CBSE CLASS 10 · MATHS & SCIENCE

Class 10 MCQ Challenge Lab

Five questions to see what clicks. Then we’ll unpack your answers together and help you choose what to practise next.

01 Have a go02 Understand why03 Try a fresh question

MATHS / CLASS 105 QUESTIONS

2x + y = 7

LINEAR EQUATIONS

Crack the equation.

Turn clues into equations, solve the pair and see where the lines meet.

5 questions3 ideas to exploreHints if you need them

SCIENCE / CLASS 105 QUESTIONS

1/f = 1/v − 1/u

LIGHT · LENSES · MIRRORS

Make sense of light.

Get your signs right, choose a formula and see what the answer means.

5 questions4 ideas to exploreHints if you need them

No sign-up · No negative marking · 10 seconds to think before each next question

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Linear equations: model, solve and classify — TutorMax original questions

Model the conditions

Define each variable with units and translate each condition separately. Item count multiplies item price.

Eliminate and check

Add or subtract complete equations. Divide by the remaining coefficient, then substitute into both original conditions.

Classify shared solutions

A contradiction gives no solution. A repeated equation leaves infinitely many points. Coefficient proportionality alone is not enough: check the constants.

Optics: signs, formulas and units — TutorMax original questions

Assign directed distances

For incident light travelling left to right, rightward distances are positive. Use the mirror pole or lens optical centre as the origin.

Choose the device formula

Mirror: 1/f=1/v+1/u. Lens: 1/f=1/v−1/u. Rearrange before substituting signed values.

Interpret magnification

For a lens, m=v/u. A negative value means inversion. The magnitude gives relative image height, not position.

Convert lens-power units

P=1/f with f in metres gives dioptres. A centimetre focal length must be divided by 100 first.

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Linear equations: model, solve and classify — TutorMax original questions

Model the conditions: Define each variable with units and translate each condition separately. Item count multiplies item price.

Eliminate and check: Add or subtract complete equations. Divide by the remaining coefficient, then substitute into both original conditions.

Classify shared solutions: A contradiction gives no solution. A repeated equation leaves infinitely many points. Coefficient proportionality alone is not enough: check the constants.

Two notebooks and a pen cost ₹70; one notebook and a pen cost ₹40. If n is notebook price and p is pen price, which pair models this?

2n+p=70; n+p=40
n+2p=70; n+p=40
2n+p=40; n+p=70

Let’s work through the answer

Define n and p in rupees. Translate each purchase separately: 2n+p=70 and n+p=40.

Solve 3a+b=29 and a+b=15. What are a and b?

a=7, b=8
a=14, b=1
a=8, b=7

Let’s work through the answer

Subtract the second equation from the first: 2a=14, so a=7. Then b=15−7=8. Check 3×7+8=29.

For x+y=11 and x−y=3, which pair is a solution?

x=7, y=4
x=4, y=7
x=14, y=3

Let’s work through the answer

Add to obtain 2x=14, so x=7. Substitute y=4 and check 7−4=3.

How many solutions do x+y=4 and 2x+2y=10 have?

None
One
Infinitely many

Let’s work through the answer

Doubling x+y=4 gives 2x+2y=8. The second equation contradicts it; the lines are distinct and parallel.

How many solutions do 2x+3y=12 and 4x+6y=24 have?

Infinitely many
None
Exactly two

Let’s work through the answer

Every term in the first equation doubles to the second. The same line is written twice.

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Optics: signs, formulas and units — TutorMax original questions

Assign directed distances: For incident light travelling left to right, rightward distances are positive. Use the mirror pole or lens optical centre as the origin.

Choose the device formula: Mirror: 1/f=1/v+1/u. Lens: 1/f=1/v−1/u. Rearrange before substituting signed values.

Interpret magnification: For a lens, m=v/u. A negative value means inversion. The magnitude gives relative image height, not position.

Convert lens-power units: P=1/f with f in metres gives dioptres. A centimetre focal length must be divided by 100 first.

Light travels left to right. An object is 36 cm left of a lens. What is its Cartesian object distance u?

−36 cm
+36 cm
−0.36 cm

Let’s work through the answer

Measure from the optical centre. The object lies 36 cm in the negative direction, so u=−36 cm.

A concave mirror has f=−12 cm and u=−36 cm. Find v using 1/f=1/v+1/u.

−18 cm
+18 cm
−9 cm

Let’s work through the answer

1/v=1/f−1/u=−1/12+1/36=−1/18. Thus v=−18 cm.

A convex lens has f=+12 cm and u=−36 cm. Find v using 1/f=1/v−1/u.

+18 cm
−18 cm
+9 cm

Let’s work through the answer

For a lens, 1/v=1/f+1/u=1/12−1/36=1/18. Thus v=+18 cm.

A lens has u=−36 cm and v=+18 cm. What does m=v/u tell you?

m=−0.5: inverted, half-height
m=+0.5: upright, half-height
m=−2: inverted, double-height

Let’s work through the answer

m=18/(−36)=−0.5. Negative means inverted; |m|=0.5 means half-height.

A convex lens in air has f=+40 cm. What is its power?

+2.5 D
+0.025 D
−2.5 D

Let’s work through the answer

+40 cm=+0.40 m. P=1/f=1/0.40=+2.5 D.

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About this preview & your answers

These are original TutorMax practice questions, not official board-paper questions. We’re still checking their fit with the 2026–27 syllabus. Five questions give us a starting point, not a predicted board grade or a complete picture of a chapter.

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