UP LT Grade Teacher Mathematics Mock Test - 2 Free Online Test 2026

Rajendra Lal Mitra (1878) is associated with Buddha Gaya: The Heritage of Sakya Muni.

• Rajendra Lal Mitra was an Indian scholar who made significant contributions to Indology.
• His work on Buddha Gaya played a pivotal role in documenting the heritage of one of Buddhism's holiest sites.

A. Cunningham (1854) is known for his work on Bhilsa Topes.

• Alexander Cunningham was a British archaeologist and army engineer known as the father of the Archaeological Survey of India.
• His exploration and documentation of the Bhilsa Topes contributed greatly to the understanding of early Buddhist architecture and monastic traditions.

J. Marshall & A.Foucher (1914) are recognized for their contributions to The monuments of Sanchi.

• John Marshall was the Director-General of the Archaeological Survey of India, and Alfred Foucher was a French scholar.
• Together, they worked on documenting and studying the monuments of Sanchi, one of the most significant Buddhist complexes.

J. Marshall (1923) is associated with the Conservation Manual.

• As the Director-General of the Archaeological Survey of India, John Marshall was instrumental in establishing conservation principles in India.
• The Conservation Manual laid down the guidelines for the preservation of historical monuments and archaeological sites in India.

Therefore, the correct pairing is:
A - IV: Rajendra Lal Mitra (1878) - Buddha Gaya: The Heritage of Sakya Muni
B - I: A. Cunningham (1854) - Bhilsa Topes
C - II: J. Marshall & A.Foucher (1914) - The monuments of Sanchi
D - III: J. Marshall (1923) - Conservation Manual

• ShaGun is a web portal launched by the former Union HRD minister Prakash Javadekar for Sarva Shiksha Abhiyan.
• The portal was developed by the World Bank in collaboration with Union Ministry of Human Resources Development.
• The name ShaGun is derived from the words ‘Shala’ means school and ‘Gun’ means quality.
• The ShaGun portal is launched with an aim to monitor schools under Sarva Shiksha Abhiyan as well as the quality of education provided by them.

Dog is the odd one out as it is the only terrestrial animal among other aquatic animals.

Uranium is a radioactive element. Uranium is a chemical element with symbol U and atomic number 92.

• Works that will serve a greater public purpose and not the purpose of few individuals need to be recommended.
• MPs can only recommend it, but District Authorities have the ultimate power to sanction it.
• Key priority sectors: Drinking water facility, education, electricity facility, non-conventional energy resources, healthcare and sanitation, irrigation facilities, railways, roads, pathways and bridges, sports, agriculture and allied activities, self-help group development, urban development.
• Works not permitted: construction of office and residential buildings for public and private agencies, land acquisition or paying compensation, naming assets after individuals, grants or loans to state/central relief fund, assets for individual benefits, works on lands belonging to religious groups, marriages, execution of works in unauthorized colonies.
• Other works permitted: construction of railway halt station, providing CCTV camera in strategic locations, installation of bio-digesters at stations, schools, hospitals, provision for fixed weighing scale machines for farmers, installation of rainwater harvesting systems in public spaces, construction of shelters for skill development.

Hence, the correct option is (A).

The International Monetary Fund (IMF) projects global economic growth to be 3.0% in 2025, an increase from the earlier forecast of 2.8%. This anticipated growth reflects resilience despite ongoing challenges such as geopolitical tensions and the impacts of the COVID-19 pandemic, showcasing the adaptability of global economies.

The Supreme Court raised concerns that the Special Intensive Revision (SIR) of electoral rolls could disenfranchise millions of marginalized individuals due to stringent documentation requirements. This shift from presumed inclusion to presumptive exclusion could undermine the democratic principle of universal adult suffrage, raising alarms about access to voting rights.

Given:

Radius = 25 cm

Length of ​chord = 48 cm

Concept used:

The perpendicular from the center of a circle to a chord bisects the chord.

Pythagoras Theorem: Hypotenuse2 = Base2 + Perpendicular²

Calculation:

OA = OB = 25 cm (Radius of circle)

AB = 48 cm

PB = AB/2 = 48/2

Using the above concept

PA = PB = 24 cm

Applying Pythagoras theorem in ΔOPB,

OB² = OP² + PB²

⇒ 25² = OP² + 24²

⇒ OP² = 625 - 576

⇒ OP2 = 49

⇒ OP = 7 cm

∴ The length of perpendicular drawn from the centre of the circle to the chord is 7 cm.

Concept:

Calculation:

Given that,

A particle having horizontal range (R) is twice the greatest height (H) attained by particle.

This mean that, R = 2H

∴ sin 2θ = sin² θ ⇒ 2sin θ.cos θ = sin² θ

tan θ = 2

also 

now using Pythagoras theorem as shown below we can find sin θ and cos θ

Therefore,  similarly 

Hence range of projectile is given as

Given:

Three sides of the traingle are a = 5, b = 7 and c = 3

Concept used:

Cosine rule = the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Example:

As per the diagram, Cosine rules to find the length of the sides a, b & c of the triangle ABC is given by

cos x = (b2 + c2 – a2)/2bc

cos y = (a2 + c2 – b2)/2ac

cos z = (a2 + b2 – c2)/2ab

Calculation:

Applying cosine formula in ΔABC

CosB = [(5² + 3² - 7²)/(2 × 5 × 3)]

⇒ CosB = [(25 + 9 - 49)/30]

⇒ CosB = [(- 15)/30]

⇒ CosB = -(1/2)

⇒ CosB = Cos120°

So, B = 120°

∴ Angle B is 120°.

