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Medium Difficulty
CBSE Class 10 Mathematics Comprehensive Mock Test
Full-syllabus mock test matching CBSE 2025 blueprint with 20 high-yield questions.
Total: 20 Questions
Answered: 0 /
Score: 0
Question 1
+1 Mark
What is the HCF of the smallest prime number and the smallest composite number?
A
1
B
2
C
4
D
6
Correct Answer: Option B
Detailed Explanation:
Smallest prime number is 2 and smallest composite number is 4. The HCF(2, 4) is 2.
Question 2
+1 Mark
If one zero of the quadratic polynomial x² + 3x + k is 2, then what is the value of k?
A
10
B
-10
C
-7
D
-2
Correct Answer: Option B
Detailed Explanation:
Substitute x = 2 into the polynomial: 2² + 3(2) + k = 0 => 4 + 6 + k = 0 => 10 + k = 0 => k = -10.
Question 3
+1 Mark
The pair of linear equations 2x - 3y = 8 and 4x - 6y = 9 has:
A
A unique solution
B
Exactly two solutions
C
Infinitely many solutions
D
No solution
Correct Answer: Option D
Detailed Explanation:
Here a1/a2 = 2/4 = 1/2, b1/b2 = -3/-6 = 1/2, and c1/c2 = -8/-9 = 8/9. Since a1/a2 = b1/b2 != c1/c2, the lines are parallel and have no solution.
Question 4
+1 Mark
What is the discriminant of the quadratic equation 2x² - 4x + 3 = 0?
A
-8
B
10
C
-16
D
8
Correct Answer: Option A
Detailed Explanation:
Discriminant D = b² - 4ac = (-4)² - 4(2)(3) = 16 - 24 = -8. Since D < 0, the equation has no real roots.
Question 5
+1 Mark
Which term of the arithmetic progression (AP) 21, 18, 15, ... is -81?
A
28th term
B
34th term
C
35th term
D
36th term
Correct Answer: Option C
Detailed Explanation:
Here a = 21, d = 18 - 21 = -3. an = a + (n - 1)d => -81 = 21 + (n - 1)(-3) => -102 = -3(n - 1) => n - 1 = 34 => n = 35.
Question 6
+1 Mark
In triangle ABC, DE || BC intersecting AB at D and AC at E. If AD = 3 cm, DB = 4 cm, and AE = 6 cm, what is the length of EC?
A
8 cm
B
7 cm
C
9 cm
D
6.5 cm
Correct Answer: Option A
Detailed Explanation:
By Basic Proportionality Theorem (Thales): AD/DB = AE/EC => 3/4 = 6/EC => 3*EC = 24 => EC = 8 cm.
Question 7
+1 Mark
What is the distance between points P(2, 3) and Q(4, 1)?
A
2 units
B
2√2 units
C
4 units
D
√8 units / 3
Correct Answer: Option B
Detailed Explanation:
Distance formula: PQ = √[(4 - 2)² + (1 - 3)²] = √[2² + (-2)²] = √[4 + 4] = √8 = 2√2 units.
Question 8
+1 Mark
If sin θ = 1/2, then what is the value of (3cos θ - 4cos³ θ)?
A
0
B
1
C
1/2
D
√3/2
Correct Answer: Option A
Detailed Explanation:
Since sin θ = 1/2, θ = 30°. Then cos θ = √3/2. Expression = 3(√3/2) - 4(√3/2)³ = 3√3/2 - 4(3√3/8) = 3√3/2 - 3√3/2 = 0.
Question 9
+1 Mark
The shadow of a vertical tower on level ground increases by 10 m when altitude of sun changes from 45° to 30°. What is the height of the tower?
A
5(√3 + 1) m
B
10(√3 - 1) m
C
5(√3 - 1) m
D
10(√3 + 1) m
Correct Answer: Option A
Detailed Explanation:
Let height be h. Shadow at 45° is h. Shadow at 30° is h√3. h√3 - h = 10 => h(√3 - 1) = 10 => h = 10/(√3 - 1) = 5(√3 + 1) m.
