Time : 3 Hours                                                                        Maximum Marks : 80

General Instructions:

(i) All questions are compulsory.

(ii) The questions paper consists of 40 questions divided into 4 sections A, B, C and D.

(iii) Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 8 questions of 3 marks each. Section D comprises of 6 questions of 4 marks each.

(iv) There is no overall choice. However, an internal choices have been provided in two questions of 1 mark each, two questions of 2 marks each, three questions of 3 marks each, and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions.

(v) Use of calculators is not permitted.

SECTION - A

Question 1:

The number 0.001 can be expressed in rational form as:

(a) 1999

(b) 10999

(c) 100999

(d) 1000999  

Question 2:

Set of natural numbers is a subset of

(a) Set of even numbers

(b) Set of odd numbers

(c) Set of composite numbers

(d) Set of real numbers

Question 3:

In which quadrant, will the point (−3, 4) lie?

(a) I quadrant

(b) II quadrant

(c) III quadrant

(d) IV quadrant

Question 4:

The value of k, if x = 2, y = −1 is a solution of the equation 2x + 3y = k is

(a) 6

(b) 7

(c) 5

(d) 1

Question 5:

The value of x if AOB is a straight line as shown in the figure, is

(a) 36°

(b) 60°

(c) 30°

(d) 35°

Question 6:

Which of the following needs a proof?

(a) Postulates

(b) Definition

(c) Proposition

(d) Axiom

Question 7:

If the supplement of an angle is three times its complement, then angle is

(a) 40°

(b) 35°

(c) 50°

(d) 45°

Question 8:

Mean of 20 observations is 17. If in the observations, observation 40 is replaced by 12, then the new mean is

(a) 17

(b) 15.6

(c) 12

(d) 9.5

Question 9:

Euclid’s Postulate 1 is

(a) A straight line may be drawn from any point to any other point.

(b) A terminated line can be produced indefinitely.

(c) All right angles are equal to one another.

(d) None of these

Question 10:

The sum of either pair of opposite angles of a cyclic quadrilateral is ____.

(a) 90°

(b) 120°

(c) 180°

(d) 360°

Question 11:

If 8x⁴− 8x² + 7 is divided by 2x + 1, then the remainder is ______.

Question 12:

The value of 110  when √10 = 3.162, is _____.

Question 13:

In a trapezium ABCD, AB ∥ CD. If ∠A = 55° and ∠B = 70° then ∠D is _____.

Question 14:

The points scored by a basketball team in a series of matches are as follows:

17, 2, 7, 27, 25, 5, 14, 18, 10. The median is _____.

Question 15:

An ____ for an experiment is the collection of some outcomes of the experiment.

Question 16:

An isosceles right-angled triangle has an area 8 cm². Calculate the perimeter of triangle.

Question 17:

If the distance between M(-1, 5) and N(x, 5) is 8 units then find the value of x

Question 18:

If ∆SKY ≅ ∆MON by SSS congruence rule, then write three equalities of corresponding angles.

Question 19:

In a cylinder, if radius is halved and height is doubled, then find the volume with respect to original volume.

Question 20:

If each observation of the data is decreased by 5, then what is the effect on the mean?

Question 21:

If (25)^{x - 1} = 5^{2x - 1} - 100, then what is the value of x?

Question 22:

Priya and Pooja have the same amount of money. If each gets Rs 4000 more, how will their new amounts be compared?

Question 23:

In the given figure, find the value of x.

Question 24:

If x² – 3x + 2 divides x³ – 6x² + ax + b exactly, then find the value of a and b.

Question 25:

Write the mirror image of the point (2, 3) and (-4, -6) with respect to x-axis.

Question 26:

Two consecutive angles of a parallelogram are (x + 60)° and (2x + 30)°. What special name can you give to this parallelogram?

SECTION - C

Question 27:

Write the shape of the quadrilateral formed by joining (1, 1), (6, 1), (4, 5) and (3, 5) on graph paper.

Question 28:

In the fig., D, E and F are, respectively the mid-points of sides BC, CA and AB of an equilateral triangle ABC. Prove that DEF is also an equilateral triangle.

Question 29:

Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is the value of y, when x = 5?

Question 30:

In the figure, O is the centre of a circle passing through points A, B, C and D and ∠ADC = 120°. Find the value of x.

Question 31:

In the figure, TR ⊥ PS, PQ || TR and PS || QR. If QR = 8 cm, PQ = 3 cm and

SP = 12 cm, find ar(PQRS).

Question 32:

The cost of a shirt of a particular brand is Rs 1000. Write a linear equation, when the cost of x shirts is Rs y . Draw the graph of this equation and find the cost of 12 such shirts from the graph.

Question 33:

Show that if two sides of a triangle are of lengths 5 cm and 1.5 cm, then the length of third side of the triangle cannot be 3.4 cm.

Question 34:

The mean of first 8 observations is 18 and last 8 observation is 20. If the mean of all 15 observations is 19, find the 8th observation.

SECTION – D

Question 35:

If x = 5 + 26  then show that x+ 1x=23  

Question 36:

Find the value of k, if x – 1 is a factor of p(x) = kx² – √2x + 1.

Question 37:

Draw graphs of 3x + 2y = 0 and 2x − 3y = 0 and what is the point of intersection of the two lines representing the above equation.

Question 38:

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

Question 39:

Prove that i=1nxi- X=0 , where A is the mean of the n observations x₁, x₂, ….., x_n.

Question 40:

What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for Stitching margins and wastage in cutting is approximately 29 cm (use π = 3.14)

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