SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions

In the above figure, ∠L = 35°, find :

1. m(arc MN)
2. m(arc MLN)

Solution :

1. ∠L = `1/2` m(arc MN) ............(By inscribed angle theorem)
   ∴ `square = 1/2` m(arc MN)
   ∴ 2 × 35 = m(arc MN)
   ∴ m(arc MN) = `square`
2. m(arc MLN) = `square` – m(arc MN) ...........[Definition of measure of arc]
   = 360° – 70°
   ∴ m(arc MLN) = `square`

In the given figure, ∠MNP = 90°, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.

In the given figure, ∠QPR = 90°, seg PM ⊥ seg QR and Q–M–R, PM = 10, QM = 8, find QR.

In the given figure, chord MN and chord RS intersect at point D.
(1) If RD = 15, DS = 4, MD = 8 find DN
(2) If RS = 18, MD = 9, DN = 8 find DS

In right-angled ΔABC, BD ⊥ AC. If AD= 4, DC= 9, then find BD.

In the given figure,
(1) m(arc CE) = 54°, m(arc BD) = 23°, find measure of ∠CAE.
(2) If AB = 4.2, BC = 5.4, AE = 12.0, find AD.
(3) If AB = 3.6, AC = 9.0, AD = 5.4, find AE.

As shown figure, ∠DFE = 90°, FG ⊥ ED, if GD = 8, FG = 12, then EG = ?

The value of 2tan45° – 2sin30° is ______.

In the figure, ΔPQR is right angled at Q, seg QS ⊥ seg PR. Find x, y.

If `sec alpha=2/sqrt3`  , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.

Prove that sin⁶θ + cos⁶θ = 1 – 3 sin²θ. cos²θ.

If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.

Prove that:

sec²θ + cosec²θ = sec²θ x cosec²θ

In triangle ABC, ∠C=90°. Let BC= a, CA= b, AB= c and let 'p' be the length of the perpendicular from 'C' on AB, prove that:

1. cp = ab

2. `1/p^2=1/a^2+1/b^2`

if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`

Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`

Prove that, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of remaining two sides.

Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ

Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)

Identify, with reason, if the following is a Pythagorean triplet.
(4, 9, 12)