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Maths Mock Test- 5 - Class 10 MCQ


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30 Questions MCQ Test - Maths Mock Test- 5

Maths Mock Test- 5 for Class 10 2025 is part of Class 10 preparation. The Maths Mock Test- 5 questions and answers have been prepared according to the Class 10 exam syllabus.The Maths Mock Test- 5 MCQs are made for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Maths Mock Test- 5 below.
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Maths Mock Test- 5 - Question 1

Triangle ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. Triangle DEF is similar to ΔABC. If EF = 4 cm, then the perimeter of ΔDEF is :

Detailed Solution for Maths Mock Test- 5 - Question 1

Maths Mock Test- 5 - Question 2

In ΔABC, AB = 3 cm, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is :

Maths Mock Test- 5 - Question 3

In an equilateral triangle ABC, if AD ⊥ BC, then:

Detailed Solution for Maths Mock Test- 5 - Question 3

Δ ABC is an equilateral triangle

By Pythagoras theorem in triangle ABD

AB2 = AD2 + BD2

but BD = 1/2 BC (∵ In a triangle, the perpendicular from the vertex to the base bisects the base)

thus AB2 = AD2 + {1/2 BC}2

AB2 = AD2 + 1/4 BC2

4 AB2 = 4AD2 + BC2

4 AB2 - BC2 = 4 AD2

(as AB = BC we can subtract them )

Thus 3AB2 = 4AD2

Maths Mock Test- 5 - Question 4

If p is a positive prime integer, then √p is –

Detailed Solution for Maths Mock Test- 5 - Question 4

Let us assume, to the contrary, that √p is
rational.
So, we can find coprime integers a and b(b ≠ 0)
such that √p = a/b
⇒ √p b = a
⇒ pb2 = a2 ….(i) [Squaring both the sides]
⇒ a2 is divisible by p
⇒  a is divisible by p
So, we can write a = pc for some integer c.
Therefore, a2 = p2c2 ….[Squaring both the sides]
⇒ pb2 = p2c2 ….[From (i)]
⇒ b2 = pc2
⇒ b2 is divisible by p
⇒ b is divisible by p
⇒ p divides both a and b.
⇒ a and b have at least p as a common factor.
But this contradicts the fact that a and b are coprime.
This contradiction arises because we have
assumed that √p is rational.
Therefore, √p is irrational.

Maths Mock Test- 5 - Question 5

LCM of three numbers 28, 44, 132 is –

Detailed Solution for Maths Mock Test- 5 - Question 5

LCM = 22. 71. 111. 31 = 924

Maths Mock Test- 5 - Question 6

Which of the following equations has - 1 as a root?

Detailed Solution for Maths Mock Test- 5 - Question 6

3x² - 2x - 5 = 0
3x² + 3x - 5x - 5 = 0
3x(x+1) - 5(x+1) = 0
(x+1)(3x-5) = 0
x = -1 and 5/3.

Hence roots of given polynomial are -1 and 5/3.

Maths Mock Test- 5 - Question 7

The quadratic equation  has

Detailed Solution for Maths Mock Test- 5 - Question 7

As, discriminant (b2 - 4ac) of the equation is negative. Therefore, no real roots.

Maths Mock Test- 5 - Question 8

If the sum of first n terms of an AP be 3n2 – n and it's common difference is 6, then its first term is :

Detailed Solution for Maths Mock Test- 5 - Question 8

Maths Mock Test- 5 - Question 9

If 7th and 13th terms of an A.P. be 34 and 64, respectively, then it's 18th term is :

Maths Mock Test- 5 - Question 10

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : An event is very unlikely to happen. Its probability is 0.0001

Reason : If P(A) denotes the probability of an event A, then 0 ≤ P (A) ≤ 1.

Detailed Solution for Maths Mock Test- 5 - Question 10
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
Maths Mock Test- 5 - Question 11

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : If a die is thrown, the probability of getting a number less than 3 and greater than 2 is zero.

Reason : Probability of an impossible event is zero.

Detailed Solution for Maths Mock Test- 5 - Question 11
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both statements are correct. Event given in Assertion is an impossible event.
Maths Mock Test- 5 - Question 12

C (O, r1) and C (O, r2) are two concentric circles with r1 > r2. AB is a chord of C (O, r1) touching C (O, r2) at C then

Detailed Solution for Maths Mock Test- 5 - Question 12


∵ AB touches
C(O, r2)
∴ OC ⊥ AB
Also, perpendicular from the centre to a chord bisects the chord.
∴ AC = BC

Maths Mock Test- 5 - Question 13

In Fig. 8.9, if ∠AOB = 125°, then ∠COD is equal to

Maths Mock Test- 5 - Question 14

Choose the correct answer from the given four options : In the formula
for finding the mean of grouped data are deviation from a of

Maths Mock Test- 5 - Question 15

For the following distribution:

The sum of upper limits of the median class and model class is

Maths Mock Test- 5 - Question 16

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : in rolling a dice, the probability of getting number 8 is zero.

