ΔDEF ~ ΔMNK. If DE = 5, MN = 6, then find the value of A(ΔDEF)/A(ΔMNK)

Concept: Similar Triangles

In the following figure, in ΔABC, ∠B = 90°, ∠C = 60°, ∠A = 30°, AC = 18 cm. Find BC.

Concept: 30 - 60 - 90 and 45 - 45 - 90 Theorem

In the following figure, m(arc PMQ) = 130^{o}, find ∠PQS.

Concept: Angle Subtended by the Arc to the Point on the Circle

If the angle θ= –60º, find the value of cosθ.

Concept: Trigonometric Ratios of Complementary Angles

Find the slope of the line with inclination 30° .

Concept: Slope of a Line

Using Euler’s formula, find V if E = 30, F = 12.

Concept: Euler's Formula

In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR.

Concept: Similarity of Triangles

In the following figure, a tangent segment PA touching a circle in A and a secant PBC is shown. If AP = 15, BP = 10, find BC.

Concept: Tangent - Secant Theorem

Draw an equilateral ΔABC with side 6.2 cm and construct its circumcircle

Concept: Construction of Triangle If the Base, Angle Opposite to It and Either Median Altitude is Given

For the angle in standard position if the initial arm rotates 25° in anticlockwise direction, then state the quadrant in which terminal arm lies (Draw the figure and write the answer).

Concept: Angles in Standard Position

Find the area of sector whose arc length and radius are 10 cm and 5 cm respectively

Concept: Areas of Sector and Segment of a Circle

Find the surface area of a sphere of radius 4.2 cm. (π=22/7)

Concept: Surface Area of a Combination of Solids

Adjacent sides of a parallelogram are 11 cm and 17 cm. If the length of one of its diagonal is 26 cm, find the length of the other.

Concept: Appolonius Theorem

In the following figure, secants containing chords RS and PQ of a circle intersects each other in point A in the exterior of a circle if m(arc PCR) = 26°, m(arc QDS) = 48°, then find:

(i) m∠PQR

(ii) m∠SPQ

(iii) m∠RAQ

Concept: Angle Subtended by the Arc to the Point on the Circle

Draw a circle of radius 3.5 cm. Take any point K on it. Draw a tangent to the circle at K without using centre of the circle.

Concept: Construction of Tangent Without Using Centre

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

Concept: Trigonometric Identities

Write the equation of the line passing through the pair of points (2, 3) and (4, 7) in the form of y = mx + c.

Concept: General Equation of a Line

Prove that “The lengths of the two tangent segments to a circle drawn from an external point are equal.”

Concept: Number of Tangents from a Point on a Circle

A person standing on the bank of river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. `(sqrt 3=1.73)`

Concept: Heights and Distances

A (5, 4), B (-3, -2) and C (1, -8) are the vertices of a triangle ABC. Find the equations of the median AD and line parallel to AC passing through the point B.

Concept: General Equation of a Line

In the following figure, AE = EF = AF = BE = CF = a, AT ⊥ BC. Show that AB = AC = `sqrt3xxa`

Concept: Similarity in Right Angled Triangles

ΔSHR ~ ΔSVU. In ΔSHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and `(SH)/(SV)=3/5`. Construct ΔSVU.

Concept: Division of a Line Segment

Water flows at the rate of 15 m per minute through a cylindrical pipe, having the diameter 20 mm. How much time will it take to fill a conical vessel of base diameter 40 cm and depth 45 cm?

Concept: Surface Area of a Combination of Solids