Board Paper of Class 10 Semester - 1 2021 Math - Solutions

• Question 1
  If (x + 2) is a factor of the polynomial x³ – kx² – 5x + 6 then the value of k is:
  (a) 1
  (b) 2
  (c) 3
  (d) –2 VIEW SOLUTION

• Question 2
  The solution set of the inequation x – 3 ≥ –5, x ∈ R is:
  (a) {x: x > –2, x ∈ R}
  (b) {x: x ≤ –2, x ∈ R}
  (c) {x: x ≥ –2, x ∈ R}
  (d) {–2, –1, 0, 1, 2} VIEW SOLUTION

• Question 3
  The product AB of two matrices A and B is possible if:
  (a) A and B have the same number of rows.
  (b) the number of columns of A is equal to the number of rows of B.
  (c) the number of rows of A is equal to the number of columns of B.
  (d) A and B have the same number of columns. VIEW SOLUTION

• Question 4
  If 70, 75, 80, 85 are the first four terms of an Arithmetic Progression, then the 10^th term is:
  (a) 35
  (b) 25
  (c) 115
  (d) 105 VIEW SOLUTION

• Question 5
  The selling price of a shirt excluding GST is ₹800. If the rate of GST is 12% then the total price of the shirt is:
  (a) ₹704
  (b) ₹96
  (c) ₹896
  (d) ₹848 VIEW SOLUTION

• Question 6
  Which of the following quadratic equations has 2 and 3 as its roots?
  (a) x² – 5x + 6 = 0
  (b) x² + 5x + 6 = 0
  (c) x² – 5x – 6 = 0
  (d) x² + 5x – 6 = 0 VIEW SOLUTION

• Question 7
  If x, 5.4, 5, 9 are in proportion then x is:
  (a) 3
  (b) 9.72
  (c) 25
  (d) 25/3 VIEW SOLUTION

• Question 8
  Mohit opened a Recurring deposit account in a bank for 2 years. He deposits ₹1000 every month and receives ₹25500 on maturity. The interest he earned in 2 years is:
  (a) ₹13500
  (b) ₹3000
  (c) ₹24000
  (d) ₹1500 VIEW SOLUTION

• Question 9
  In the given AB = 24 cm, AC = 18 cm, DE = 12 cm, DF = 9 cm and ∠BAC = ∠EDF. Then ∆ABC ~ ∆DEF by the condition:
  
  (a) AAA
  (b) SAS
  (c) SSS
  (d) AAS VIEW SOLUTION

• Question 10
  If A = $\left[\begin{array}{cc}5& 10\\ 3& -4\end{array}\right]$ and I = $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ then AI is equal to
  (a) $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
  
  (b) ​$\left[\begin{array}{cc}5& 10\\ -3& 4\end{array}\right]$
  
  (c) ​$\left[\begin{array}{cc}5& 10\\ 3& -4\end{array}\right]$
  
  (d) ​$\left[\begin{array}{cc}15& 15\\ -1& -1\end{array}\right]$ VIEW SOLUTION

• Question 11
  The polynomial x³ – 2x² + ax + 12 when divided by (x + 1) leaves a remainder 20, then 'a' is equal to:
  (a) –31
  (b) 9
  (c) 11
  (d) –11 VIEW SOLUTION

• Question 12
  In an Arithmetic Progression (A.P.) if, first term is 5, common difference is –3 and the n^th term is –7, then n is equal to:
  (a) 5
  (b) 17
  (c) –13
  (d) 7 VIEW SOLUTION

• Question 13
  In the given figure PQ is parallel to TR, then by using condition of similarity:
  
  (a) $\frac{\mathrm{PQ}}{\mathrm{RT}}=\frac{\mathrm{OP}}{\mathrm{OT}}=\frac{\mathrm{OQ}}{\mathrm{OR}}$
  
  (b) $\frac{\mathrm{PQ}}{\mathrm{RT}}=\frac{\mathrm{OP}}{\mathrm{OR}}=\frac{\mathrm{OQ}}{\mathrm{OT}}$
  
