Dakshana Mock Test Season IX

Dakshana Mock Test Season IX

1] If ABC is a right angled triangle at B and M, N are the mid-points of AB and BC, then 4(AN² + CM²) is equal to

i. 4AC²
ii. 6AC²
iii. 5AC²
iv. 5AC²/4

2] At the foot of mountain the elevation of its summit is 45°, after ascending 1000m towards the mountain up a stop of 30° inclination, the elevation is found to be 60°. Find the height of the mountain.

i. 1.3km
ii. 1.366km
iii. 2.72km
iv. None of these

3] If 4 points A(6,3), B(-3,5), C(4,-2) and D(x,3x) are given such away that ar(DBC) / ar(ABC) = 1/2, then the value of x is

i. 3/8 or -14/8
ii. 2 or -3
iii. 11/8 or -3/8
iv. None of these

4] The orthocentre of the triangle ABC is B and the circumcentre is S(a,b). If A is the origin then the co-ordinate of C are

i. (2a,2b)
ii. (a/2,b/2)
iii. (√(a²+b²),0)
iv. None of these

5] If the centroid of the triangle formed by the points (a,b), (b,c), (c,a) is at the origin, then a³ + b³ + c³ = ?

i. abc
ii. a-b-c
iii. 3abc
iv. 0

6] A person on the top of a tower observes a scooter moving with uniform velocity towards the base of the tower. He finds that the angle of depression changes from 30° to 60° in 18 minutes. The scooter will reach the base of the tower in next ____.

i. 9 minutes
ii. 18/√3-1 minutes
iii. 6√3 minutes
iv. None of these

7] In a triangle ABC, D and E are points on AB and AC, respectively such that DE II BC and AD = 3x-2, AE = 5x-4, BD = 7x-5 and CE = 5x-3, therefore the value of x is

i. only 1
ii. only 7/10
iii. 1 or 7/10
iv. 10/7

8] sin⁶A + cos⁶A is equal to

i. 1 - 3sin²Acos²A
ii. 1 - 3sinAcosA
iii. 1 + 3sin²Acos²A
iv. 1

9] ABC is a triangle right angled at B and P and Q are points on AB and BC, respectively. Then, which of the following option is correct based on given information.

i. AQ² + CP² = 2(AC² + PQ²)
ii. AQ² + CP² = AC² + PQ²
iii. AQ² + CP² = 1/2(AC² + PQ²)
iv. AQ + CP = 1/2(AC + PQ)

10] The elevation of a tower at a station A due north of it is 45° and at a station B due west of A is 30°. If AB = 40m, find the height of the tower.

i. 20m
ii. 28.28m
iii. 38.5m
iv. None of these

11] O is orthocentre of a triangle PQR, which is formed by joining the mid-points of the sides of a triangle ABC.
Fill in the blanks.
O is _____ of triangle ABC

i. orthocentre
ii. incentre
iii. circumcentre
iv. centroid

12] ABC is a right-angled triangle at A and AD is perpendicular to the hypotenuse. Then, BD/CD is equal to

i. AB²/AC²
ii. AB/AD
iii. AC/AB
iv. AD/AB

13] If secα and cosecα are the roots of the equation x2-px+q=0, then

i. p2+q2=2q
ii. p2-q2=2q
iii. p2+q2=2p
iv. p2-q2=2p

14] The bisectors of the angles of an acute angled triangle ABC meets BC, CA and AB at X, Y and Z respectively, then

i. BX*CY*AZ = XC*YA*ZB
ii. BX*AY*AZ = XC*CY*ZB
iii. BX*ZB*AZ = XC*YA*CY
iv. None of these

15] If 0° < x < 45° and 45° < y < 90°, then which one of the following must be correct?

i. sinx = siny
ii. sinx < siny
iii. sinx > siny
iv. None of these

16] If the number 2345p60q is exactly divisible by 3 and 5 then, maximum value of p+q is

i. 13
ii. 10
iii. 11
iv. 12

17] A vertical tower PQ subtends equal angles of 30° at each of the two places A and B, 60 meter apart on the ground. If AB subtends an angle of 60° at P(the foot of the tower), then the height of the tower is

i. 20√3 meter
ii. 20 meter
iii. 60√3 meter
iv. 60 meter

18] In a triangle ABC, right-angled at B, there is a point D on AB and point E on AC such that DE is perpendicular to AC. Therefore, ∠ABC = ∠AED = 90°. Then, state which of the given statements are true.

Statements:
I. ABC and AED are similar triangles.
II. The four points B, C, E and D will lie on a circle.

i. Only I
ii. Only II
iii. Both I and II
iv. None of these

19] If secA + tanA = x, then secA = ?

i. (x²-1)/x
ii. (x²-1)/2x
iii. (x²+1)/x
iv. (x²+1)/2x

20] The value of cosx° - sinx°(0 ≤ x < 45) is

i. 0
ii. positive
iii. negative
iv. sometimes positive and sometimes negative

21] A tower subtends an angle α at a point A in the plane of its base and the angle of depression of the foot of the tower at a height 'b' just above A is β. Then, the height of the tower is

i. b*tanα*cotβ
ii. b*cotα*tanβ
iii. b*tanα*tanβ
iv. b*cotα*cotβ

22] If cosθ + secθ = 2, then the value of cos²θ + sec²θ is

i. 1
ii. 2
iii. 4
iv. None of these

23] If tanθ = p/q, then the value of (psinθ - qcosθ)/(psinθ + qcosθ) is

i. (p²-q²)/(p²+q²)
ii. (p²+q²)/(p²-q²)
iii. 0
iv. None of these

24] The straight lines x+y=0, 3x+y-4=0, x+3y-4=0 form a triangle which is

i. Isosceles
ii. Equilateral
iii. Right angled
iv. None of these

25] The points (1,2), (3,8) and (x,20) are collinear, when x is equal to

i. 4
ii. 5
iii. 6
iv. None of these

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