Maximum Marks : 80                                                              Time Taken : 3 Hours

 

General Instructions:

(i) All the questions are compulsory.

(ii) The question 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 choice has 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

(Q1- Q10) Multiple Choice Questions

Question 1:

If A, B and C are interior angles of a triangle ABC, then  =

(i) sin

(ii) cos

(iii) sin A

(iv) cos A                                                                                                                              1

 

 Question 2:

The slope of the line 5x - 8y = -2, is

(i)                                      

(ii)  

(iii)

(iv)                                                                                                                                1  

 

Question 3:

The distance of the points (6, 8) from the origin is

(i) 9                                         

(ii) 10                                        

(iii) 12

(iv) 14                                                                                                                                    1

 

Question 4:

If the system of equations 2x + 3y = 5, 4x + ky = 10 has infinitely solutions, then the value of k is

(i)

(ii) 4

(iii) 6

(iv) 10                                                                                                                                  1

 

Question 5:

The LCM of smallest two digit composite number and the smallest composite number is

(i) 12

(ii) 4

(iii) 20

(iv) 44                                                                                                                                          1

 

Question 6:

If mean is 11 and median is 13 then value of mode is

(i) 15

(ii) 13

(iii) 11

(iv) 17                                                                                                                                        1

 

Question 7:

In an AP, the first term is 7, common difference is 3 and total number of terms is 8, then the nth term of AP is

(i) 15

(ii) 22

(iii) 28

(iv) 34                                                                                                                                        1

 

Question 8:

If tan² 45° - cos² 30° = A * sin 45° * cos 45°, then the value of A = 

(i) 2

(ii) -2

(iii)

(iv)                                                                                                                           1

 

Question 9:

The zeroes of the polynomial x² – 3 are

(i) 3, 3

(ii) 3, -3

(iii) √3, √3

(iv) -√3, √3                                                                                                                  1

 

Question 10:

The value of p if (21, 1) is a solution of the equation px + 12y = 7

(i)

(ii)  

(iii)

(iv)                                                                                                                       1

 

(Q 11- Q 15) Fill in the blanks 

Question 11:

The sum of the AP -37, -33, -29,…………. to 12 terms, is _________.         1 

 

Question 12:

If the sides of two similar triangles are in the ratio 9 : 16 then the areas of these triangles are in the ratio _________.                                                           1

 

Question 13:

If α and β are the zeroes of the polynomial x² - 2x + k and α - β = 8 then the value of k is ______.                                                                                                  1                                

 

Question 14:

The probability that a prime number selected at random from the numbers (1, 2, 3, .........., 35) is                                 1

 

Question 15:

Two cubes each with 6 cm edge are joined end to end. The surface area of the resulting cuboid is _______.                  1

 

(Q 16- Q 20) Answer the following:

Question 16:

In the given figure, if ∠RPS = 25°, the find the value of ∠ROS.                              1

 

Question 17:

If the roots of the equation 2x² - 5x + b = 0 are in the ratio of 2 : 3, then find the value of b?                                             1

 

Question 18:

For an AP, if a₂₅ – a₂₀ = 45, then find the value of common difference.   1

 

Question 19:

Find two irrational numbers between 2 and 2.5.                                    1

 

Question 20:

In the given figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that Δ ABD ~ Δ ECF.           1

 

SECTION – B

Question 21:

The sum of the digits of two-digit number is 10, while when the digits are reversed, the number decrease by 54. Find the changed number.                   2

 

Question 22:

Prove that the parallelogram circumscribing a circle is a rhombus.           2

 

Question 23:

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.                                                                          2

 

Question 24:

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 450. When he moves 20 m away from the bank, he finds the angle of elevation to be 300. Find the height of the tree.                                                                                                                                   2

 

Question 25:

A number is selected from the numbers 2, 3, 3, 5, 5, 5, 7, 7, 7, 7, 9, 9, 9, 9, 9 at random. Find the probability of getting

(a) Median                                               (b) Mode                                                        2

 

Question 26:

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.                                            2

 

SECTION - C

Question 27:

Given that √2 is irrational then prove that 6 + √2 is an irrational number.    3

 

Question 28:

Solve the equation: 1 + 4 + 7 + 10 + ............+ x = 287                                               3

 

Question 29:

Solve the following systems of equations:

 

                                                                                                               3

 

Question 30:

If roots of the equation x² - mx + 12 = 0 are in ratio 1 : 3 then find the value of m.                                                                                                                                3

Question 31:

In a classroom, 4 friends are seated at the points A, B, C and D as shown in the figure.

Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.                                        3

 

Question 32:

If sin θ + cos θ = 1 then prove that cos θ - sin θ = ±1                                            3

 

Question 33:

During the medical check-up of 35 students of a class, their weights were recorded as follows:

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.                  3

 

Question 34:

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.                      3

 

SECTION – D

Question 35:

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are  of the corresponding sides of the first triangle. Give the justification of the construction.                                                                               4

 

Question 36:

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.                                                                  4

 

Question 37:

A train travelling at a uniform speed for 360 km would have taken 48 minutes less to travel the same distance if its speed work 5 km per hour more. Find the original speed of the train.                                                                                  4  

 

Question 38:

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminum sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)                                                                                                                  4

 

Question 39:

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60⁰. After some time, the angle of elevation reduces to 30⁰ as shown in the figure. Find the distance travelled by the balloon during the interval.                            4

 

Question 40:

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f.     4

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