SSC (English Medium) 10th Standard - Maharashtra State Board Question Bank Solutions

Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:

sin θ × cosec θ = ______

Measure of an arc of a sector of a circle is 900 and its radius is 7cm. Find the perimeter of the sector.
(A) 44 cm (B) 25 cm (C) 36 cm (D) 56 cm

In ΔMNP, ∠MNP = 90˚, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.

Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.

In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.

Find the value of sin 30° + cos 60°.

Choose the correct alternative:

1 + tan² θ = ?

If sec θ = `25/7`, then find the value of tan θ.

In the given figure, seg AB is a diameter of a circle with centre O. The bisector of ∠ACB intersects the circle at point D. Prove that, seg AD ≅ seg BD.
Complete the following proof by filling in the blanks.

Proof: Draw seg OD.

∠ACB = ______      ...(Angle inscribed in semicircle)
∠DCB = ______      ...(CD is the bisector of ∠C)
m(arc DB) = ______   ...(Inscribed angle theorem)
∠DOB = ______      ...(Definition of measure of an arc)(I)

seg OA ≅ seg OB       ...( ____________ )(II)

∴ line OD is ______ of seg AB.     ...[From (I) and (II)]
∴ seg AD ≅ seg BD.

If tan θ = 2, where θ is an acute angle, find the value of cos θ. 

Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A. 

If the angles of a triangle are 30°, 60°, and 90°, then shown that the side opposite to 30° is half of the hypotenuse, and the side opposite to 60° is `sqrt(3)/2` times of the hypotenuse.

If sin θ = `1/2`, then find the value of θ. 

Choose the correct alternative: 

In right-angled triangle PQR, if hypotenuse PR = 12 and PQ = 6, then what is the measure of ∠P? 

A circle is inscribed in square ABCD of side 14 cm. Complete the following activity to find the area of the shaded portion.
  Activity:

Area of square ABCD = ______

= 14²  
 = 196 cm² 
Area of circle = πr²     = `22/7xx 7^2`   
= ____ cm²

Area of shaded portion = Area of square ABCD – Area of circle   

 = 196 – _______

= _____ cm²

If cosθ = `5/13`, then find sinθ. 

Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle. 

Find the length of diagonal of the square whose side is 8 cm.

Find the side of the square whose diagonal is `16sqrt(2)` cm.

If sec θ = `25/7`, find the value of tan θ.

Solution:

1 + tan² θ = sec² θ

∴ 1 + tan² θ = `(25/7)^square`

∴ tan² θ = `625/49 - square`

= `(625 - 49)/49`

= `square/49`

∴ tan θ = `square/7` ........(by taking square roots)