CBSE Class 10 Marking Scheme 2022 for Maths Basic

Marking Scheme
Class- X Session- 2021-22
TERM 1
Subject- Mathematics (Basic)

Q. CORRECT HINTS/SOLUTION
N. OPTION
1 (d) P(perfect Square)=5/45=1/9
2 (c) length of the arc= Ɵ /360˚ (2πr)=(60˚/360˚)x2x(22/7)x21=22cm
3 (a) TanƟ = sinƟ/cosƟ = sinƟxsecƟ = xy
4 (d) The lines are parallel hence No solution
5 (b) P(even composite no) =2/6=1/3
6 (a) Let the cost of one chair=Rs. x
Let the cost of one table=Rs. y
8x+5y=10500
5x+3y=6450
Cost of each chair= x= Rs. 750
7 (c) CosƟ=I-cos2Ɵ=sin2Ɵ
Therefore Sin2Ɵ+sin4Ɵ=cosƟ+cos2Ɵ=1
8 (a) Terminating
9 (c ) 23x33
10 (c) 1st No. x 2nd No. = HCF X LCM
12960=18 X LCM
LCM=720
11 (c) AE/AC=DE/BC=a/a+b=x/y
X=ay/(a+b)
12 (d) (2x4+1x1)/3 , (2x6+1x3)/3
=(3,5)
13 (c) 3825=32x52x17
14 (d) AB2=AD2+BD2
AB=5cm
AC2=AB2+CB2
AC=13 cm
Cot 𝛉=CB/AB=12/5
15 (a) x+y=12
X-y=8
X=10,y=2
16 (d) AB2=AC2+AC2
=AC2+BC2
Hence, angle C=90°
17 (d) Let the zeroes be a and b
Then, a=-1 , a+b=-(-7)/1
Hence, b=7+1=8
18 (a) P(same no on each die)=6/36=1/6
19 (b) (2,6)=((3p-2)/2, (4+2q)/2)
3p-2=4, 4+2q=12
P=2, q = 4 hence p+q = 6
20 (c ) 147/120= 49/40=49/23x5

Three decimal places
21 (d ) Perimeter of protractor=Circumference of semi-circle + 2 x radius
=πr+2r

22 (c) 0≤ P( E) ≤1
23 (b) CD/BD=BD/AD
BD2=CDXAD=6X3
BD=3√2 cm
24 (b ) 3/6=5/k ⇒K=10
25 (d ) C1/C2=2πr/2πR
2π/4π=2πr/2πR
r/R=1/2
A1/A2=πr2/πR2=(r/R)2=(1/2)2=1/4
A2=4A1
26 (d) sinƟ=a/b
H2=P2+B2
b2=a2+B2
B=√(b2-a2)
tanƟ=P/B=a/√(b2-a2)
27 (a) x+y=2sin2Ɵ+2cos2Ɵ+1
=2(sin2Ɵ+ cos2Ɵ)+1
=2+1=3
28 (b) 2πr- r=37
r{2x(22/7)-1}=37
r=37x7/37
r=7
circumference=2x(22/7)x7=44cm
29 (c) 1=1
2=2×1
3=3×1
4=2×2
5=5×1
6=2×3
7=7×1
8=2×2×2
9=3×3
10 = 2 × 5
So, LCM of these numbers = 1 × 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2520
Hence, least number divisible by all the numbers from 1 to 10 is 2520
30 ( c) LCM 0f 4,7,14=28
Bells will they ring together again at 6:28 AM
31 (b) Let age of Father=x Years
Let age of son = y years
x+y = 65
2(x-y)=50
Father’s Age =x = 45 years
32 ( c) (tanƟcosecƟ)2-(sinƟsecƟ)2
=tan2Ɵcosec2Ɵ-sin2Ɵsec2Ɵ
=(sin2Ɵ/cos2Ɵ)x1/ sin2Ɵ - sin2Ɵx1/cos2Ɵ
=(1- sin2Ɵ)/ cos2Ɵ= cos2Ɵ/ cos2Ɵ =1
2 2
33 ( d) A1/A2=(P1/P2) =(26/39)

A1/A2=(2/3)2=4/9
34 (a ) Let no of Cars=x
Let no of motorcycles=y
X+y=20
4x+2y=56
No of cars=x=8
35 ( c) H2=P2+B2
H2=152+82
H=17m
36 ( c) (altitude)2=(side)2-(side/2)2
=82-42= 64-16 =48
Altitude=4√3 cm
37 (d) P=3/9=1/3
38 ( b) Ɵ/360˚xπr2=1/6x πr2
Ɵ=60˚
39 ( d) Height of Vertical stick/Shadow of vertical stick=height of tower/shadow of tower
20/10=Height of tower/50
Height of tower=100 m
40 (d) 37x+43y=123 ____(1)
43x+37y=117 ____(2)
Adding (1) and (2)
X+y=3 ______(3)
Subtracting (2) from (1)
-x+y=1..............(4)
Adding (3) and (4),
2y=4
y=2
⇒ x=1
∴ solution is x=1 and y=2
41 ( b) AB=√{(4-1)2+(0-4)2}
=√(32+42)
AB=5 units
42 (a) (x-7)2+(y-1)2=(x-3)2+(y-5)2
X2+49-14x+y2+1-2y=x2+9-6x+y2+25-10y
Simplifying
x-y=2
43 (a ) 3x + y – 9 = 0
Let R divide the line in ratio k:1
R( 2k+1/k+1, 7k+3/k+1)
3(2k+1/k+1)+( 7k+3/k+1)-9=0
4k-3=0
K=3/4
3:4
44 ( c) Distance of M from X-axis=√(2-2)2+(0-3)2=√9=3units
45 (b) ( (1+3)/2 , (4+5)/2) = (4/2, 9/2) = (2, 9/2)
46 (c) Cubic
47 (d ) Four Zeroes as the curve intersects the x-axis at 4 points
48 ( d) p≠0
49 (d) 3 Zeroes as the curve intersects the x-axis at 3 points
50 ( c) -3,-1,2