Let p, q and r be the sides opposite to the angles P ,Q,R respectively in a ∆ PQR. If r 2 sin P sin Q = pq, then the triangle is

acute angled but not equilateral

JEE Questions for Maths Properties Of Triangle Quiz 2

The area of the ∆ ABC, in which a = 1, b = 2, ∠C = 60^o, is

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4 sq units
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1/2 sq units
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√3/2 sq units
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√3 sq units

In a ∆ABC, b = √3, c = 1 and ∠A = 30^o, then the largest angle of the triangle is

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60o
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135o
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90o
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120o

The angles of a triangle are in the ratio 3 : 5 : 10. Then, the ratio of the smallest side to the greatest side is

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1 : sin 10o
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1 : 2 sin 10o
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1 : cos 10o
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1 : 2 cos 10o

If sin A : sin B : sin C = 3 : 4 : 5, then cos A : cos B is equal to

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4 : 3
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5 : 3
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3 : 4
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3 : 5

If two angles of a triangle are 45^o and tan^-1 (2), then the third angle is

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60o
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75o
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tan-1 3
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90o

If ∆ = a² - (b - c)², where ∆ is the area of ∆ABC, then tan A is equal to

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15/16
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8/17
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8/15
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1/2
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11/15

If in a ∆ABC, a = 5, b = 4, A = π/2 + B, then C

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is tan-1 (1/2)
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is tan-1 (9/40)
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cannot be evaluated
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is tan-1 (1/9)
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is 2 tan-1 (1/40)

In a ∆ABC, a (cos² B + cos² C ) + cos A (c cos C + b cos B) is equal to

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a
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b
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c
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a + b + c

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a
0%
b
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c
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0

Two sides of a triangle are given by the roots of the equations x² - 5x + 6 = 0 and the angle between the sides is π/3. Then, the perimeter of the triangle is

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5 + √2
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5 + √3
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5 + √5
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5 + √7

If a, b and c are the sides of a triangle such that a⁴ + b⁴ + c⁴ = 2c² (a² + b²), then the angles opposite to the side c is

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45o or 90o
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30o or 135o
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45o or 135o
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60o or 120o

If in a ∆ABC, r₁ = 2r₂ = 3 and r₂ = 6, then a equals

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4
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1
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2
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3

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right angled
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isosceles
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equilateral
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None of these

In a ∆ABC, if a = 3, b = 4, c = 5, then the distance between iis incentre and circumcentre is

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1/2
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√3/2
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3/2
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5/2
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√5/2

In an equilateral triangle of side 2√3 cm, the circumradius e is

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1 cm
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√3 cm
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2 cm
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2√3 cm
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4 cm

In ∆ABC, ∠A = π/2, b = 4, c = 3, then the value of R/r is

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5/2
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7/2
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9/2
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35/24

In ∆ABC with usual notation, observe the two statements given below
I . rr₁r₂r₃ = ∆²
II. r₁r₂ + r₂r₃ + r₃r₁ = s²
Which of the following is correct?

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Both I and II are correct
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I and II are incorrecty
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I is incorrect, II is correct
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I is correct, II is correct

In a triangle, if r₁ + r₃ = k cos² B/2, then k is equal to

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R
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2R
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3R
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4R

If PQR be a triangle of area ∆ with a = 2, b = 7/2 and c = 5/2, where a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R, respectively.
Maths-Properties of Triangle-46442.png

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3/4∆
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45/4∆
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(3/4∆)2
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(45/4∆)5

Let p, q and r be the sides opposite to the angles P ,Q,R respectively in a ∆ PQR. If r² sin P sin Q = pq, then the triangle is

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equilateral
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acute angled but not equilateral
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obtuse angled
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right angled

Let ABC be a triangle such that ∠ACB = π/6 and let a, b and 6 c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a = x² + x + 1, b = x² - 1 and c = 2x + 1 is (are )

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-(2 + √3)
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1 + √3
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2 + √3
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4√3

If angles A, B and C are in AP, then (a + c)/b is equal to

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0%
2)
0%
0%

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a2 + b2 - c2
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C2 + a2 - b2
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b2 - a2 - c2
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c2 - a2 - b2

The sides BC, CA and AB of a ∆A BC are of lengths a, b and c, respectively. If D is the mid-point of BC and AD is perpendicular to AC, then the value of cos A cos C is