Mathematics : Gujarat Board Examination : 2023

 

Time : 3 hrs. Total Marks : 80

1. Write in clear and legible handwriting.

2. This question paper has four sections A,B,C and D and question number from 1 to 39

3. All questions are compulsory. Internal options are given

4. Numbers to the right represents the mark to for the question

5. Draw the neat diagram , wherever necessary

6. New section should be written on new page and write the answer in the numerical order

SECTION A(16 marks)

Answer the following as per the instruction given.This section has 16 questions and each carries 1 mark each. 

Write true or false for the following questions ( 1 to 4)

1. HCF( 17,23)=1 

2. If p(x) = x2 - 7x + 10 then , no of zeros are three

3. If sinA = 1 than A = 900

4. The value of SinA and CosA can never be greater than 1

Select the most appropriate alternative from the given alternatives ( 5 to 10)

5. If p and q are positive integers where p = ab2 and q = a3b where a and b are prime numbers then LCM ( p,q) = _____

1. ab

2. a2b2

3. a3b2

4. a3b3

6. Graphically , pair of linear equations 6x -3y + 10 = 0 and 2x - y + 9 = 0 represents two lines which are 

1. Intersection exactly at one point

2. Intersecting exactly at two points

3. Coincident

4. Parallel

7. If roots of quadratic equation ax2 + bx + c = 0 , a  ≠ 0, are real and distinct than 

1. b2 - 4ac ﹤0

2. b2 - 4ac = 0

3. b2 - 4ac ﹥0

4. b2 - 4ac ≠ 0

8. If A(0,6) and B(0,-2) , than distance between A and B is __

1. 6

2. 8

3. 4

4. 2

9.  Probability of getting 80 marks out of 80 marks in Mathematics is

1. 79/80

2. 1/80

3. 1/81

4. 79/81

10.  For the given figure , if y = p(x), then no. of zeros are 

1. 1

2. 2

3. 3

4. 0

Fill up the blanks ( 11 to 16)

11.  The abscissa of point of intersection of less than type and of more than type cumulative frequency curves of a grouped data gives its _____ ( Mean , median, mode)

12.  Probability of a sure event is ____ (0,1,2)

13. A tangent to circle intersect in_____point ( 0,1,2)

14. A circle which touches all sides of quadrilateral A,B,C,D , If AB=7, BC=3, CD=4 then AD =__ (8,7,11)

15. Length of Minor arc is ___ (𝛑r𝜃/180, 𝛑r2𝜃/360,𝜃/360)

16.  If the radius of the circle is doubled than area becomes ____times(2,3,4)

SECTION B (20 marks)

Solve the following ( 17 to 26) , Each carries two(2) marks.

17. Find the zeros of quadratic equations X2 + 2X - 8 = 0

OR

Find the quotient and remainder for

(3x2 - x3 - 3x + 5)  / (x-1-x2) 

18.  Find the quadratic polynomial whose sum and product of its zero given by respectively ( ¼, -1)

19. No of three digit numbers divisible by 3.

20. Evaluate 2tan245 + cos230 - sin260

OR

If sin3A = cos(A-26) where 3A is an acute angel, find the value of A.

21. Find the value of y for which distance between points P(2,-3) and Q(10,y) is 10 units.

22. An observer 1.5 meter tall is 28.5 meters away from a chimney. Angel of elevation of top of the chimney from her eyes is 450. What is the height of the chimney ?

23. From a point Q, length of tangent to circle is 24 cm. Point Q is 25 cm away from the centre of the circle. Find the radius of the circle.

OR

In the figure , TP and TQ are tangent to the circle with centre of O,so that angle ∠POQ= 1100 then find ∠PTQ

24. The edge of cube is 5 cm then find the total surface area of the cube.

OR

A solid shown in the figure is made of cylinder (A ) with Hemispherical depression (B) , Then write the formula to find total surface area of the the solid

25. ∑ fidi = -26, a = 30, ∑ fi = 13 then find X (x bar, mean).

26. A box contains 3 blue, 2 white and 4 red marbles. Alok drawn a marble at random. What is the probability that it will be

1. White

2. Not red.

SECTION C (24 marks)

Answer the following as asked with calculation (27 to 34) each carries 3 marks.

27.  Solve the pair of linear equations with elimination method.

2x + 3y = 46 AND 3x + 5y = 74

OR

Difference of two natural number is 5 and difference of their reciprocal is 1/10, find these two numbers.

28. Find the nature of roots of the given quadratic equation. If real root exists , find them. 2x2-6x +3 = 0

OR

A train travels 360 km at uniform speed. If the speed have been 5km / hr more it would have taken 1 hour less for the same journey. Find the speed of the train.

29. Find the sum of the first 40 positive  integers divisible by 6.

30. Find the twentieth term from the last term of AP 3,8, 13….253.

31. Find the value of K for which point are colinear (8,1) (k,-4), (2,-5)

OR

In what ratio does the point (-4,6) divide the line segment joining points A(-6,10) and B(3,-8)

32. The table below shows the daily expenditure on food of 25 households in a locality.

Daily expenditure in Rs.	100-150	150-200	200-250	250-300	300-350
No of households	4	5	12	2	2

Find the mean daily expenditure on food by suitable method

33. A die is thrown once, find the probability of getting

1. A prime number

2. A number lying between 2 and 6

3. An odd number.

34. One card is drawn from the well shuffled deck of 52 cards. Find the probability of getting

1. A kind of red colour

2. Not a spade

3. The queen of heart

SECTION D (20 marks)

Solve the following,( 35 to 39) Each carries 4 marks each.

35. State and prove the pythagoras theorem

OR

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

36. The median of the distribution given below is 28.5. Find the value of P and Q

Weight in kg	0-10	10-20	20-30	30-40	40-50	50-60	Total
No of student	5	P	20	15	Q	5	60

37. Draw a triangle ABC with side AB=6 CM, BC = 5 CM and ∠ABC = 600. Then construct a triangle whose side are ¾ of the corresponding side of the triangle ABC

OR

Construct a tangent to circle with radius 4 cm from a point on concentric circle of radius 6 cm and measure its length.

38. A survey conducted on 20 household in a locality by a group of a student resulted in following frequency table for number of family members in a household.

Family size	1-3	3-5	5-7	7-9	9-11
No of family	7	8	2	2	1

Find the mode of this data.

39. A metallic sphere of radius 4.2 cm is melted and recast into shape of a cylinder of radius 6 cm. Find the height of the cylinder.

OR

A Wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure. If the height of cylinder is 10 cm and its base is of  radius 3.5 cm, find the total surface area of this article.