Question 10
+1 Mark
How many tangents can a circle have from an external point?
A
1
B
2
C
Infinitely many
D
0
Correct Answer: Option B
Detailed Explanation:
Exactly two tangents can be drawn to a circle from a point lying outside the circle.
Question 11
+1 Mark
If the perimeter and area of a circle are numerically equal, what is the radius of the circle?
A
2 units
B
π units
C
4 units
D
7 units
Correct Answer: Option A
Detailed Explanation:
2πr = πr² => 2r = r² => r = 2 units (since r > 0).
Question 12
+1 Mark
What is the empirical relationship between the three measures of central tendency (Mean, Median, Mode)?
A
Mode = 2 Median - 3 Mean
B
Mode = 3 Median - 2 Mean
C
Median = 3 Mode - 2 Mean
D
Mode = 3 Mean - 2 Median
Correct Answer: Option B
Detailed Explanation:
Karl Pearson's empirical formula states: Mode = 3 Median - 2 Mean.
Question 13
+1 Mark
A card is drawn from a well-shuffled deck of 52 playing cards. What is the probability of getting a face card?
A
1/13
B
3/13
C
4/13
D
9/52
Correct Answer: Option B
Detailed Explanation:
Total face cards (Jack, Queen, King in 4 suits) = 3 * 4 = 12. Probability = 12/52 = 3/13.
Question 14
+1 Mark
If the sum of first n terms of an AP is Sn = 3n² + 5n, what is its 10th term?
A
62
B
65
C
59
D
68
Correct Answer: Option A
Detailed Explanation:
an = Sn - S(n-1). a10 = S10 - S9. S10 = 3(100) + 50 = 350. S9 = 3(81) + 45 = 243 + 45 = 288. a10 = 350 - 288 = 62.
Question 15
+1 Mark
The coordinates of the midpoint of line segment joining A(-5, 4) and B(7, -8) are:
A
(1, -2)
B
(2, -4)
C
(1, 2)
D
(-6, 6)
Correct Answer: Option A
Detailed Explanation:
Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2) = ((-5 + 7)/2, (4 - 8)/2) = (2/2, -4/2) = (1, -2).
Question 16
+1 Mark
What is the value of (sec² θ - tan² θ)?
A
0
B
1
C
-1
D
2
Correct Answer: Option B
Detailed Explanation:
Fundamental Pythagorean trigonometric identity: 1 + tan² θ = sec² θ => sec² θ - tan² θ = 1.
Question 17
+1 Mark
A solid metallic sphere of radius 6 cm is melted and recast into small spheres of radius 2 cm each. How many such small spheres are formed?
A
9
B
18
C
27
D
36
Correct Answer: Option C
Detailed Explanation:
Number of spheres = Volume of large sphere / Volume of small sphere = (4/3 π R³) / (4/3 π r³) = (6/2)³ = 3³ = 27.
Question 18
+1 Mark
The decimal expansion of the rational number 14587 / (1250) will terminate after how many decimal places?
A
One
B
Two
C
Three
D
Four
Correct Answer: Option D
Detailed Explanation:
1250 = 2 * 625 = 2^1 * 5^4. The highest power of 2 or 5 in the denominator is 4, so it terminates after 4 decimal places.
Question 19
+1 Mark
If two positive integers a and b are written as a = x³y² and b = xy³, where x and y are prime numbers, then HCF(a, b) is:
A
xy
B
xy²
C
x³y³
D
x²y²
Correct Answer: Option B
Detailed Explanation:
HCF is the product of the smallest power of each common prime factor: HCF(a, b) = x^(min(3,1)) * y^(min(2,3)) = xy².
Question 20
+1 Mark
In a single throw of two dice, what is the probability of getting a doublet (both dice showing same number)?
A
1/12
B
1/6
C
5/36
D
1/4
Correct Answer: Option B
Detailed Explanation:
Total outcomes = 36. Doublets are (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) = 6 outcomes. Probability = 6/36 = 1/6.