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

Base of a triangle is 9 and height is 5. Base of another triangle is 10 and height is 6. Find the ratio of areas of these triangles.

In the given figure, BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find `("A"(∆"ABC"))/("A"(∆"ADB"))`

In adjoining figure, PQ ⊥ BC, AD ⊥ BC then find following ratios.

1. `("A"(∆"PQB"))/("A"(∆"PBC"))`
2. `("A"(∆"PBC"))/("A"(∆"ABC"))`
3. `("A"(∆"ABC"))/("A"(∆"ADC"))`
4. `("A"(∆"ADC"))/("A"(∆"PQC"))`

 In trapezium PQRS, side PQ || side SR, AR = 5AP, AS = 5AQ then prove that, SR = 5PQ 

In trapezium ABCD, side AB || side DC, diagonals AC and BD intersect in point O. If AB = 20, DC = 6, OB = 15 then Find OD. 

∆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`.

∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm. `"AM"/"AH" = 7/5`. Construct ∆AHE.

∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1 cm, ∠B = 40°, BC = 4.8 cm, \[\frac{AC}{LN} = \frac{4}{7}\]. Construct ∆ABC and ∆LBN.

Construct ∆PYQ such that, PY = 6.3 cm, YQ = 7.2 cm, PQ = 5.8 cm. If \[\frac{YZ}{YQ} = \frac{6}{5},\] then construct ∆XYZ similar to ∆PYQ.

Find the distance between the following pair of point.

 P(–5, 7), Q(–1, 3)

Find the distance between the following pair of points.

R(0, -3), S(0, `5/2`)

Find the distance between the following pair of points.

L(5, –8), M(–7, –3)

Find the distance between the following pair of point.

T(–3, 6), R(9, –10)

Find the distance between the following pairs of point.

W `((- 7)/2 , 4)`, X (11, 4)

Determine whether the points are collinear.

A(1, −3), B(2, −5), C(−4, 7)

Determine whether the points are collinear.

 L(–2, 3), M(1, –3), N(5, 4)

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

Out of the dates given below which date constitutes a Pythagorean triplet?

Determine whether the point is collinear.

R(0, 3), D(2, 1), S(3, –1)

Determine whether the points are collinear.

P(–2, 3), Q(1, 2), R(4, 1)