Grade 10 · Board practice
NCERT Exemplars
The NCERT Exemplar is the official higher-order problem book — its questions are tougher than the textbook and roughly 1 in 5 board questions is pitched at this level. Every link below opens the genuine NCERT PDF for that chapter (straight from ncert.nic.in), and each card previews a few real questions. 27 chapters across Maths and Science.
These are the authoritative documents from NCERT — the same ones your school recommends. Open a chapter's PDF for the full set; the previews here show the style so you know what to expect.
Mathematics
All answers (PDF) ↗Higher-order problems from the official NCERT Exemplar — about 20% of board questions are pitched at this level.
Real Numbers
Learn this chapter →MCQFor some integer m, every even integer is of the form
- m
- m + 1
- 2m ✓
- 2m + 1
MCQThe largest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is
- 13 ✓
- 65
- 875
- 1750
Polynomials
Learn this chapter →MCQIf one of the zeroes of the quadratic polynomial (k–1)x² + kx + 1 is –3, then the value of k is
- 4/3 ✓
- –4/3
- 2/3
- –2/3
MCQThe number of polynomials having zeroes as –2 and 5 is
- 1
- 2
- 3
- more than 3 ✓
Short answerFind the zeroes of the polynomial x² + (1/6)x – 2, and verify the relation between the coefficients and the zeroes.
Work it out, then check against the official answers PDF.
Pair of Linear Equations in Two Variables
Learn this chapter →MCQThe pair of equations x = a and y = b graphically represents lines which are
- parallel
- intersecting at (b, a)
- coincident
- intersecting at (a, b) ✓
Quadratic Equations
Learn this chapter →MCQWhich of the following is a quadratic equation?
- x² + 2x + 1 = (4 – x)² + 3
- –2x² = (5 – x)(2x – 2/5)
- (k+1)x² + (3/2)x = 7, where k = –1
- x³ – x² = (x – 1)³ ✓
Short answerDoes (x – 1)² + 2(x + 1) = 0 have a real root? Justify your answer.
Work it out, then check against the official answers PDF.
Arithmetic Progressions
Learn this chapter →MCQIn an AP, if d = –4, n = 7, aₙ = 4, then a is
- 6
- 7
- 20
- 28 ✓
MCQThe 11th term of the AP: –5, –5/2, 0, 5/2, … is
- –20
- 20 ✓
- –30
- 30
Triangles
Learn this chapter →MCQIf in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ, then
- △PQR ~ △CAB ✓
- △PQR ~ △ABC
- △CBA ~ △PQR
- △BCA ~ △PQR
Short answerIt is given that △DEF ~ △RPQ. Is it true to say that ∠D = ∠R and ∠F = ∠P? Why?
Work it out, then check against the official answers PDF.
Coordinate Geometry
Learn this chapter →MCQThe distance of the point P(2, 3) from the x-axis is
- 2
- 3 ✓
- 1
- 5
MCQThe distance between the points A(0, 6) and B(0, –2) is
- 6
- 8 ✓
- 4
- 2
Introduction to Trigonometry
Learn this chapter →MCQIf cos A = 4/5, then the value of tan A is
- 3/5
- 3/4 ✓
- 4/3
- 5/3
MCQIf sin A = 1/2, then the value of cot A is
- √3 ✓
- 1/√3
- √3/2
- 1
Some Applications of Trigonometry
Learn this chapter →Short answerThe angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
Work it out, then check against the official answers PDF.
