UP LT Grade Teacher Mathematics Mock Test - 1 Free Online Test 2026

Non-Cooperation Movement (1920) → (II): Launched by Mahatma Gandhi as a mass movement against British rule after the Jallianwala Bagh Massacre. It aimed at boycotting British goods, institutions, and services.
Quit India Movement (1942) → (I): Launched by Mahatma Gandhi with the slogan "Do or Die" to demand an immediate end to British rule in India.
Civil Disobedience Movement (1930) → (III): Started with the Dandi March led by Gandhi to break the salt monopoly of the British.
Partition of Bengal (1905) → (IV): Implemented by Lord Curzon to divide Bengal based on religious lines, leading to widespread protests and the Swadeshi Movement.

Sthanakvasi don't differ much from the other Svetambara Jainas, hence now-a-days they invariably call themselves as Svetambara Sthanakvasi.

Treaty of Allahabad ( 16 August 1765), it was the outcome of the Battle of Buxar (1764). Robert Clive (Governor General of Bengal) made a separate treaty with Mughal Emperor Shah Alam II and Nawab of Awadh Shuja-ud-daullah. A/c to this treaty, Mughal Emperor granted Fiscal Rights (Diwani) to the East India Company at Bengal, Bihar and Orissa.

The Constitution is the highest law in a country, which sets the rules and framework for the government and its functions.

The Bharachukki Falls is situated at a distance of about 130 km from Bangalore. This waterfall is actually a part of the Shivanasamudram Falls.

There is no single definition that can define the term economic growth. However, there are various indicators that explain the term.
 

The correct answer is primary socialisation 

Explanation:

Socialization is the process through which communities transact or educate their members about the norms and values of society to be socially acceptable. Socialization is a combination of personality development and cultural development.

It is an act which ensures the:

• transmission of manners and culture.
• adaptation of social norms and values.
• internalization of attitudes and customs of society.

All types of socialization may be classified into two broad groups, viz. primary socialization and secondary socialization. This division is based on the primary and secondary needs of individuals.

Important Points

Let's understand in brief the types of Socialization:

Hence, it could be concluded that family plays a primary role in the socialization of the child.

Vitamin D is necessary for developing and maintaining strong, healthy bones and absorption.

A key feature of the Sawalkote Hydroelectric Project is its expected capacity of 1,856 Megawatts. This project is aimed at asserting control over water resources in Jammu and Kashmir and is significant for India's energy infrastructure development.

Concept Used:

1. a logx = log (x^a)

2. e^log(n) = n

3. ∫xⁿdx = 

Application:

We have,

I = e5 log x

or, I =  = x⁵

Hence, ∫x⁵ dx = x⁶/6 + C

Explanations:

Group Homorphisms :

Let (G,o) & (G’,o’) be 2 groups, a mapping “f ” from a group (G,o) to a group (G’,o’) is said to be a homomorphism

if –f(a o b) = f(a) o' f(b) for all a, b ∈ G

∴ option 1 is correct 

Given:

D, E and F finish the puzzle in a competition with the probability of ¾, 4/9 and 2/5 respectively.

Concepts used:

Probability that at least one of them will finish the competition = 1 - P (No one will finish the competition)

Calculation:

D, E and F finish the puzzle in a competition with the probability of ¾, 4/9 and 2/5 respectively.

⇒ P (No one will finish the competition) = {1 – (3/4)} × {1 – (4/9)} × {1 – (2/5)} = 1/4 × 5/9 × 3/5 = 1/12

Probability that at least one of them will finish the competition = 1 - P (No one finishes the competition)

⇒ Probability that at least one of them finishes the competition = 1 – (1/12) = 11/12

∴ Probability that at least one of them will finish the competition is 11/12.

Given:

Concept used:

Trace of the Matrix: Sum of the diagonal Elements of the Matrix.

Calculations:

$A=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right]$

The diagonal elements are 2, 2

⇒ Sum of the diagonal elements is 2 + 2 = 4

∴ Trace = 4 

Let ϕ = x + y + z - 5

⇒ 

⇒ 

Concept:

Hyperbola:

>

Concept:

In a G.P.,

nth term is calculated by: a_n = ar^n-1, where a = first term and r = common ratio.

