1st Preparatory Question Paper SSLC - Mathematics | Dharwad | Nurav Classes | YPN

The following is the Question Paper of 1^st Preparatory for SSLC Students of Dharwad.

MATH1001-QP01

Question Paper

1st Preparatory Math Question Paper - 01

- Dharwad District

SSLC PREPARATORY EXAMINATION

Time: 3:00hrs

Subject: Mathematics

Marks: 80

1. Choose the correct answer: [8×1=8]
   1. Common difference of A.P. -5, -1, 3, 7,... is __________.
      
      1. -4
      2. 4
      3. 2
      4. 3
   
   
   2. If pair of linear equations in two variable X & Y a₁x+b₁y+c₁=0 & a₂x+b₂y+c₂=0 are intersecting lines, then, __________.
      
      1. $\frac{a_1}{a_2}=\frac{b_1}{b_2}$
      
      
      2. $\frac{a_1}{a_2}\neq\frac{b_1}{b_2}$
      
      
      3. $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
      
      
      4. $\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}$
      
      
   
   
   3. The co-ordinates of the origin are, __________.
      
      1. (1, 1)
      2. (2, 2)
      3. (3,3)
      4. (0, 0)
   
   
   4. The number of zeroes in the following figure are, __________.
      
      1. 4
      2. 2
      3. 3
      4. 5
   
   
   5. Discriminant of $ax^2+bx+c=0$ is __________.
      
      1. $b^2+4a$
      2. $b^2-4a$
      
      
      3. $-\frac{b}{a}$
      
      
      4. $b^2-4ac$
   
   
   6. If $sin A = \frac{3}{5}$ then the value of $cos A$ is __________.
      
      1. $\frac{4}{5}$
      
      
      2. $\frac{3}{4}$
      
      
      3. $\frac{4}{3}$
      
      
      4. $\frac{5}{4}$
      
      
   
   
   7. If the probality os an event is p(E) then the value of p(Ē) is __________.
      
      1. p(Ē)=1+p(E)
      2. p(Ē)=1-p(E)
      3. p(Ē)=1×p(E)
      4. p(Ē)=1/p(E)
   
   
   8. The Total Surface Area of the cylinder is __________.
      
      1. $\pi r l$
      2. $2\pi r h $
      3. $ 2\pi(r+h)$
      4. $\pi r(l+l)$
   
   



2. Very Short Answers: [6×1=6]
   9. If 'a' is the first term & 'd' is the common difference of an AP, then the n^th term is __________.
   10. If x+y=14 & x-y=4, then the value of x is __________.
   11. A tangent to a circle intersects it in __________ points.
   12. Area of the sector of angle θ is __________.
   13. The product of zeroes of (x²-3) is __________.
   14. If r₁ & r₂ are the radii of frustum of a cone of height 'h' then its slant height l=__________.



3. Answer the following questions: [16×2=32]
   15. In the adjoining figure ΔABC & ΔAMP are two right triangles, right angled at B & M respectively;
       Prove that $\frac{CA}{PA}=\frac{BC}{MP}$
   
   
   16. A ladder 10m long reaches a window 8m above the ground. Find the distance of the foot of the ladder from the base of the wall.
   
   
   17. The difference between two numbers is 26 and one number is three times the other; Find them.
   
   
   18. Find the area of the shaded region in the figure given below. If ABCD is a square of side 14cm and APD & BPD are semicircles.
   
   
   19. Draw a circle of radius 4cm from a point 8cm away from its center, construct the pair of tangents to the circle.
   
   
   20. Find the distance between the pairs of points (2, 3) & (4, 1).
   
   
   21. Find the ratio in which the line segment joining the points (-3,10) & (6,-8) is divided by (-1,6).
   
   
   22. Use Euclid's division algorithm to find the HCF of 135 & 225.
   
   
   23. Show that $5-\sqrt{3}$ is irrational.
   
   
   24. Divide the polynomial p(x) by the polynomial g(x) and find the quotient, remainder when $p(x)=x^3-3x^2+5x-3$ and $g(x)=x^2-2$.
   
   
   25. Find the zeroes of $x^2-2$. If $p(x)=3x^3-5x^2-11x-3, find p(-1)$.
   
   
   26. Find the roots of the quadratic equation $3x^2-5x+2=0$ using the quadratic formula.
   
   
   27. If cotθ=7/8 then find the value of $\frac{(1+sin\theta)(1-sin\theta)}{(1+cos\theta)(1-cos\theta)}$
   
   
   28. Find the value of $[sin 60^\circ . cos 30^\circ + sin 30^\circ . cos 60^\circ ]$.
   
   
   29. A die is thrown once, find the probability of getting a prime number.
   
   
   30. A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of the same radius, the total height of the toy is 15.5cm. Find the total surface area of the toy.
   
   



4. Answer the following: [6×3=18]
   31. Prove that the lengths of tangents drawn from an external point to a circle are equal.
       
       OR
       
       Two tangents TP & TQ are drawn to a circle with center 'O' from an external point 'T'; prove that the ∠PTQ=∠OPQ
   
   
   32. Construct a triangle similar to the given triangle ABC with its sides equal to 5/3 of the corresponding sides of the triangle ABC whose lengths are 5cm, 6cm & 7cm.
   
   
   33. The difference of the squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
       Find the roots of the equation $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}$.
   
   
   34. Draw the less than type ogive curve for the given data.
       

       C.I	f
       38-40	3
       40-42	5
       42-44	9
       44-46	14
       46-48	28
       48-50	32
       50-52	35

   
   
   35. Determine the mode of the following data.
       

       C.I	f
       0-20	10
       20-40	35
       40-60	52
       60-80	61
       80-100	38
       100-120	29

       
       
       OR
       
       
       Determine the median of the following data.

       CI	f
       0-10	7
       10-20	14
       20-30	13
       30-40	12
       40-50	20
       50-60	11
       60-70	15
       70-80	8

       
       
   
   
   36. A drinking glass is in the shape of a frustum of a cone of height 14cm. The diameters of its two circular ends are 4cm & 2cm; Find the capacity of the glass.
       
       OR
       
       A cone of height 24cm and the radius of the base 6cm is made up of modelling clay. A child reshapes it in the form os a sphere. Find the radius of the sphere.
   
   



5. Answer the following questions: [4×4=16]
   37. Find the sum of first 24 terms of the list of numbers whose n^thterm is a_n=3+2n.
       
       OR
       
       If the sum of the first 7 terms of an AP is 49 and that of the 17 terms is 289. Find the sum of the first 'n' terms.
   
   
   38. Prove that the ratio of the area of two similar triangles is equal to the square of the ratio of their corresponding sides.
   
   
   39. Solve them graphically, x+3y=6 & 2x-3y=12.
   
   
   40. The angles of elevation of the top of a tower from two points at a distance of 4m & 9m from the base of the tower and the same straight line with it are complementary. Prove that the height of the tower is 6m.
   
   

Question Paper Ends

Goto Solutions

Next Question Paper

To Continue Reading, use the following links:

Previous

• NA
  NA
  - NA
• Goto Question Paper
• Solution

Current

• SSLC Question Papers
  Mathematics 1st Preparatory Question Paper - 01
  - Dharwad District
• Solutions

Next

• SSLC Question Papers
  Mathematics 1st Preparatory Question Paper - 01
  - Dharwad District
• Question Paper
• Solution

This Question Paper was brought to you by NuravClasses and YourPalNurav