6cm (b) 7cm (c) 8cm (d) 9cm
3. In the given figure, DE ∥ BC, AE = a units, EC =b units, DE =x units and
BC = y units. Which of the following is true?
ab ax ay x a
(a) x (b) y (c) x (d)
ay ab ab y b
4. ΔABC~ΔPQR. If AM and PN are altitudes of ΔABC and ΔPQR
respectively and AB2 : PQ2 = 4 : 9, then AM : PN =
(a) 3 : 2 (b) 16 : 81 (c) 4 : 9 (d) 2 : 3
5. The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. PQ/AB
is equal to
(a) 7/8 (b) 6/7 (c) 7/6 (d) 8/7
6. In the below left sided figure, if M and N are points on the sides OP and OS respectively of
∆OPS, such that MN || PS, then the length of OP is :
(a) 6.8 cm (b) 17 cm (c) 15.3 cm (d) 9.6 cm
7. In the above right sided figure ∆ABC is shown. DE is parallel to BC. If AD = 5 cm, DB = 2.5 cm
and BC = 12 cm, then DE is equal to
(a) 10 cm (b) 6 cm (c) 8 cm (d) 7.5 cm
8. In ∆ABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the length of AC.
(a) 12 cm (b) 20 cm (c) 6 cm (d) 14 cm
In the following questions 9 and 10, a statement of assertion (A) is followed by a statement of reason
(R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
9. Assertion (A): D and E are points on the sides AB and AC respectively of a ΔABC such that AD
= 5.7cm, DB = 9.5cm, AE = 4.8cm and EC = 8cm then DE is not parallel to BC.
Reason (R): If a line divides any two sides of a triangle in the same ratio then it is parallel to the
third side.
10. Assertion (A): D and E are points on the sides AB and AC respectively of a ΔABC such that
DE║BC then the value of x is 4, when AD = x cm, DB = (x – 2) cm, AE = (x + 2) cm and EC =
(x – 1) cm.
Reason (R): If a line is parallel to one side of a triangle then it divides the other two sides in the
same ratio.
SECTION – B
Questions 11 to 14 carry 2 marks each.
11. The line segment AB joining the points A(3, –4) and B(1, 2) is trisected at the points P(p, –2)
and Q(5/3, q). Find the values of p and q.
12. Diagonals AC and BD of trapezium ABCD with AB||DC intersect each other at point O. Show
that OA/OC = OB/OD.
13. Find the middle terms of the A.P. 7, 13, 19 .... 241.
14. Determine the A.P. whose third term is 16 and 7th term exceeds the 5th term by 12.
SECTION – C
Questions 15 to 18 carry 3 marks each.
15. D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC, prove that CA2 = CB.
CD
16. In the given figure, MNOP is a parallelogram and AB || MP. Prove that QC || PO.
OR
A girl of height 100 cm is walking away from the base of a lamp post at a speed of 1.9 m/s. If the
lamp is 5 m above the ground, find the length of her shadow after 4 seconds.
17. Which term of the A.P. 3, 15, 27, 39, .... will be 120 more than its 21st term?
18. A bird is sitting on the top of a tree, which is 80 m high. The angle of elevation of the bird from
a point on the ground is 45°. The bird flies away from the point of observation horizontally and
remains at a constant height. After 2 seconds, the angle of elevation of the bird from the point of
observation becomes 30°. Find the speed of the flying bird.
SECTION – D
Questions 19 to 24 carry 5 marks.
cos 2 B cos 2 A sin 2 A sin 2 B 20. cot A cosec A 1 1 cos A
19. tan 2 A tan 2 B
cos 2 B.cos 2 A cos 2 A cos 2 B cot A – cosec A + 1 sin A
2
21. sin cos 1
1 sin 22. sin cos3
1 sin cos
sin cos 1 cos 1 cot cos sin
23. sin A cos A 24. tan cot
1 1 tan cot 1 sec cosec
sec A tan A 1 cosec A cot A 1 1 cot 1 tan
