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

Q.1-Q.10 are multiple choice questions. Select the most appropriate answer from the given options.

Question 1:

The number 23.43 can be expressed in rational form as:

(a)

(b)

(c)

(d)

 

Question 2:

 If p(x) = x² – 2√2x + 1, then find the value of p(2√2)

(a)

(b) 1

(c) 2√2

(d) 5 - √2

 

Question 3:

If p(a, b) lies in II quadrant then which of the following is true about a and b?

(a) a > 0, b > 0

(b) a > 0, b < 0

(c) a < 0, b > 0

(d) a < 0, b < 0

 

Question 4:

The values of x and y, if two ordered pairs (x – 3, – 6) and (4, x + y) are equal, are:

(a) x = 7 and y = 13

(b) x = -7 and y = 13

(c) x = 7 and y = –13

(d) x = -7 and y = –13

 

Question 5:

If AB || CD, EF ⊥ CD and ∠GED = 135° as per the figure given below.

Then the value of ∠AGE is

(a) 55°

(b) 85°

(c) 105°

(d) 135°

 

Question 6:

“Lines are parallel if they do not intersect” is stated in the form of

(a) Definition

(b) Proof

(c) Postulate

(d) Axiom

 

Question 7:

In ∆PQR, PQ = QR and ∠R = 50°, then the measure of ∠Q is

(a) 40°

(b) 60°

(c) 80°

(d) 100°

 

Question 8:

If a cuboid has length, breadth and height are 15 cm, 10 cm and 20 cm respectively, then what is its surface area?

(a) 760 cm²

(b) 1050 cm²

(c) 1175 cm²

(d) 1300 cm²

 

Question 9:

What is the probability of getting an odd number less than 4, if a die is thrown?

(a)

(b)

(c)

(d)

 

Question 10:

In the given figure, BC is the diameter of the circle and ∠BAO = 60°. Then ∠ADC is equal to

                                                    

(a) 40°

(b) 60°

(c) 80°

(d) 100°

 

(Q.11-Q.15) Fill in the blanks:

Question 11:

If ABCD is a parallelogram, then the measure of ∠A – ∠C is _______.

 

Question 12:

If a planar region formed by a figure T is made up of two non-overlapping planar regions formed by figures P and Q, then ar(T) = ______.

 

Question 13:

The angles of a quadrilateral are in the ratio 4: 5: 10: 11. The smallest angle is _____.

 

Question 14:

If the mean of 2, 4, 6, 8, x, y is 5 then the value of x + y is ______.

 

Question 15:

A process that has a well-defined collection of outcomes is called a/an ______.

 

(Q.16-Q.20) Answer the following:

Question 16:

What is the degree of zero polynomial?

 

Question 17:

If the coordinates of a point B(3, -2) and then signs of both coordinates of point B are interchanged, then it will lie in which quadrant ?

 

Question 18:

Is ∆ABC possible, if AB = 6 cm, BC = 4 cm and AC = 1.5 cm?

 

Question 19:

How much ice-cream can be put into a cone with base radius 3.5 cm and height 12 cm?

 

Question 20:

Find the range of the given data: 25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20.

 

Question 21:

If 7^{2x + 3} = 1, then what is the value of x?

 

Question 22:

Explain Euclid’s fifth postulate?

 

Question 23:

E and F are respectively the mid-points of equal sides AB and AC of Δ ABC as shown in the given figure. Show that BF = CE

 

Question 24:

Find the value of m, if x + 4 is a factor of the polynomial x² + 3x + m.

 

Question 25:

A point lies on x-axis at a distance of 9 units from y-axis. What are its coordinates? What will be the coordinates of a point, if it lies on y-axis at a distance of -9 units from x-axis?

 

Question 26:

Show that in a right angled triangle, the hypotenuse is the longest side.

 

SECTION - C

Question 27:

In the given figure, ABCD is a rectangle with length 6 cm and breadth 3 cm. O is the mid-point of AB. Find the coordinates of A, B, C and D.

 

Question 28:

ABCD is a parallelogram in which ∠ADC = 75° and side AB is produced to point E as shown in the figure. Find x + y.

 

Question 29:

A fraction becomes  when 2 is subtracted from the numerator and 3 is added to the denominator. Represent this situation as a linear equation in two variables. Also, find two solutions for this.

 

Question 30:

In the figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.

                                                     

 

Question 31:

The area of the parallelogram ABCD is 90 cm² . Find

(i) ar(Parallelogram ABEF)

(ii) ar(Δ ABD)

(iii) ar(Δ BEF)

                                             

 

Question 32:

Draw the graph of x + y = 7.

 

Question 33:

If the sides of a triangle are x ,(x + 1), (2x - 1) and its area is x√10 sq units then find the value of x.

 

Question 34:

Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. The median of the data is 24. Find the value of x.

 

SECTION – D

Question 35:

Simplify:  

 

Question 36:

What must be added to polynomial f(x) = x⁴ + 2x³ – 2x² + x – 1 so that resulting polynomial is exactly divisible by x² + 2x – 3?

 

Question 37:

Draw the graph of equation 5x + 3y = 4 and check whether

(a) x = 2, y = 5

(b) x = − 1, y = 3 are solution.

                                

Question 38:

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

 

Question 39:

In a mathematics test given to 15 students, the following marks (out of 100) are recorded:

41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60

Find the mean, median and mode of this data.

 

Question 40:

The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm³ = 1l)

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