SSC (Marathi Semi-English) इयत्ता १० वी - Maharashtra State Board Question Bank Solutions

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)

Identify, with reason, if the following is a Pythagorean triplet.

(5, 12, 13)

Identify, with reason, if the following is a Pythagorean triplet.
(24, 70, 74)

Identify, with reason, if the following is a Pythagorean triplet.
(10, 24, 27)

Identify, with reason, if the following is a Pythagorean triplet.
(11, 60, 61)

For finding AB and BC with the help of information given in the figure, complete following activity.

AB = BC ..........

∴ ∠BAC =

∴ AB = BC = × AC

                 = × `sqrt8`

                 = × `2sqrt2`

                 =

In the given figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, find (1) EG (2) FD and (3) EF

In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ² = 4PM² – 3PR².

Walls of two buildings on either side of a street are parallel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street, its top touches the window of the other building at a height 4.2 m. Find the width of the street.

In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.