**General Instruction for CBSE
question Paper**

(i) **All** questions are compulsory.

(ii) The question paper consists of **30**
questions divided into four sections A, B, C and D. Section A
comprises of **ten** questions of **1**
mark each. Section B comprises of **five** questions
of **2** marks each. Section C comprises of
**ten** questions of **3** marks each and
Section D comprises of **five** questions of
**6** marks each.

(iii) All questions in Section A are to be answered in one word
one sentence or as per the exact requirement of the question.

(iv) There is no overall choice. However, an internal choice has
been provided in **one** questions of
**2** marks each, **three** questions of
**3** marks each and **two** questions of
**6** marks each. You have to attempt only one of the
alternative in all such questions.

(v) In question on construction, the drawings should be neat and
exactly as per the given measurements.

(vi) Use of calculators is not permitted.

**SECTION A**

**1.** The decimal expansion of the rational number
will terminate after how many places of
decimals ?

**2.** For what value of k,(-4) is zero of the
polynomial

**3.** For what value of , are three consecutive terms of an A.P
?

**4.** In fig. 1, CP and CQ are tangents to a
circle with centre O. ARB is another
tangent touching the circle at R. If CP = 11 cm, and BC = 7 cm,
then find the length of BR.

**5.** In Fig. 2, Express x in terms
of a, b and c where a, b and c are length of LM, MN and NK
respectively.

**6.** If then the value of

**7.** Find the value of a so that the point (3, a)
lies on the lines represented by

**8.** A cylinder and a cone are the same base
radius and of same height. Find the ratio of the volume of cylinder
to that of the cone.

**9.** Find the distance between the points

**10.** Write the median class of the following
distribution :

**Classes** |
**Frequency** |

0-10 |
4 |

10-20 |
4 |

20-30 |
8 |

30-40 |
10 |

40-50 |
12 |

50-60 |
8 |

60-70 |
4 |

**Section B**

**11.** If the polynomial is divided by another
polynomial the remainder comes out be (ax + b), find a and
b.

**12.** find the value(s) of k for which the pair
of linear equation kx - 3y = k - 2 and 12x + ky = k has no
solution.

**13.** If the sum of first n
terms of an A.P. is given by then find its nth term.

**14.** Two tangents PA and PB are drawn to a
circle with centre O from an external point P. Prove that

**OR**

Prove that the parallelogram circumscribing a circle is a
rhombus.

**15.** Simplify :

**Section C**

**16.** Prove that is an
irrational number.

**17.** Solve the following pair of equations :

**18.** The sum of 4th and 8th terms of an A.P. is
24 and sum of 6th and 10th terms. is 44. Find A.P.

**19.** Construct a
ABC in which BC = 6.5 cm, AB = 4.5 cm and
Construct a triangle similar
to this triangle whose sides are
of the corresponding sides of the triangle ABC.

**20.** In Fig. 4,
is right angled at C and DE AB. Prove that
and hence find the
lengths of AE and DE.

**OR**

In Fig. 5, DEFG is a square and
Show that

**21.** Find the value of geometrically.

**OR**

Without using trigonometrical table, evaluate :

**22.** Find the point on y-axis which is
equidistant from the points (5, -2) and (-3, 2).

**OR**

The line segment joining the points A (2,1) and B (5, -8) is
trisected at the points P and Q such that P is nearer to A. If P
also lies on the line given by Find the value of k.

**23.** If P(x,y) is any point on the line joining
the points A (a, 0) and B (0, b), then show that

**24.** In Fig. 6, PQ = 24 cm, PR = 7 cm and O is
the centre of the circle. Find the area of shaded region (take
= 3.14 )

**25.** The king, queen and jack of clubs are
removed from a deck of 52 playing cards and the remaining cards are
shuffled. A card is drawn from the remaining cards. Find the
probability of getting a card of (i) heart (ii) queen (iii)
clubs.

**Section D**

**26.** The sum of the squares of two consecutive
odd numbers is 394. Find the numbers.

**OR**

Places A and B are 100 km apart on a highway. One car starts
from A and another from B at the same time. If the cars travel in
the same direction at different speeds, they meet in 5 hours. If
they travel towards each other. they meet in 1 hour. What are the
speeds of the two cars ?

**27.** Prove that, If a line is drawn parallel to
one side of a triangle to intersect the other two sides in distinct
points, the other two sides are divided in the same ratio.

Using the above result, do the following :

In Fig 7, DE||BC and BD = CE. Prove that is an isosceles triangle.

**28.** A straight highway leads to the foot of a
tower. A man standing at the top of the tower observes a car at an
angle of depression of Which is approaching the foot of the tower with
a uniform speed. Six seconds later the angle of depression of the
car is found to be Find the time taken by the car to reach the
foot of the tower from this point.

**29.** From a solid cylinder whose height is 8 cm
and radius 6 cm, a conical cavity of height 8 cm and of base radius
6 cm, is hollowed out. Find the volume of the remaining solid
correct to two places of decimals. Also find the total surface area
of the remaining solid. ( taken = 3.1416 )

**OR**

In Fig 8, ABC is a right triangle
right angled at A. Find the area of shaded region if AB = 6 cm, BC
= 10 cm and O is the centre of the incircle of (taken = 3.14)

**30.** The following table gives the daily income
of 50 workers of a factory :

Daily income (in Rs.) |
100-120 |
120-140 |
140-160 |
160-180 |
180-200 |

Number of workers |
12 |
14 |
8 |
6 |
10 |

Find the Mean. Mode and Median of the above data.

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