Mathematics — Suggested Paper 1

1(i). If x - 2 is a factor of x3 - kx - 12, then the value of k is :

1(ii). If matrix A = [[2, 2], [0, 2]] and A² = [[4, x], [0, 4]],

1(iii). The given quadratic equation 3x² + √7x + 2 = 0 has:

1(iv). In the given figure AB = 24 cm, AC = 18 cm, DE = 12 cm, DF = 9 cm and ∠BAC = ∠EDF. Then ΔABC ~ ΔDEF by the condition

1(v). Question 1(xiv): A rectangular sheet of paper of size 11 cm × 7 cm is first rotated about the side 11 cm and then about the side 7 cm to form a cylinder, as shown in the diagram. The ratio of their curved surface areas is:

1(vi). Rakhi’s mobile number has the following integers : 1, 6, 9, 8, 9, 1, 7, 8, 9 The mode of the above given data is :

1(vii). The nth term of an Arithmetic Progression (A.P.) is 2n + 5. The 10th term is :

1(viii). The marked price of a refrigerator is ₹ 12,000 and GST paid by the customer is ₹ 2,160. The rate of GST is:

1(ix). Which of the following cannot be the probability of any event:

1(x). The given table shows the distance covered and the time taken by a train moving at a uniform speed along a straight track. The values of x and y are :

1(xi). Mr. Anuj deposits ₹500 per month for 18 months in a recurring deposit account at a certain rate. If he earns ₹570 as interest at the time of maturity, then his matured amount is:

1(xii). The sum invested to purchase 15 shares of a company of nominal value ₹ 75 available at a discount of 20% is:

1(xiii). Points A(x, y), B(3, -2) and C(4, -5) are collinear. The value of y in terms of x is ∶

1(xiv). Question: The solution set for the inequation 2x + 4 ≤ 14, x ∈ W is :

1(xv). The coordinates of the vertices of △ABC are respectively (-4, -2), (6, 2) and (4, 6). The centroid G of △ABC is :

2(i)(a). ∠OQM

2(i)(b). ∠QNS

2(i)(c). ∠QOS

2(i)(d). ∠QMS

2(ii)(i). first term

2(ii)(ii). common difference

2(ii)(iii). sum of the first 20 terms.

2(iii). Solve the following quadratic equation : x² + 4x - 8 = 0. Give your answer correct to one decimal place.

3(i). Find the value of 'a' if x - a is a factor of the polynomial 3x³ + x² - ax - 81.

3(ii)(i). radius of the cylinder.

3(ii)(ii). curved surface area of the cylinder. [Take π = 3.1]

3(iii)(a). construct an equilateral triangle ABC of side 5 cm.

3(iii)(b). construct the circumcircle of ΔABC.

3(iii)(c). construct the locus of points which are equidistant from AB and BC. Mark the point where the circumcircle and locus meet, as D.

3(iii)(d). give the geometrical name of quadrilateral ABCD

4(i)(a). a multiple of 5

4(i)(b). a perfect square

4(i)(c). a prime number ?

4(ii). A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more it would have taken 1 hour less. Find x the original speed.

4(iii). A solid is in the shape of a hemisphere of radius 7 cm, surmounted by a cone of height 4 cm. The solid is immersed completely in a cylindrical container filled with water to a certain height so that the solid is completely submerged in water. If the radius of the cylinder is 14 cm, find the rise in the water level.

5(a). Using properties of proportion, solve for x. Given that x is positive: (2x + √(4x² - 1)) / (2x - √(4x² - 1)) = 4

5(b). If A = [[2, 1], [0, 3]], B = [[0, 1], [-1, 2]] and C = [[1, -1], [2, 0]], find AC + B² - 10C.

5(c). Prove that (1 + cot θ - cosec θ)(1 + tan θ + sec θ) = 2

6(i). Suresh has a recurring deposit account in a bank. He deposits ₹2000 per month and the bank pays interest at the rate of 8% per annum. If he gets ₹1040 as interest at the time of maturity, find in years total time for which the account was held.

6(ii). The following table gives the duration of movies in minutes. Using step–deviation method, find the mean duration of the movies.

6(iii)(a). find (a + b) / (a - b)

6(iii)(b). Hence using properties of proportion, find a : b.

7(a). The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.

7(c). Using ruler and a compass only construct a semi-circle with diameter BC = 7 cm. Locate a point A on the circumference of the semicircle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Measure ∠ADC and write it down.

7(b)(i). Slope of BC.

7(b)(ii). Equation of a line perpendicular to BC and passing through A.

8(a)(i). Calculate the interest for the 6 months from January to June 2016, at 6% per annum

8(a)(ii). If the account is closed on 1st July 2016, find the amount received by the account holder.

8(b)(i). Plot the following points: A(0, 4), B(2, 3), C(1, 1) and D(2, 0)

8(b)(ii). Reflect points B, C, D on the y-axis and write down their coordinates. Name the images as B’, C’, D’ respectively.

8(b)(iii). Join the points A, B, C, D, D’, C’, B’ and A in order, so as to form a closed figure. Write down the equation of the line of symmetry of the figure formed.

9(a)(i). the monthly installment

9(a)(ii). the amount of maturity

9(b)(i). Frame a frequency distribution table

9(b)(ii). To calculate mean

9(b)(iii). To determine the Modal class

9(c). A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.

10(i)(a). Prove that : (sec θ − cos θ)(cosec θ − sin θ) = sin θ cos θ

10(ii)(a). discounted price of the TV set.

10(ii)(b). amount paid by the customer to clear the bill.

10(iii)(a). Prove that : ΔADE ~ ΔABC and hence find DE : BC.

10(iii)(b). Prove : ΔDFE ~ ΔCFB

10(iii)(c). Given, area of ΔDFE = 16 square units, find the area of ΔCFB.