NATA Practice Set 1

If log₂(x) = 5, then x equals:

1. A.10
2. B.25
3. C.32✓
4. D.64

Correct answer: C

The roots of the equation x² − 7x + 12 = 0 are:

1. A.2 and 6
2. B.3 and 4✓
3. C.1 and 12
4. D.−3 and −4

Correct answer: B

The determinant of a 2×2 matrix [[a, b], [c, d]] is:

1. A.ab − cd
2. B.ac − bd
3. C.ad − bc✓
4. D.ad + bc

Correct answer: C

In coordinate geometry, the slope of a line passing through (2, 5) and (6, 13) is:

1. A.1
2. B.2✓
3. C.3
4. D.4

Correct answer: B

The derivative of sin(x) · cos(x) with respect to x is:

1. A.cos(2x)✓
2. B.sin(2x)
3. C.−sin(2x)
4. D.2cos(2x)

Correct answer: A

The maximum value of the function f(x) = 3 + 4x − x² is:

1. A.3
2. B.5
3. C.7✓
4. D.9

Correct answer: C

How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition?

1. A.20
2. B.60✓
3. C.120
4. D.125

Correct answer: B

The mean of 5 numbers is 12. If one number is excluded, the mean becomes 10. The excluded number is:

1. A.14
2. B.16
3. C.18
4. D.20✓

Correct answer: D

Which Indian architect designed the Indian Institute of Management Ahmedabad campus in collaboration with Louis Kahn?

1. A.Charles Correa
2. B.Balkrishna Doshi✓
3. C.Raj Rewal
4. D.Achyut Kanvinde

Correct answer: B

If the sum of the interior angles of a polygon is 1080°, how many sides does it have?

1. A.6
2. B.7
3. C.8✓
4. D.10

Correct answer: C

In a Venn diagram, the shaded region representing elements in A but not in B is denoted as:

1. A.A ∩ B
2. B.A ∪ B
3. C.A − B✓
4. D.A'

Correct answer: C

Which of the following statements can be concluded from the diagram: All squares are rectangles, all rectangles are parallelograms?

1. A.All parallelograms are squares
2. B.All squares are parallelograms✓
3. C.No rectangle is a square
4. D.Some parallelograms are not rectangles

Correct answer: B

A shopkeeper sells an article at 20% profit. If the cost price is ₹500, the selling price is:

1. A.₹550
2. B.₹600✓
3. C.₹625
4. D.₹700

Correct answer: B

"All roses are flowers. Some flowers are red. Therefore, some roses are red." This argument is:

1. A.Logically valid
2. B.Logically invalid✓
3. C.Tautological
4. D.Contradictory

Correct answer: B

If it is established that 'if it rains, the ground is wet' and 'the ground is not wet', which conclusion follows?

1. A.It rained
2. B.It did not rain✓
3. C.The ground might be wet
4. D.No conclusion can be drawn

Correct answer: B

A mirror image of the letter 'R' when placed in front of a vertical mirror on its right side will appear as:

1. A.Same as R
2. B.Upside-down R
3. C.Laterally reversed R✓
4. D.Rotated 90° clockwise

Correct answer: C

In geometric composition, a regular tessellation can be created using which of the following regular polygons?

1. A.Regular pentagon
2. B.Regular hexagon✓
3. C.Regular octagon
4. D.Regular heptagon

Correct answer: B

A cone is a 3D shape generated by rotating which 2D shape about one of its sides?

1. A.Circle
2. B.Right-angled triangle✓
3. C.Rectangle
4. D.Semicircle

Correct answer: B

In a two-point perspective drawing, where are the two vanishing points located?

1. A.One on the horizon line and one above it
2. B.Both on the horizon line, left and right✓
3. C.Both below the horizon line
4. D.One at the centre and one at the edge

Correct answer: B

Complementary colours are those that are:

1. A.Adjacent on the colour wheel
2. B.Opposite each other on the colour wheel✓
3. C.Shades of the same hue
4. D.All warm colours

Correct answer: B

The visual weight of an element in a composition is increased by:

1. A.Making it lighter in colour
2. B.Using a darker and more saturated colour✓
3. C.Placing it at the centre
4. D.Reducing its size

Correct answer: B

The rule of thirds in visual composition divides the frame into how many equal parts?

1. A.4
2. B.6
3. C.9✓
4. D.12

Correct answer: C

The electric field at a distance r from a point charge Q is proportional to:

1. A.Q/r
2. B.Q/r²✓
3. C.Q²/r
4. D.Q/r³

Correct answer: B

The SI unit of electric current is:

1. A.Volt
2. B.Ohm
3. C.Ampere✓
4. D.Watt

Correct answer: C

Faraday's law of electromagnetic induction states that the induced EMF is proportional to:

1. A.The magnetic flux itself
2. B.The rate of change of magnetic flux✓
3. C.The square of the magnetic field
4. D.The area of the conductor

Correct answer: B

Total internal reflection occurs when light travels from a:

1. A.Rarer medium to a denser medium
2. B.Denser medium to a rarer medium at an angle greater than the critical angle✓
3. C.Vacuum to glass
4. D.Any medium to any other medium

Correct answer: B

In the periodic table, elements in the same group have the same number of:

1. A.Total electrons
2. B.Neutrons
3. C.Valence electrons✓
4. D.Electron shells

Correct answer: C

A sigma (σ) bond is formed by:

1. A.Lateral overlap of p-orbitals
2. B.Head-on overlap of atomic orbitals✓
3. C.Transfer of electrons
4. D.Sharing of electrons with a coordinate bond only

Correct answer: B

At 0°C and 1 atm, which of the following gases has the highest density?

1. A.Helium
2. B.Nitrogen
3. C.Oxygen
4. D.Carbon dioxide✓

Correct answer: D

The speed of sound in air at 20°C is approximately 343 m/s. If the frequency of a sound wave is 686 Hz, its wavelength is:

1. A.0.25 m
2. B.0.5 m✓
3. C.1.0 m
4. D.2.0 m

Correct answer: B