• Vector quantities refer to the physical quantities characterized by the presence of both magnitudes as well as direction.
• For example, displacement, force, torque, momentum, acceleration, velocity, etc.
• A scalar is a quantity that is fully described by a magnitude only.
• It is described by just a single number.
• Some examples of scalar quantities include speed, volume, mass, temperature, power, energy, and time.

Shortcut Trick
Given Expression is 

We can write this expression like

∴ The value of n is 99.

Alternate Method
Given:

The give expression 1/ (1×2) + 1/ (2×3) + 1/ (3×4) …………. 1/n(n+1) = 99/100

Calculation       

1/ (1×2) + 1/ (2×3) + 1/ (3×4) …………. 1/n(n+1) = 99/100

Is also 1/ (1×2) + 1/ (2×3) + 1/ (3×4) …………. 1/99(99+1)

Comparing both sides,  

1/n(n+1) = 1/99(99+1)

Here n = 99

Hence, the value of n = 99

Concept:

For unique solution:

Determinant of A, |A|≠ 0

where A is any matrix

Calculation:

|A| ≠ 0

⇒ 1 (2k - 12) - (k - 3) + 1 (4 - 2) = 0

⇒ k - 7 = 0

⇒ k = 7

So, The following simultaneous equations will not have a unique solution for k equal to 7

Concept:

Non-homogeneous equation of type AX = B has infinite solutions;

if ρ(A | B) = ρ(A) < Number of unknowns

Calculation:

Given:

2x + 3y = 1

4x + 6y = λ

The augmented matrix is given by:

Applying R2 → R2 – 2R₁

For the system to have infinite solutions, the last row must be a fully zero row.

So if λ = 2 then the system of equations has infinitely many solutions.

Key Points:

Remember the system of equations

AX = B have

1) Unique solution, if ρ(A : B) = ρ(A) = Number of unknowns.

2) Infinite many solutions, if ρ(A : B) = ρ(A) < Number of solutions

3) No solution, if ρ(A : B) ≠ ρ(A).

Calculation:

Given: Focus: (±2, 0) and eccentricity = 1/4

⇒ Focus = (±ae, 0) = (±2, 0)

⇒ ae = 2

⇒ a × (1/4) = 2

∴ a = 8

⇒ a² = 64

Now,

a²e² = a² – b²

⇒ 2² = 8² - b²

∴ b² = 60

Given:

The mean of 25 observations is 36

The mean of the first 13 observations is 32 and that of the last 13 observations is 39 

Concept used:

Mean = sum of all observation/total number of observation

Calculation:

The sum of all 25 observation = 25 × 36 = 900

Sum of first 13 observations = 13 × 32 = 416

Sum of last 13 observations = 13 × 39 = 507

∴ 13^th term = (416 + 507) - 900 = 923 - 900 = 23

Concept:

Following steps to finding maxima and minima using derivatives.

• Find the first derivative of the function.
• Set the derivative equal to 0 and solve. This gives the values of the maximum and minimum points.
• Now we have to find the second derivative.
  • If f"(x) is less than 0 then the given function is said to be maxima
  • If f"(x) Is greater than 0 then the function is said to be minima

Calculation

Given:

 where a, b and x > 0

Now 

,f''(x) = + ve

∴  f(x) has the least value at 

Concept:

Given:

For the given figure, ABCD is a cyclic quadrilateral with AB as the diameter of the circle.

∠ADC = 2∠CBA

Concept used:

(1) The sum of the opposite angles of cyclic quadrilateral = 180∘

(2) The angle subtended by the diameter of the circle at any point on the circumference is 90∘.

(3) The sum of all internal angles of the triangle is 180^∘

Calculation:

According to the question, the required figure is:

The sum of the opposite angles of cyclic quadrilateral = 180∘

Therefore,

⇒ ∠ADC + ∠CBA = 180∘

⇒ 2∠CBA + ∠CBA = 180∘

⇒ 3∠CBA = 180∘

⇒ ∠CBA = 60∘

The angle subtended by the diameter of the circle at any point on the circumference is 90^∘.

∠ACB = 90^∘

Now,

In ΔACB,

⇒ ∠ACB + ∠CBA + ∠CAB = 180∘

⇒ 90^∘ + 60^∘ + ∠CAB = 180^∘

⇒ ∠CAB = 30^∘

∴ The required answer is 30∘.

Concept:

A differential equation is solved by separating the variables and then eliminating the differential terms by integrating both sides.

Calculation:

Given, 

⇒      -----(i)

Let y = v.x ⇒ 

Putting the value of y and  in (i),

⇒ 

∴ The correct answer is option (4).

15 + 0 = 15
17 + 1 = 18
Therefore, 15 + 0 < 17 + 1

Petrol filled on Monday = 40 litres

Petrol filled on the next day (Tuesday) = 50 litres

Cost of 1 litre of petrol =Rs. 44 

Now, the amount spent in overall petrol =Rs. (44 × (40+50))

=44 × 90
=44 × (100−10)
Since, Distributive property over subtraction:
a×(b−c)=(a×b)−(a×c)

⇒44×(100−10)

=44×100−44×10

=4400–440

=3960

Therefore, he spent Rs. 3960 on petrol.

Number of children = 64 

Nukmber of buttons = 256