SSC (English Medium) 10th Standard - Maharashtra State Board Important Questions

Find the perimeter of a square if its diagonal is `10sqrt2` cm:

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

In ΔPQR, seg PM is a median, PM = 9 and PQ² + PR²  = 290. Find the length of QR. 

Find the side of a square whose diagonal is `10sqrt2` cm.

Draw ∠ABC of measure 105° and bisect it.

Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.

Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.

∆PQR ~ ∆LTR. In ∆PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆PQR and ∆LTR, such that `"PQ"/"LT" = 3/4`.

Prove that “That ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.”

Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.

Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.

∆PQR ~ ∆LTR. In ∆PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆PQR and ∆LTR, such that `"PQ"/"LT" = 3/4`.

Find distance between point Q(3, –7) and point R(3, 3)

Solution: Suppose Q(x₁, y₁) and point R(x₂, y₂)

x₁ = 3, y₁ = –7 and x₂ = 3, y₂ = 3

Using distance formula,

d(Q, R) = `sqrt(square)`

∴ d(Q, R) = `sqrt(square - 100)`

∴ d(Q, R) =  `sqrt(square)`

∴ d(Q, R) = `square`

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

Prove that:

sec²θ + cosec²θ = sec²θ x cosec²θ

Prove that: If the angles of a triangle are 45° – 45° – 90°^, then each of the perpendicular sides is \[\frac{1}{\sqrt{2}}\]times the hypotenuse.”

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

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