Board Paper of Class 10 2013 Maths - Solutions

• Question 1
  In n[P(A)] = 64, then n(A) is:
  
  (a) 6
  
  (b) 8
  
  (c) 4
  
  (d) 5 VIEW SOLUTION

• Question 2
  If a, b, c are in G.P, then $\frac{a-b}{b-c}$ is equal to :
  
  (a) $\frac{a}{b}$
  
  (b) $\frac{b}{a}$
  
  (c) $\frac{b}{c}$
  
  (d) $\frac{c}{b}$ VIEW SOLUTION

• Question 3
  The next term of $\frac{1}{20}$ in the sequence $\frac{1}{2}, \frac{1}{6}, \frac{1}{12}, \frac{1}{20}$ ............. is
  
  (a) $\frac{1}{24}$
  
  (b) $\frac{1}{22}$
  
  (c) $\frac{1}{30}$
  
  (d) $\frac{1}{18}$ VIEW SOLUTION

• Question 4
  The square root of $49{\left(x^2-2xy+y^2\right)}^2$ is :
  
  (a) 7|x – y|
  
  (b) 7 (x + y) (x – y)
  
  (c) 7 (x + y)²
  
  (d) 7 (x – y)² VIEW SOLUTION

• Question 5
  The remainder when x² – 2x + 7 is divided by x + 4 is :
  
  (a) 28
  
  (b) 29
  
  (c) 30
  
  (d) 31 VIEW SOLUTION

• Question 6
  If $\mathrm{A}=\left(\begin{array}{cc}7& 2\\ 1& 3\end{array}\right) \mathrm{and} \mathrm{A}+\mathrm{B}=\left(\begin{array}{cc}-1& 0\\ 2& -4\end{array}\right), \mathrm{then} \mathrm{matrix} \mathrm{B} = ?$
  
  (a) $\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$
  
  (b) $\left(\begin{array}{cc}6& 2\\ 3& -1\end{array}\right)$
  
  (c) $\left(\begin{array}{cc}-8& -2\\ 1& -7\end{array}\right)$
  
  (d) $\left(\begin{array}{cc} 8& 2\\ -1& 7\end{array}\right)$ VIEW SOLUTION

• Question 7
  Area of the triangle formed by the points (0, 0), (2, 0) and (0, 2) is :
  
  (a) 1 sq. unit
  
  (b) 2 sq. unit
  
  (c) 4 sq. unit
  
  (d) 8 sq. unit VIEW SOLUTION

• Question 8
  If a straight line y = 2x + k passes through the point (1, 2), then the value of k is equal to :
  
  (a) 0
  
  (b) 4
  
  (c) 5
  
  (d) –3 VIEW SOLUTION

• Question 9
  In the figure, PA and PB are tangents to the circle drawn from an external point P. Also, CD is a tangent to the circle at Q.
  
  
  
  If PA = 8 cm and CQ = 3 cm then PC is equal to:
  
  (a) 11 cm
  
  (b) 5 cm
  
  (c) 24 cm
  
  (d) 38 cm VIEW SOLUTION

• Question 10
  If the sides of two similar triangles are in the ratio 2 : 3, then their areas are in the ratio :
  
  (a) 9 : 4
  
  (b) 4 : 9
  
  (c) 2 : 3
  
  (d) 3 : 2 VIEW SOLUTION

• Question 11
  In the adjoining figure ∠ABC = ?
  
  
  
  (a) 45°
  
  (b) 30°
  
  (c) 60°
  
  (d) 50° VIEW SOLUTION

• Question 12
  (1 + tan²θ) sin²θ  = ?
  
  (a) sin²θ
  
  (b) cos²θ
  
  (c) tan²θ
  
  (d) cot²θ VIEW SOLUTION

• Question 13
  The total surface area of a solid hemisphere of diameter 2 cm is equal to :
  
  (a) 12 cm²
  
  (b) 12π cm²
  
  (c) 4π cm²
  
  (d) 3π cm² VIEW SOLUTION

• Question 14
  Variance of the first 11 natural numbers is :
  
  (a) $\sqrt{5}$
  
  (b) $\sqrt{10}$
  
  (c) $5\sqrt{2}$
  
  (d) 10 VIEW SOLUTION

• Question 15
  A card is drawn from a pack of 52 cards at random. The probability of getting neither an ace nor a king card is :
  
  (a) $\frac{2}{13}$
  
  (b) $\frac{11}{13}$
  
  (c) $\frac{4}{13}$
  
  (d) $\frac{8}{13}$ VIEW SOLUTION