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

In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS² + TQ² = TP² + TR² (As shown in the figure, draw seg AB || side SR and A-T-B)

Some question and their alternative answer are given. Select the correct alternative.

If a, b, and c are sides of a triangle and a² + b² = c², name the type of triangle.

Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.

Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was \[15\sqrt{2}\]

In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:
4(BL² + CM²) = 5 BC²

Prove that:

`(sin^2θ)/(cosθ) + cosθ = secθ`

In ∆ABC, seg AD ⊥ seg BC, DB = 3CD.

Prove that: 2AB² = 2AC² + BC²

Prove that:

Sin⁴θ - cos⁴θ = 1 - 2cos²θ

In a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)

Prove that:

`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.

Prove that:

`"tanθ"/("secθ"  –  1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`

The radius of a circle is 10 cm. The measure of an arc of the circle is 54^°. Find the area of the sector associated with the arc. (\[\pi\]= 3.14 )

The measure of an arc of a circle is 80° and its radius is 18 cm. Find the length of the arc. (π = 3.14)

Area of a sector of a circle of radius 15 cm is 30 cm² . Find the length of the arc of the sector.

If sin θ = `11/61`, find the values of cos θ using trigonometric identity.

Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`

The area of a sector of a circle of 6 cm radius is 15 π sq. cm. Find the measure of the arc and the length of the arc corresponding to the sector.

In the given figure, seg AB is a chord of a circle with centre P. If PA = 8 cm and distance of chord AB from the centre P is 4 cm, find the area of the shaded portion. ( \[\pi\] = 3.14, \[\sqrt{3}\]= 1.73 )

In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region