Application:

In a G.P., If sixth term is 32

⇒ a₆ = ar^6-1 = 32

⇒ ar⁵ = 32......(equation 1)

And the eighth term is 128

⇒ a₈ = ar^8-1 = 128

⇒ ar⁷ = 128....(equation 2)

Dividing equation 1 by equation 2, we get,

r² = 4

⇒ r = 2

Total people = 60

Hindi speaking people = 25

Both speaking people = 15

Only English speaking people = 60 - 25 = 35

So total English speaking people = 15 + 35 = 50

Below is the Venn diagram and shaded area represents the English speaking people.

Hence, correct answer is '50'.

Given:

For any two real number, an operation defined
by a * b = 1 + ab

Concept used:

a * b = b * a for all a, b ∈ G (commutative property)

a * (b * c) = (a * b) * c for all a, b, c ∈ G (associative property)

Calculation:

1) Commutive property:

a * b = 1 + ab = 1 + ba = b * a

⇒ commutativity satisfied 

2) Associative property:

(a * b) * c = (1 + ab) * c = 1 + (1 + ab)c = 1 + c + abc

a * (b * c) = a * (1 + bc) = 1 + a(1 + bc) = 1 + a + abc

a * (b * c) ≠ (a * b) * c

⇒ associativity not satisfied

∴ option 3 is correct 

Given:

65 x3y4z5, 117 x2y3z3, 156 x6y5z⁷

Calculation:

65 = 13 × 5,

117 = 13 × 9

156 = 13 × 12

So, the HCF of 65, 117, and 156 is 13.

Again,

The HCF of x², x^3, and x⁶ = x²

The HCF of y³, y⁴, and y⁵ = y³

The HCF of z³, z⁵, and z⁷ = z³

The HCF of  x3y4z5, x2y3z3, and x6y5z⁷ = x²y³z³

So, the HCF of 65 x3y4z5, 117 x2y3z3, 156 x6y5z⁷ is 13x2y3z3

∴ The HCF is 13x2y3z3

Given:

17P = 9Q = 7R

Calculation:

LCM (17, 9, 7) = 1071

17P = 9Q = 7R

⇒ 

⇒ 

Now, P ∶ Q ∶ R = 63 : 119 : 153

∴ P ∶ Q ∶ R is 63 : 119 : 153.

Calculation:

The function f(x) is define, if

4 - x² ≠ 0

2² - x2 ≠ 0

⇒ (2 - x)(2 + x) ≠ 0

⇒ x ≠ 2, -2

⇒ Domain D = R - {-2, 2}

∴ The correct option is (2)

Calculation:

Given, Curves are y² = 2y - x and y-axis.

⇒ x = 2y - y² ...(1) and x = 0 ....(2)

From (1) and (2), we get,

2y - y² = 0

⇒ y(2 - y) = 0

⇒ y = 0 or y = 2

Thus the curve meets the y-axis at (0,0) and (0,2)

So, the required area = 

= 

Concept:

If f(x) =  such that, 

,

{ form }

then, by L's hospital Rule,

Calculation:

∴ The correct answer is option (4).

Concept:

The general equation of the ellipse is:

Here, coordinates of foci are (±ae, 0).

Also, we have b² = a²(1 - e²), where e is the eccentricity.

Calculation:

Since the coordinates of the foci are (±3, 0).

⇒ ae = 3

⇒ a × (1/3) = 3 (∵ e = 1/3)

⇒ a = 9

Now, b2 = a2(1 - e2)

$\Rightarrow b^2=81\left(1-\frac{1}{9}\right)$

⇒ b² = 72

On putting the value of a² and b² in the general equation of an ellipse, we get

Hence, the equation of the ellipse is .

Concept:

If the differential equation is in the form  where f(x, y) and ϕ(x, y) are homogeneous functions of the same degree in x and y

To solve this homogeneous equation

(i) Put y = vx, then 

(ii) Separate the variables v and x and integrate

Calculation:

The given differential equation is

(x + y) (dx – dy) = dx + dy

⇒ (x + y) dx – (x + y) dy = dx + dy

⇒ (x + y – 1) dx = (x + y + 1) dt

Let,  

The equation for the angle bisector for ax2 + 2hxy + by2 = 0 is given by

Given:

x2 + 2pxy - y2 = 0 and x2 - 2qxy - y2 = 0 bisect angles between each other.

Calculation:

Concept:

Any number proportional to direction cosines is called direction ratio.

The angle between two two lines is given by

→ ,

where, (a1, b1, c1) = direction ratios of line 1

and (a2, b2, c2) = direction ratios of line 2

10 + 10 = 20