Board Paper of Class 10 2015 Maths - Solutions

• Question 1
  If f : A → B is a bijective function and if n(A) = 5, then n(B) is equal to:
  
  (a) 10
  
  (b) 4
  
  (c) 5
  
  (d) 25 VIEW SOLUTION

• Question 2
  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 3
  The common ratio of the G.P. $a^{m-n}, a^m, a^{m+n}$ is :
  
  (a) a^m
  
  (b) a^–m
  
  (c) aⁿ
  
  (d) a^–n VIEW SOLUTION

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

• Question 5
  b = a + c and the equation ax² + bx + c = 0 has equal roots then :
  
  (a) a = c
  
  (b) a = – c
  
  (c) a = 2c
  
  (d) a = – 2c VIEW SOLUTION

• Question 6
  If $\left(\begin{array}{cc}3x+7& 5\\ y+1& 2-3x\end{array}\right)=\left(\begin{array}{cc}1& y-2\\ 8& 8\end{array}\right)$, then the value of x and y respectively are:
  
  (a) –2, 7
  
  (b) $-\frac{1}{3}, 7$
  
  (c) $-\frac{1}{3}, -\frac{2}{3}$
  
  (d) 2, –7 VIEW SOLUTION

• Question 7
  The centroid of the triangle with vertices at (–2, –5), (–2, 12) and (10, –1) is :
  
  (a) (6, 6)
  
  (b) 4, 4)
  
  (c) (3, 3)
  
  (d) (2, 2) VIEW SOLUTION

• Question 8
  The value of k if the straight lines 3x + 6y + 7 = 0 and 2x + ky = 5 are perpendicular is:
  
  (a) 1
  
  (b) – 1
  
  (c) 2
  
  (d) $\frac{1}{2}$ VIEW SOLUTION

• Question 9
  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 10
  If the tangents PA and PB from an external point P to a circle with centre O are inclined to each other at an angle of 40° then ∠POA =
  
  (a) 70°
  
  (b) 80°
  
  (c) 50°
  
  (d) 60° VIEW SOLUTION

• Question 11
  If x = a sec θ, y = b tan θ, then the value of $\frac{x^2}{a^2}-\frac{y^2}{b^2}=:$
  
  (a) 1
  
  (b) –1
  
  (c) tan²θ
  
  (d) cosec²θ VIEW SOLUTION

• Question 12
  (cos² θ – 1) (cot² θ + 1) + 1 =
  
  (a) 1
  
  (b) –1
  
  (c) 2
  
  (d) 0 VIEW SOLUTION

• Question 13
  The ratios of the respective heights and the respective radii to two cylinders are 1 : 2 and 2 : 1 respectively. Then their respective volumes are in the ratio:
  
  (a) 4 : 1
  
  (b) 1 : 4
  
  (c) 2 : 1
  
  (d) 1 : 2 VIEW SOLUTION

• Question 14
  The variance of  10, 10, 10, 10, 10, is:
  
  (a) 10
  
  (b) $\sqrt{10}$
  
  (c) 0
  
  (d) 5 VIEW SOLUTION

• Question 15
  Probability of getting 3 heads and 3 tails in tossing a coin 3 times is :
  
  (a) $\frac{1}{8}$
  
  (b) $\frac{1}{4}$
  
  (c) $\frac{3}{8}$
  
  (d) $\frac{1}{2}$ VIEW SOLUTION