TG EAMCET Mathematics MCQs: Practice Questions for Engineering Aspirants

141. If \( \Delta ABC \) is a triangle with sides \( a \), \( b \), and \( c \), then the relation between the sides and angles of the triangle is given by:

a) Law of Sines
b) Law of Cosines
c) Law of Tangents
d) Both a and b

Answer: d) Both a and b

142. In a triangle, if the angle \( A = 90^\circ \), then the area of the triangle is given by:

a) \( \frac{1}{2} \times a \times b \)
b) \( \frac{1}{2} \times b \times c \)
c) \( \frac{1}{2} \times c \times a \)
d) \( \frac{1}{2} \times a \times b \times c \)

Answer: a) \( \frac{1}{2} \times a \times b \)

143. Which of the following is the half-angle formula for \( \sin \left(\frac{A}{2}\right) \) in a triangle?

a) \( \sqrt{\frac{1 - \cos A}{2}} \)
b) \( \sqrt{\frac{1 + \cos A}{2}} \)
c) \( \sqrt{\frac{1 - \sin A}{2}} \)
d) \( \sqrt{\frac{1 + \sin A}{2}} \)

Answer: a) \( \sqrt{\frac{1 - \cos A}{2}} \)

144. The formula for the area of a triangle with sides \( a \), \( b \), and \( c \) using Heron's formula is:

a) \( \sqrt{s(s-a)(s-b)(s-c)} \), where \( s = \frac{a + b + c}{2} \)
b) \( \frac{1}{2}ab \sin C \)
c) \( \frac{1}{2}bc \sin A \)
d) \( \frac{1}{2}ac \sin B \)

Answer: a) \( \sqrt{s(s-a)(s-b)(s-c)} \), where \( s = \frac{a + b + c}{2} \)

145. The tangent of an angle in a triangle is related to the sides by:

a) \( \tan A = \frac{b}{c} \)
b) \( \tan A = \frac{a}{b} \)
c) \( \tan A = \frac{c}{a} \)
d) None of the above

Answer: d) None of the above

146. If the radius of the incircle of a triangle is denoted by \( r \), the area of the triangle is given by:

a) \( A = r \times s \), where \( s \) is the semiperimeter
b) \( A = r \times a \)
c) \( A = r \times b \)
d) \( A = r \times c \)

Answer: a) \( A = r \times s \), where \( s \) is the semiperimeter

147. The excircles of a triangle are the circles:

a) Tangent to one side and the extensions of the other two sides
b) Tangent to all three sides
c) Tangent to the two angles of the triangle
d) Located inside the triangle

Answer: a) Tangent to one side and the extensions of the other two sides

148. The relation between the sides and angles of a triangle is given by which law for an angle opposite to side \( a \)?

a) Law of Sines
b) Law of Cosines
c) Law of Tangents
d) Both a and b

Answer: a) Law of Sines

149. For any triangle, the formula for the area using the sides \( a \), \( b \), and \( c \) is:

a) \( A = \frac{1}{2}ab \sin C \)
b) \( A = \frac{1}{2}ac \sin B \)
c) \( A = \frac{1}{2}bc \sin A \)
d) All of the above

Answer: d) All of the above

150. If the semiperimeter of a triangle is \( s \), the area of the triangle with sides \( a \), \( b \), and \( c \) can be expressed as:

a) \( A = \sqrt{s(s-a)(s-b)(s-c)} \)
b) \( A = \sqrt{s(s-a)(s-b)(s-c)} \)
c) \( A = \sqrt{a \times b \times c} \)
d) \( A = \frac{1}{2} \times a \times b \)

Answer: b) \( A = \sqrt{s(s-a)(s-b)(s-c)} \)

TG EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

TG EAMCET Trigonometry MCQs

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