Section A (40 Marks)

(Attempt all questions from this section)

Question 1:

Choose the correct answers to the questions from the given options.

(Do not copy the questions, write the correct answers only.)

(i) If , the value of x and y respectively are:

(a) 2, –2

(b) –2, 1

(c) 1, 2

(d) –2, 2

 

(ii) The printed price of an article is ₹ 1600. If the rate of GST is 18% then the GST charged is :

(a) ₹ 288

(b) ₹ 308

(c) ₹ 28.8

(d) ₹ 144

 

(iii) In the given circle, O is a centre and ∠ BDC = 42°, then ∠ ACB is equal to

(a) 42°

(b) 45°

(c) 48°

(d) 60°

 

(iv) A letter is chosen at random from all the letters of the English alphabets. The probability that the letter chosen is a consonant, is:

(a)

(b)

(c)

(d)

 

(v) One root of the quadratic equation – 3x – 2ax – 6a = 0 is -3, find its other root.

(a) a

(b) 2

(c) 2a

(d) 3a

 

(vi) If x – 2 is a factor of 2x⁵ – 6x⁴ – 2ax³ + 6ax² + 4ax + 8, then the value of a is

(a) 1

(b) 1.5

(c) 2

(d) 2.5

 

(vii) In the given figure ∠BAP = ∠DCP = 70°, PC = 6 cm and CA = 4 cm, then PD : DB is:

 

 

(ix) A point P (-2, 3) is reflected in line x = 2 to point P’. The coordinates of P’ are

(a) (2,3)

(b) (0,3)

(c) (4,3)

(d) (6,3)

 

(x) Sum of infinite terms of G.P. : 1 +  +  + . . . .

(a)

(b)

(c)

(d)

 

(xi) The duplicate ratio of 4 : 7  is

(a) 7 : 4

(b)  :

(c)  :

(d) 16 : 49

 

(xii) If the difference of Mode and Median of a data is 42, then the difference of median and mean is

(a) 42

(b) 21

(c) 14

(d) 7

 

(xiii) The curved surface area of a cylinder is 264 m² and its volume is 924 m³. The height of the cylinder is

(a) 3 m

(b) 4 m

(c) 6 m

(d) 8 m

 

(xiv) Praveen deposits ₹ 500 every month in a recurring deposit account for 12 months. If he receives ₹ 6,325 at the time of maturity, then find the amount of  interest he earns.

(a) ₹ 600

(b) ₹ 325

(c) ₹ 6000

(d) ₹ 625

 

(xv) Smallest value of x for which 5 – 2x < , where x is an integer, is

(a)

(b) 0

(c) 1

(d) 2

 

Question 2:

(i) When  + 3  – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.

(ii) Salman deposits ₹ 1000 every month in a recurring deposit account for 2 years. If he receives ₹ 26000 on maturity, find the rate of interest.

(iii) Prove that tangents drawn at the ends of a diameter of a circle are parallel.

 

Question 3:

(i) Find the value of m for which the equation  + (m + 1)x + 1 = 0 has real and equal roots.

(ii) If sin(A + B) = 1 and cos(A - B)= , 0°< A+B ≤ 90° and A> B, then find the measures of angles A and B.

(iii) P and Q have co-ordinates (0, 5) and (-2, 4).

(a) P is invariant when reflected in an axis. Name the axis.

(b) Find the image of Q on reflection in the axis found in (a).

(c) (0, k) on reflection in the origin is invariant. Write the value of k.

(d) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.

 

SECTION B (40 Marks)

(Attempt any four questions from this section)

Question 4:

(i) If A = , B =  and , then find the value of a + b.

(ii) A line AB meets the x-axis at point A and y-axis at point B. The point P(−4, −2) divides the line segment AB internally such that AP : PB = 1 : 2, Find:

(a) the co-ordinates of A and B

(b) equation of line through P and perpendicular to AB.

(iii) In the fig. FEC   GDB and 1 = 2.

Prove that ADE   ABC

 

Question 5:

(i) The price of a T.V. set inclusive of sales tax of 9% is ₹ 13,407. Find its marked price. If sales tax is increased to 13%, how much more does the customer has to pay for the T.V. ?

(ii) Dipak buys a table marked at ₹ 4,000 at a discount of 25% on the marked price. If the rate of tax is 18% , then calculate the tax on the table. Also find the total amount to be paid by Dipak.

(iii) In the figure, if ∠ACB = ∠CDA, AC = 6 cm and AD = 3 cm, then find the length of AB.

 

Question 6:

(i) Calculate the mode for the following frequency distribution.

Class-interval	Frequency
1-4	2
5-8	5
9-12	8
13-16	9
17-20	12
21-24	14
25-28	14
29-32	15
33-36	11
37-40	10

(ii) How many terms of the series 18 + 15 + 12 + ……. when added together will give 45 ?

(iii) A line AB meets the x-axis at point A and y-axis at point B. The point P(−4, −2) divides the line segment AB internally such that AP : PB = 1 : 2, Find:

(a) the co-ordinates of A and B

(b) equation of line through P and perpendicular to AB.

 

Question 7:

(i) A bag contains 18 balls out of which x balls are white. If one ball is drawn at random, the probability of drawing a white ball is y. Now place this ball and 10 more white balls in the bag. Now if a ball is drawn from the bag, the probability of drawing the white ball is 2y. Find x.

(ii) Two pipes running together can fill a cistern in 3  hours. If one pipe takes 3 hours more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

(iii) A solid is in the form of a cone mounted on a hemisphere in such a way that the centre of base of cone just coincide with centre of the base of the hemisphere. Slant height of the cone is l and radius of the base of the cone is r, where r is the radius of the hemisphere. Prove that the surface are of the solid is (11r + 2l)r sq. units.

 

Question 8:

(i) If the zeroes of the polynomial ax² + bx + c are in the ratio p : q, then find the value of  + .

(ii) The age of father is equal to the square of the age of his son. The sum of the age of father and five times the age of the son is 66 years. Find their ages.

 

Question 9:

(i) If 5x + 6y : 8x + 5y = 8 : 9, find x : y.

(ii) An A.P. consists of 50 terms of which 3^rd term is 12 and the last term is 106. Find the 29^th term of the A.P.

(iii) Find the area of a sector of a circle, when radius of a circle is 8 cm and the angle subtended by a chord at the centre of the circle is 60°. 

 

Question 10:

(i) Find the values of m and n so that x – 1 and x + 2 both are factors of  + (3m + 1)  + nx – 18.

(ii) If the median of the following distribution is 27, find the missing frequencies x and y.

Class	0-10	10-20	20-30	30-40	40-50	50-60	Total
Frequency	5	x	20	14	y	8	68

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