Reason : It's an impossible event.

Detailed Solution for Maths Mock Test- 5 - Question 16
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Assertion and Reason both are correct. Also Reason is the correct explanation of the Assertion.
Maths Mock Test- 5 - Question 17

The system of equations x – 4y = 8, 3x – 12y = 24

Detailed Solution for Maths Mock Test- 5 - Question 17

Given

Therefore, the system has infinite many solution.

Maths Mock Test- 5 - Question 18

If x sin (90° – θ) cot (90°- θ) = cos (90° – θ) then x is

Maths Mock Test- 5 - Question 19

If A and B are the angles of a right angled triangle ABC, right angled at C, then 1+cot2A =​

Detailed Solution for Maths Mock Test- 5 - Question 19
ABC is a Δ, right angle at c.
1 +cot^2 =?........ 
we know that.....
Cosec^2 - cot^2= 1...
So,
=> 1+ cot^2
=> cosec^2 A
=> (AB)^2/( CB)^2 
= sec ^2B.
Maths Mock Test- 5 - Question 20

If a is a positive integer and p be a prime number and p divides a2, then

Detailed Solution for Maths Mock Test- 5 - Question 20

If a is a positive integer and p be a prime number and p divides a2
So it implies that p divides a . 

Maths Mock Test- 5 - Question 21

If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is

Detailed Solution for Maths Mock Test- 5 - Question 21

By Euclid’s Division Algorithm:

We use the form:
b = aq + r, where 0 ≤ r < a

Step 1:
117 = 65 × 1 + 52

Step 2:
65 = 52 × 1 + 13

Step 3:
52 = 13 × 4 + 0

Since the remainder becomes 0, the last non-zero remainder is the HCF.
So, HCF of 65 and 117 is 13 ......(i)

We are also given:
HCF (65, 117) = 65m - 117 ......(ii)

Now, from equation (i) and (ii), we get:
65m - 117 = 13

Solving this:
65m = 130
m = 2

Maths Mock Test- 5 - Question 22

The angle of elevation of the sun when the length of the shadow of the tree is √3 times the height of the tree is​

Maths Mock Test- 5 - Question 23

The probability that a number selected at random from the numbers 1, 2, 3 ... 15 is a multiple of 4 is

Detailed Solution for Maths Mock Test- 5 - Question 23

The numbers that is a multiple of 4 present between 1-15 are 4,8,12.
total numbers between 1 to 15=15,
the probability of getting a number that is a multiple of 4= number of favourable outcomes of event e/ total number of outcomes.
=3/15
=1/5

Maths Mock Test- 5 - Question 24

A cubical ice cream brick of edge 22 cm is to be distributed among some children by filling ice cream cones of radius 2 cm and height 7 cm upto its brim. How many children will get the ice cream cones?

Maths Mock Test- 5 - Question 25

Match the column 

Maths Mock Test- 5 - Question 26

If the diameter of semicircular protractor is 14 cm, then its perimeter is:​

Detailed Solution for Maths Mock Test- 5 - Question 26

Diameter=14, Radius=d/2=14/2=7cm
Perimeter of the semi- circle= Boundary of the semi-circle =Circumference of the semi-circle +Diameter= πr+D=

Maths Mock Test- 5 - Question 27

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is​

Maths Mock Test- 5 - Question 28

The solution of px + qy = p – q and qx – py = p + q is

Detailed Solution for Maths Mock Test- 5 - Question 28





Maths Mock Test- 5 - Question 29

The difference between two numbers is 26 and one number is three times the other. The numbers are

Detailed Solution for Maths Mock Test- 5 - Question 29

Let the two numbers be x and y. 
According to question, x−y = 26 and x = 3y 
Putting the value of x in x−y = 26 we get 3y−y = 26 ⇒ y = 13 And x = 3 × 13 = 39

Maths Mock Test- 5 - Question 30

The distance between the points A (0, 6) and B (0, -2) is

Detailed Solution for Maths Mock Test- 5 - Question 30

Since both these points lie on a straight line i.e x axis, distance will be the difference between the respective y coordinates
(0,-2) & (0,6)  =>  6-(-2)) = 6+2 = 8

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