MCA NIMCET Properties Of Triangle Previous Year Question Paper and Solution with PDF

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MCA NIMCET Previous Year Questions (PYQs)

MCA NIMCET Properties Of Triangle PYQ

Qus : 1MCA NIMCET PYQ

If $\Delta=a^2-(b-c)^2$, where $\Delta$ is the are of the triangle ABC, then $tanA=$

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2019 PYQ

Solution

Qus : 2MCA NIMCET PYQ

In a triangle ABC, if the tangent of half the difference of two angles is equal to one third of the tangent of half the sum of the angles, then the ratio of the sides opposite to the angles is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2022 PYQ

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Qus : 3MCA NIMCET PYQ

In an acute-angled ΔABC the least value of secA+secB+secC is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 4MCA NIMCET PYQ

If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in HP, then sin A, sin B, sin C are in

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2017 PYQ

Solution

If altitudes of a triangle are in HP then its side will be in AP because sides are inverse proportion to height as area is constant. a, b, c are sides of triangle.

a, b, c are in A.P.

sin A, sin B, sin C are in A.P.

Qus : 5MCA NIMCET PYQ

In a triangle, if the sum of two sides is x and their product is y such that (x+z)(x-z)=y, where z is the third side of the triangle , then triangle is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2021 PYQ

Solution

Qus : 6MCA NIMCET PYQ

In a triangle ABC, $a\cos ^2\frac{C}{2}+\, c\, \, {\cos }^2\frac{A}{2}=\frac{3b}{2}$ then the sides of the triangle are in

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2021 PYQ

Solution

Qus : 7MCA NIMCET PYQ

In a triangle ABC, let angle C = π/2. If R is the inradius and R is circumradius of the triangle ABC, then 2(r + R) equals

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2017 PYQ

Solution

Qus : 8MCA NIMCET PYQ

In a triangle ABC, angle A=90° and D is the midpoint of AC. What is the value of

equal to?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2018 PYQ

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Qus : 9MCA NIMCET PYQ

What is the largest area of an isosceles triangle with two edges of length 3?

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2017 PYQ

Solution

Qus : 10MCA NIMCET PYQ

If A, B and C is three angles of a ΔABC, whose area is Δ. Let a, b and c be the sides opposite to the angles A, B and C respectively. Is $s=\frac{a+b+c}{2}=6$, then the product $\frac{1}{3} s^{2} (s-a)(s-b)(s-c)$ is equal to

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 11MCA NIMCET PYQ

The perimeter of a $\Delta ABC$ is 6 times the arithmetic mean of the sines of its angles. If the side a is 1, then the angle A is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2023 PYQ

Solution

Quick Solution

Given: Perimeter = 6 × Arithmetic Mean of sin A, sin B, sin C

Using Law of Sines: $ \frac{a}{\sin A} = 2R $, and a = 1 ⇒ $ \sin A = \frac{1}{2R} $

Assume $ A = 30^\circ \Rightarrow \sin A = \frac{1}{2} \Rightarrow 2R = 2 $

⇒ b = 2 sin B, c = 2 sin C

Perimeter = $ 1 + b + c = 1 + 2 \sin B + 2 \sin C $

Mean = $ \frac{\sin A + \sin B + \sin C}{3} $

Check: $ 1 + 2\sin B + 2\sin C = 6 \cdot \frac{1/2 + \sin B + \sin C}{3} $ ✅

✅ Final Answer: 30°

Qus : 12MCA NIMCET PYQ

In ΔABC, if a = 2, b = 4 and ∠C = 60°, then A and B are respectively equal to

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2014 PYQ

Solution

Qus : 13MCA NIMCET PYQ

If the angles of a triangle are in the ratio 2 : 3 : 7, then the ratio of the sides opposite to these angles is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2015 PYQ

Solution

Qus : 14MCA NIMCET PYQ

A harbour lies in a direction 60° South of West from a fort and at a distance 30 km from it, a ship sets out from the harbour at noon and sails due East at 10 km an hour. The time at which the ship will be 70 km from the fort is

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MCA NIMCET Previous Year PYQMCA NIMCET NIMCET 2015 PYQ

Solution

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