pre board 2024 mathematics important questions

Pre-Board January 2024  

  Mathematics

 (i) Which of the following numbers is a rational number?

   (c) 0.101001000….

   

(ii) If α and β are the zeros of quadratic polynomial \( p(x) = ax^2 + bx + c \), \( a \neq 0 \), then factors of \( p(x) \) are:

   (a) \( x - \alpha, x - \beta \)

   

(iii) What is the degree of a linear polynomial?

   (a) 1

   

(iv) What will be the condition of lines when the equations \( 3x - y = 3 \) and \( 9x - 3y = 9 \) are represented by a graph?

   (c) Coincide

   

(v) A quadratic equation \( ax^2 + bx + c = 0 \) has unique real roots if:

   (c) \( b^2 - 4ac < 0 \)

   

(vi) If the first term of an A.P. is \( a \) and \( d \) is the common difference, then its nth term is:

   (c) \( a + (n-1)d \)

   

(vii) Which of the following is not a criterion for the similarity of two triangles?

   (a) AAA

   

(viii) How many tangents can be drawn to a circle from a point that lies on it?

   (c) 2

   

(ix) \( 3\sin^2 A + 3\cos^2 A \) is equal to:

   (a) 1

   

(x) Value of \( \tan 300 \) is:

    (b) \( \frac{\sqrt{3}}{3} \)

    

(xi) Find the central angle if the area of the corresponding sector is one fourth of the area of the circle.

    (a) \( 90^\circ \)

    

(xii) What is the length of a cuboid by joining the edges of three cubes of side 4 cm each?

     (b) 8 cm

     

(xiii) What is the relation between the volumes of a cylinder and a cone of the same radius and same height?

      (b) \( 3 \times \) Volume of a cylinder = Volume of cone

      

(xiv) What is the class mark of the class interval 10-25?

      (a) 12.5

      

(xv) If Y, R, and B are the fundamental events of an experiment, then \( P(Y) + P(B) + P(R) \) will be:

     (d) 1

     

(xvi) Probability of a sure event will be:

      (b) 1