Circles
Learn this chapter →MCQIf the angle between two radii of a circle is 130°, then the angle between the tangents at the ends of the radii is
- 90°
- 50° ✓
- 70°
- 40°
Areas Related to Circles
Learn this chapter →MCQIf the area of a circle is equal to the area of a square, then the ratio of their perimeters is
- 1 : 1
- 2 : π
- π : 2
- √π : 2 ✓
Surface Areas & Volumes
Learn this chapter →MCQA cylinder, a cone and a hemisphere are of equal base and have the same height. The ratio of their volumes is
- 3 : 1 : 2 ✓
- 1 : 2 : 3
- 2 : 1 : 3
- 1 : 3 : 2
Statistics
Learn this chapter →MCQWhile computing the mean of grouped data, we assume that the frequencies are
- evenly distributed over all the classes
- centred at the class marks of the classes ✓
- centred at the upper limits of the classes
- centred at the lower limits of the classes
Probability
Learn this chapter →MCQIf an event cannot occur, then its probability is
- 1
- 3/4
- 1/2
- 0 ✓
MCQThe probability that a non-leap year selected at random will contain 53 Sundays is
- 1/7 ✓
- 2/7
- 3/7
- 5/7
Science
All answers (PDF) ↗Assertion–reason, MCQ and descriptive questions from the official NCERT Exemplar — the higher-order practice CBSE now leans on.
Chemical Reactions and Equations
Learn this chapter →MCQWhich of the following is a displacement reaction?
- CaCO₃ → CaO + CO₂
- CaO + H₂O → Ca(OH)₂
- 2FeSO₄ → Fe₂O₃ + SO₂ + SO₃
- Fe + CuSO₄ → FeSO₄ + Cu ✓
Acids, Bases and Salts
Learn this chapter →MCQWhich one of the following types of medicines is used for treating indigestion?
- Antibiotic
- Analgesic
- Antacid ✓
- Antiseptic
Metals and Non-metals
Learn this chapter →MCQWhich of the following metals exists in liquid state at room temperature?
- Na
- Hg ✓
- Cu
- Al
Carbon and its Compounds
Learn this chapter →MCQBuckminsterfullerene is an allotropic form of
- phosphorus
- sulphur
- carbon ✓
- tin
Life Processes
Learn this chapter →MCQThe kidneys in human beings are a part of the system for
- nutrition
- respiration
- excretion ✓
- transportation
Control and Coordination
Learn this chapter →MCQThe brain is responsible for
- thinking
- regulating the heart beat
- balancing the body
- all of the above ✓
How do Organisms Reproduce?
Learn this chapter →MCQWhich of the following is the correct sequence of events of sexual reproduction in a flower?
- pollination, fertilisation, seed, embryo
- fertilisation, pollination, embryo, seed
- pollination, fertilisation, embryo, seed ✓
- embryo, seed, pollination, fertilisation
Heredity and Evolution
Learn this chapter →MCQA trait in an organism is influenced by
- paternal DNA only
- maternal DNA only
- both maternal and paternal DNA ✓
- neither paternal nor maternal DNA
Light – Reflection and Refraction
Learn this chapter →MCQWhich of the following can make a parallel beam of light when light from a point source is incident on it?
- Concave mirror as well as convex lens ✓
- Convex mirror as well as concave lens
- Two plane mirrors placed at 90° to each other
- Concave mirror as well as concave lens
The Human Eye and the Colourful World
Learn this chapter →MCQThe human eye forms the image of an object at its
- cornea
- iris
- pupil
- retina ✓
Electricity
Learn this chapter →MCQA cell, a resistor, a key and an ammeter are arranged as shown in the circuit diagrams. The current recorded in the ammeter will be
- maximum in (i)
- maximum in (ii)
- maximum in (iii)
- the same in all the cases ✓
Magnetic Effects of Electric Current
Learn this chapter →MCQChoose the incorrect statement from the following regarding magnetic lines of field
- The direction of magnetic field at a point is taken to be the direction in which the north pole of a compass needle points
- Magnetic field lines are closed curves
- If magnetic field lines are parallel and equidistant, they represent zero field strength ✓
- Relative strength of magnetic field is shown by the degree of closeness of the field lines
Our Environment
Learn this chapter →MCQWhich of the following groups contain only biodegradable items?
- Grass, flowers and leather ✓
- Grass, wood and plastic
- Fruit-peels, cake and lime-juice
- Cake, wood and grass
Source: NCERT Exemplar Problems, Class X (Mathematics & Science) — published by the National Council of Educational Research and Training, ncert.nic.in. Links point to the official PDFs; trykarkedekho does not host or alter them.