1 Marking Scheme Class- X Session- 2021-22 PRE-BOARD 1-TERM 1 Subject- Mathematics (Standard) SECTION A QN Correct Option HINTS/SOLUTION MARKS 1 (b) If xy=180 and HCF (x, y) =3, then find the LCM (x, y). Solution: 1 2 (a) For what value of k, the pair of equation 4x-3y = 9, 2x + k y = 11 has no solution. Solution: 1 3 (b) The areas of two similar triangles ∆ABC and ∆PQR are 25 cm2 and 49 cm2 respectively. If QR = 9.8 cm, find BC Solution: The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. Here, area of ∆ABC = 25 cm², area of ∆PQR = 49 cm², QR = 9.8 cm BC = ? 1 DELHI PUBLIC SCHOOL BANGALORE & MYSORE
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1
Marking Scheme
Class- X Session- 2021-22
PRE-BOARD 1-TERM 1
Subject- Mathematics (Standard)
SECTION A
QN Correct
Option HINTS/SOLUTION
MARKS
1 (b) If xy=180 and HCF (x, y) =3, then find the LCM (x, y).
Solution:
1
2 (a) For what value of k, the pair of equation 4x-3y = 9, 2x + k y =
11 has no solution.
Solution:
1
3 (b)
The areas of two similar triangles ∆ABC and ∆PQR are 25 cm2
and 49 cm2 respectively. If QR = 9.8 cm, find BC
Solution:
The ratio of the areas of two similar triangles is equal to the ratio
of the squares of their corresponding sides.
Here,
area of ∆ABC = 25 cm²,
area of ∆PQR = 49 cm²,
QR = 9.8 cm
BC = ?
1
DELHI PUBLIC SCHOOL BANGALORE & MYSORE
2
Therefore,
4 (d)
If the sum and the product of zeros of the polynomial ax²-6x-c is
equal to 12 find the values of a and c
Solution:
1
5
(a)
The probability of selecting a rotten apple randomly from a heap of
900 apples is 0.18. What is the number of rotten apples in the heap?
Solution:
1
6 (d)
If ABC and DEF are two triangles and AB/DE = BC/DF, then the
two triangles are similar if:
Solution: If the sides of a triangle are respectively proportional to
the sides of another triangle, their corresponding angles are equal
∴ ∠𝐵 = ∠𝐷
1
3
7 (b)
If tan α =5/12 find the value of sec α.
Solution:
1
8 (c)
Which of the following numbers is irrational?
Solution:
Here , which is a rational number
and , which is a rational number
and , which is a rational number
but , which is an irrational number
Hence is an irrational number.
1
9 (a)
If the point (x, 4) lies on the circle whose center is at the origin
and diameter is 10, then find x
Solution:
1
10 (d)
If the distance between the points (4, p) and (1,0) is 5, then the value
of p is:
Solution:
1
4
11 (b)
The prime factorization of the number 140 is:
Solution:
Correct Answer: (b)
1
12 (c)
The least number that is divisible by all the numbers from 1 to 5
is:
Solution:
Answer: (b) 60
Explanation: The least number will be LCM of 1, 2, 3, 4, 5.
Hence, LCM (1, 2, 3, 4, 5) = 2 x 2 x 3 x 5 = 60
1
13 (b)
If tan α=√3 and tan β=𝟏
√𝟑, 0<𝛂, 𝛃< 𝟗𝟎°, then find the value
of cot(α+β).
Solution:
1
14 (a)
1
5
15 (d)
Solution:
1
16 (b)
ΔABC is an equilateral triangle whose sides measure 12 cm each.
Then, the length of its altitude AD is:
Solution:
The altitude of an equilateral triangle bisects its base. BD = DC =
6 cm
Now, ABD is right-angled at D.
Thus, by Pythagoras theorem,
= 144 - 36
= 108
cm.
1
6
17 (b)
If triangles ABC and DEF are similar and AB=4 cm, DE=6 cm,
EF=9 cm and FD=12 cm, the perimeter of triangle is:
Solution:
Explanation: ABC ~ DEF
AB=4 cm, DE=6 cm, EF=9 cm and FD=12 cm
AB/DE = BC/EF = AC/DF
4/6 = BC/9 = AC/12
BC = (4.9)/6 = 6 cm
AC = (12.4)/6 = 8 cm
Perimeter = AB+BC+AC
= 4+6+8
=18 cm
1
18 (a)
If tan θ =1
√3 , then evaluate
cosec ²θ− sec²θ
cosec ²θ+ sec²θ .
Solution:
1
19 (d)
Solve for x and y: 2x+3y=7 and 4x+3y=11
Solution:
1
7
20 (a)
Two dice are thrown simultaneously. what is the probability that the
sum of the two numbers appearing on the top is 13?
Solution:
For a dice, the maximum number that it has is 6.
For two dices thrown, the maximum possible number that can be
obtained is
6+6=12.
Thus, obtaining the sum 13 is an unlikely event to happen in the
throwing of the two dice.
So, the probability of an unlikely event is zero. Here too, the
probability is zero.
Final Answer
The probability is zero.
1
SECTION B
21 (c)
Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively.
Find the maximum capacity of a bag so that the wheat can be packed
in exact number of bags.
Solution
Explanation: [Hint. HCF of 490, 588, 882 = 98 kg]
To find the maximum capacity of the bag to pack all the weight in
exact number of bags, we need to find the HCF of these weights
490=2*5*7*7
588=2*2*3*7*7
882=2*3*3*7*7
common factors are-2 and 7(occurring twice)
so HCF=7*7*2=98
so the capacity of the bag is 98 kg
1
22 (c)
The perimeters of two similar triangles are 25 cm and 15 cm
respectively. If one side of the first triangle is 9 cm, then find the
corresponding side of second triangle.
Solution
Assume ΔABC & ΔPQR to be the 2 triangles. ΔABC ≌ ΔPQR,
Then the ratio of perimeter= ratio of corresponding sides