DAY 3 ALGEBRA HISTORY GEOGRAPHY | Free Mock Test 2026 | 120 MCQs

Question 1

Solve: 4x + 5 = 3x + 12.

Accepted Answer

A) 7

Question 2

If 2x + 3y = 13 and 3x + 2y = 12, then x - y equals:

Accepted Answer

A) -1

Question 3

A man has 5 more two-rupee coins than one-rupee coins. If the total value is ₹58, the number of two-rupee coins is:

Accepted Answer

A) 21

Question 4

The equation of the line passing through (2, 3) and (4, 7) is y = mx +

Accepted Answer

A) The value of c is:

Question 5

If 3(x - 2) = 2(x + 1), then x equals:

Accepted Answer

A) 8

Question 6

The sum of two numbers is 25 and their difference is 5. The product of the numbers is:

Accepted Answer

A) 150

Question 7

Which ordered pair is the solution of 5x - 2y = 1 and 2x + y = 4?

Accepted Answer

A) (1, 2)

Question 8

A linear equation in two variables has:

Accepted Answer

A) infinitely many solutions

Question 9

If ax + by = c and dx + ey = f have no solution, then:

Accepted Answer

A) a/d = b/e ≠ c/f

Question 10

The sum of three consecutive integers is 72. The largest integer is:

Accepted Answer

A) 25

Question 11

Solve for x: (x/2) + (x/3) = 10.

Accepted Answer

A) 12

Question 12

If the point (2, k) lies on the line 3x + 4y = 18, then k equals:

Accepted Answer

A) 3

Question 13

The roots of x² - 7x + 12 = 0 are:

Accepted Answer

A) 3 and 4

Question 14

If one root of x² + px + 8 = 0 is 2, then p equals:

Accepted Answer

A) -6

Question 15

The quadratic equation whose roots are 5 and -3 is:

Accepted Answer

A) x² - 2x - 15 = 0

Question 16

The discriminant of 2x² - 3x + 5 = 0 is:

Accepted Answer

A) -31

Question 17

For what value of k does x² + kx + 16 = 0 have equal roots?

Accepted Answer

A) ±8

Question 18

If α and β are roots of x² - 5x + 6 = 0, then α² + β² equals:

Accepted Answer

A) 13

Question 19

The equation x² - 4x + 3 = 0 has:

Accepted Answer

A) two distinct real roots

Question 20

A rectangular garden has length 4 m more than breadth and area 60 m². Its breadth is:

Accepted Answer

A) 6 m

Question 21

If x² - 2x + m = 0 has one root -1, then the other root is:

Accepted Answer

A) 3

Question 22

Solve: 3x² + 2x - 1 = 0.

Accepted Answer

A) x = -1 or 1/3

Question 23

The sum and product of the roots of 2x² - 6x + 4 = 0 are respectively:

Accepted Answer

A) 3 and 2

Question 24

Which condition ensures that ax² + bx + c = 0 has no real roots?

Accepted Answer

A) b² - 4ac < 0

Question 25

Expand (2x + 3)².

Accepted Answer

A) 4x² + 12x + 9

Question 26

If a + b = 7 and a - b = 3, then a² - b² equals:

Accepted Answer

A) 21

Question 27

If x + 1/x = 5, then x³ + 1/x³ equals:

Accepted Answer

A) 110

Question 28

The value of 101² using identity is:

Accepted Answer

A) 10201

Question 29

Factorise: x² - 9.

Accepted Answer

A) (x - 3)(x + 3)

Question 30

If x + y = 12 and xy = 32, then x² + y² equals:

Accepted Answer

A) 80

Question 31

Expand (a -

Accepted Answer

A) ³.

Question 32

If a + b + c = 6 and a² + b² + c² = 14, then ab + bc + ca equals:

Accepted Answer

A) 11

Question 33

The value of 999² using identity is:

Accepted Answer

A) 998001

Question 34

If x - 1/x = 4, then x² + 1/x² equals:

Accepted Answer

A) 18

Question 35

Factorise: 8x³ - 27.

Accepted Answer

A) (2x - 3)(4x² + 6x + 9)

Question 36

If x + y = 4 and x² + y² = 10, then xy equals:

Accepted Answer

A) 3

Question 37

The remainder when x³ - 2x² + x - 5 is divided by x - 2 is:

Accepted Answer

A) -3

Question 38

For the polynomial p(x) = x² + 5x + 6, the zeros are:

Accepted Answer

A) -2 and -3

Question 39

If x - 1 is a factor of x² - kx + 6, then k equals:

Accepted Answer

A) 7

Question 40

The degree of the polynomial 3x⁴ - 2x² + 7x - 1 is:

Accepted Answer

A) 4

Question 41

If p(x) = x³ + ax² + bx + 6 has zeros 1, -2, and c, then c equals:

Accepted Answer

A) 3

Question 42

When x³ + 3x² - x - 3 is divided by x + 1, the remainder is:

Accepted Answer

A) 0

Question 43

The polynomial 2x² - 3x + 1 has zeros α and β. The value of α/β + β/α is:

Accepted Answer

A) 5/2

Question 44

If p(x) = 2x³ - 5x² + 3x - 1, the value of p(1) - p(-1) is:

Accepted Answer

A) 10

Question 45

The factorised form of x² - 5x + 6 is:

Accepted Answer

A) (x - 2)(x - 3)

Question 46

A polynomial of degree 2 is called:

Accepted Answer

A) quadratic

Question 47

Solve: 3x - 2 > 7.

Accepted Answer

A) x > 3

Question 48

Solve: -2x + 5 ≤ 9.

Accepted Answer

A) x ≥ -2

Question 49

Solve x² - x - 6 < 0.

Accepted Answer

A) -2 < x < 3

Question 50

The solution of (x - 1)/(x + 2) > 0 is:

Accepted Answer

A) x < -2 or x > 1

Question 51

Solve |x - 3| < 2.

Accepted Answer

A) 1 < x < 5

Question 52

Which inequality is equivalent to 2x + 1 ≥ 5x - 2?

Accepted Answer

A) x ≤ 1

Question 53

The solution set of x² - 4x + 4 ≤ 0 is:

Accepted Answer

A) {2}

Question 54

For what values of x is x² - 9 > 0?

Accepted Answer

A) x < -3 or x > 3

Question 55

The graph of y = x² - 4 is a parabola opening:

Accepted Answer

A) upward

Question 56

The line y = -2x + 5 has a slope of:

Accepted Answer

A) -2

Question 57

The x-intercept of y = 3x - 6 is:

Accepted Answer

A) 2

Question 58

The vertex of the parabola y = (x - 2)² + 3 is:

Accepted Answer

A) (2, 3)

Question 59

The graph of y = x³ passes through which point?

Accepted Answer

A) (1, 1)

Question 60

The line through (0, 2) with slope 3 has equation:

Accepted Answer

A) y = 3x + 2

Question 61

sin 30° + cos 60° equals:

Accepted Answer

A) 1

Question 62

tan 60° × cot 30° equals:

Accepted Answer

A) 3

Question 63

sin² θ + cos² θ = ?

Accepted Answer

A) 1

Question 64

If sin θ = 3/5 and θ is acute, then cos θ equals:

Accepted Answer

A) 4/5

Section	Questions
Linear Equations in One and Two Variables	12
Quadratic Equations	12
Algebraic Identities	12
Polynomials	10
Inequalities	8
Basic Graphs	6
Trigonometry	15
Co-ordinate Geometry	15
Modern Indian History	15
Geography	10
Traditional GK	5

DAY 3 ALGEBRA HISTORY GEOGRAPHY | Free Mock Test 2026 | 120 MCQs

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