  (c) $\frac{\mathrm{PQ}}{\mathrm{RT}}=\frac{\mathrm{OR}}{\mathrm{OP}}=\frac{\mathrm{OQ}}{\mathrm{OT}}$
  
  (d) $\frac{\mathrm{PQ}}{\mathrm{RT}}=\frac{\mathrm{OP}}{\mathrm{OR}}=\frac{\mathrm{OT}}{\mathrm{OQ}}$
    VIEW SOLUTION

• Question 14
  If a, b, c and d are proportional then $\frac{\mathrm{a}+\mathrm{b}}{\mathrm{a}-\mathrm{b}}$ is equal to:
  (a) $\frac{\mathrm{c}}{\mathrm{d}}$
  
  (b) $\frac{\mathrm{c}-\mathrm{d}}{\mathrm{c}+\mathrm{d}}$
  
  (c) $\frac{\mathrm{d}}{\mathrm{c}}$
  
  (d) $\frac{\mathrm{c}+\mathrm{d}}{\mathrm{c}-\mathrm{d}}$ VIEW SOLUTION

• Question 15
  The first four terms of an Arithmetic Progression (A. P.), whose first term is 4 and common difference is  −6, are:
  (a) 4, –10, –16, –22
  (b) 4, 10, 16, 22
  (c) 4, –2, –8, –14
  (d) 4, 2, 8, 14 VIEW SOLUTION

• Question 16
  One of the roots of the quadratic equation x² – 8x + 5 = 0 is 7·3166. The root of the equation correct to 4 significant figures is:
  (a) 7.3166
  (b) 7.317
  (c) 7.316
  (d) 7.32 VIEW SOLUTION

• Question 17
  (x + 2) and (x + 3) are two factors of the polynomial x³ + 6x² + 11x + 6. If this Polynomial is completely factorised the result is:
  (a) (x – 2) (x + 3) (x + 1)
  (b) (x + 2) (x – 3) (x – 1)
  (c) (x + 2) (x + 3) (x – 1)
  (d) (x + 2) (x + 3) (x + 1) VIEW SOLUTION

• Question 18
  The sum of the first 20 terms of the Arithmetic Progression 2, 4, 6, 8.......................is:
  (a) 400
  (b) 840
  (c) 420
  (d) 800 VIEW SOLUTION

• Question 19
  The solution set on the number line of the linear inequation:
  
  2y – 6 < y + 2 ≤ 2y, y ∊ N is
  
  (a) 
  
  (b) 
  
  (c) 
  
  (d)  VIEW SOLUTION

• Question 20
  If x, y, z are in continued proportion then (y² + z²) : (x² + y²) is equal to:
  (a) z : x
  (b) x : z
  (c) zx
  (d) (y + z) : (x + y) VIEW SOLUTION

• Question 21
  The marked price of an article is ₹5000. The shopkeeper gives a discount of 10%. If the rate of GST is 12%, then the amount paid by the customer including GST is:
  (a) ₹5040
  (b) ₹6100
  (c)  ₹6272
  (d) ₹6160 VIEW SOLUTION

• Question 22
  If $\mathrm{A}=\left[\begin{array}{cc}3& 5\\ 1& 4\end{array}\right], \mathrm{B}=\left[\begin{array}{cc}2& 4\\ 0& 3\end{array}\right]$ and $\mathrm{C}=\left[\begin{array}{cc}1& -1\\ 2& 1\end{array}\right],$ then 5A – BC is equal to:
  
  (a) $\left[\begin{array}{cc}-5& -23\\ 1& 17\end{array}\right]$
  
  (b) $\left[\begin{array}{cc}5& 23\\ 1& 17\end{array}\right]$
  
  (c) $\left[\begin{array}{cc}-2& 8\\ -3& 3\end{array}\right]$
  
  (d) $\left[\begin{array}{cc}5& 23\\ -1& 17\end{array}\right]$ VIEW SOLUTION

• Question 23
  In the given figure ABCD is a trapeziune in which DC is parallel to AB.
  AB = 16 cm and DC = 8 cm. OD = 5 cm, OB = (y + 3) cm, OA = 11 cm and OC = (x – 1) cm.
  Using the given information answer the following questions.
  
