Duration: 2h

In the given figure, seg XY || seg BC, then which of the following statements is true?

\[\frac{AB}{AC} = \frac{AX}{AY}\]

\[\frac{AX}{XB} = \frac{AY}{AC}\]

\[\frac{AX}{YC} = \frac{AY}{XB}\]

\[\frac{AB}{YC} = \frac{AC}{XB}\]

Chapter: [1] Similarity

Select the correct alternative for the following question.

(3) If ∆ABC ~ ∆PQR and `(AB)/(PQ) = 7/5`, then ...............

(B) ∆PQR is bigger.

(C) Both triangles will be equal.

(D) Can not be decided.

Chapter: [5] Geometric Constructions

Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.

9 cm

4 cm

6 cm

\[2\sqrt{6}\] cm

Chapter: [2] Pythagoras Theorem

**Choose the correct alternative.**

∠ACB is inscribed in arc ACB of a circle with centre O. If ∠ACB = 65°, find m(arc ACB).

65°

130°

295°

230°

Chapter: [3] Circle

In the given figure, BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find \[\frac{A\left( ∆ ABC \right)}{A\left( ∆ ADB \right)} .\]

Chapter: [1] Similarity

∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm. \[\frac{AM}{AH} = \frac{7}{5} .\]Construct ∆AHE.

Chapter: [5] Geometric Constructions

Determine whether the following point is collinear.

D(–2, –3), E(1, 0), F(2, 1)

Chapter: [4] Co-ordinate Geometry

Find the surface area and the volume of a beach ball shown in the figure

Chapter: [7] Mensuration

Are the triangles in the given figure similar? If yes, by which test ?

Chapter: [1] Similarity

In ∆ABC, point M is the midpoint of side BC.

If, AB^{2 }+ AC^{2 }= 290 cm^{2}, AM = 8 cm, find BC.

Chapter: [2] Pythagoras Theorem

In the given figure, O is the centre of the ci

rcle. Seg AB, seg AC are tangent segments. Radius of the circle is *r *and *l*(AB) = *r *, Prove that, ▢ABOC is a square.

Chapter: [3] Circle

∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1cm, ∠B = 40°, BC = 4.8 cm,

Chapter: [5] Geometric Constructions

From the top of the light house, an observer looks at a ship and finds the angle of depression to be 30°. If the height of the light-house is 100 meters, then find how far the ship is from the light-house.

Chapter: [6] Trigonometry

If \[\sin\theta = \frac{7}{25}\], find the values of cosθ and tanθ.

Chapter: [6] Trigonometry

In the given figure, O is the centre of the circle and B is a point of contact. seg OE ⊥ seg AD, AB = 12, AC = 8, find

(1) AD (2) DC (3) DE.

Chapter: [3] Circle

In the given figure, a cylindrical wrapper of flat tablets is shown. The radius of a tablet is 7 mm and its thickness is 5 mm. How many such tablets are wrapped in the wrapper?

Chapter: [7] Mensuration

If ∆ABC ~ ∆PQR, A (∆ABC) = 80, A (∆PQR) = 125, then fill in the blanks. \[\frac{A\left( ∆ ABC \right)}{A\left( ∆ . . . . \right)} = \frac{80}{125} \therefore \frac{AB}{PQ} = \frac{......}{......}\]

Chapter: [1] Similarity

In the given figure, M is the centre of the circle and seg KL is a tangent segment.

If MK = 12, KL = \[6\sqrt{3}\] then find –

(1) Radius of the circle.

(2) Measures of ∠K and ∠M.

Chapter: [3] Circle

In the given figure, the vertices of square DEFG are on the sides of ∆ABC. ∠A = 90°. Then prove that DE^{2} = BD × EC (Hint : Show that ∆GBD is similar to ∆CFE. Use GD = FE = DE.)

Chapter: [1] Similarity

Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.

Chapter: [5] Geometric Constructions

Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.

Chapter: [4] Co-ordinate Geometry

The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B.

Chapter: [4] Co-ordinate Geometry

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)

Chapter: [2] Pythagoras Theorem

In the given figure, a ∆ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of ∆ABC is 84 cm^{2}.

Chapter: [3] Circle

The difference between outer and inner curved surface areas of a hollow right circular cylinder 14cm long is 88cm^{2}. If the volume of metal used in making cylinder is 176cm^{3}.find the outer and inner diameters of the cylinder____?

Chapter: [7] Mensuration

Prove that:

Chapter: [6] Trigonometry

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

Chapter: [7] Mensuration

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