  
  
  
  (i) From the given figure name the pair of similar triangles:
  (a) ∆OAB, ∆OBC
  (b) ∆COD, ∆AOB
  (c) ∆ADB, ∆ACB
  (d) ∆COD, ∆COB
  
  (ii) The corresponding proportional sides with respect to the pair of similar triangles obtained in (i):
  
  (a) $\frac{\mathrm{CD}}{\mathrm{AB}}=\frac{\mathrm{OC}}{\mathrm{OA}}=\frac{\mathrm{OD}}{\mathrm{OB}}$
  
  (b) $\frac{\mathrm{AD}}{\mathrm{BC}}=\frac{\mathrm{OC}}{\mathrm{OA}}=\frac{\mathrm{OD}}{\mathrm{OB}}$
  
  (c) $\frac{\mathrm{AD}}{\mathrm{BC}}=\frac{\mathrm{BD}}{\mathrm{AC}}=\frac{\mathrm{AB}}{\mathrm{DC}}$
  
  (d) $\frac{\mathrm{OD}}{\mathrm{OB}}=\frac{\mathrm{CD}}{\mathrm{CB}}=\frac{\mathrm{OC}}{\mathrm{OA}}$
  
  (iii) The ratio of the sides of the pair of similar triangles is:
  (a) 1 : 3
  (b) 1 : 2
  (c) 2 : 3
  (d) 3 : 1
  
  (iv) Using the ratio of sides of the pair of similar triangles the values of x and y are respectively:
  (a) x = 4.6, y = 7
  (b) x = 7, y = 7
  (c) x = 6.5, y = 7
  (d) x = 6.5, y = 2 VIEW SOLUTION

• Question 24
  Two cars X and Y use 1 litre of diesel to travel x km and (x + 3) km respectively. If both the cars covered a distance of 72 km, then:
  
  (i) the number of litres of diesel used by car X is:
  
  (a) $\frac{72}{x-3} \mathrm{litres}$
  
  (b) $\frac{72}{\mathrm{x}+3} \mathrm{litres}$
  
  (c) $\frac{72}{\mathrm{x}} \mathrm{litres}$
  
  (d) $\frac{12}{\mathrm{x}} \mathrm{litres}$
  
  (ii) the number of litres of diesel used by car Y is:
  
  ​(a) $\frac{72}{x-3} \mathrm{litres}$
  
  (b) $\frac{72}{\mathrm{x}+3} \mathrm{litres}$
  
  (c) $\frac{72}{\mathrm{x}} \mathrm{litres}$
  
  (d) $\frac{12}{\mathrm{x}+3} \mathrm{litres}$
  
  (iii) If car X used 4 litres of diesel more than car Y in the journey, then:
  
  ​(a) $\frac{72}{x-3}-\frac{12}{x}=4$
  
  (b) $\frac{72}{\mathrm{x}+3}-\frac{72}{x}=4$
  
  (c) $\frac{72}{\mathrm{x}}-\frac{72}{x+3}=4$
  
  (d) ​$\frac{72}{\mathrm{x}-3}-\frac{72}{x+3}=4$
  
  (iv) The amount of diesel used by the car X is:
  (a) 6 litres
  (b) 12 litres
  (c) 18 litres
  (d) 24 litres VIEW SOLUTION

• Question 25
  Joseph has a recurring deposit account in bank for two years at the rate of 8% per annum simple interest.
  
  (i) If at the time of maturity, Joseph receives ₹2000 as interest then the monthly instalment is:
  (a) ₹1200
  (b) ₹600
  (c) ₹1000
  (d) ₹1600
  
  (ii) The total amount deposited in the bank:
  (a) ₹25000
  (b) ₹24000
  (c) ₹26000
  (d) ₹23000
  
  (iii) The amount Joseph receives on maturity is:
  (a) ₹27000
  (b) ₹25000
  (c) ₹26000
  (d) ₹28000
  
  (iv) If the monthly instalment is ₹100 and the rate of interest is 8%, in how many months Joseph will receive ₹52 as interest?
  (a) 18
  (b) 30
  (c) 12
  (d) 6 VIEW SOLUTION