TN 10th Standard Mathematics - Multiple Choice Questions Bank (EM)
Introduction Welcome back to our educational portal! If you are a Class 10 student preparing for your Mathematics board exams, mastering the 1-mark multiple-choice questions is essential for scoring high marks.
Below, we have provided a comprehensive chapter-wise breakdown of important 1-mark questions for 10th Standard Mathematics (English Medium). You can also download the complete PDF at the bottom of this post!
1. Relations and Functions
Multiple choice questions
If n(A x B) = 6 and A = {1, 3} then n(B) is
(1) 1 (2) 2 (3) 3 (4) 6 A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n[(A U C) x B] is
(1) 8 (2) 20 (3) 12 (4) 16 If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true.
(1) (A x C) ⊂ (B x D) (2) (B x D) ⊂ (A x C) (3) (A x B) ⊂ (A x D) (4) (D x A) ⊂ (B x A) If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is
(1) 3 (2) 2 (3) 4 (4) 8 The range of the relation R = {(x, x²) | x is a prime number less than 13} is
(1) {2, 3, 5, 7} (2) {2, 3, 5, 7, 11} (3) {4, 9, 25, 49, 121} (4) {1, 4, 9, 25, 49, 121} If the ordered pairs (a+2, 4) and (5, 2a+b) are equal then (a, b) is
(1) (2, -2) (2) (5, 1) (3) (2, 3) (4) (3, -2) Let n(A) = m and n(B) = n then the total number of non-empty relations that can be defined from A to B is
(1) m^n (2) n^m (3) 2^(mn) - 1 (4) 2^(mn) If {(a, 8), (6, b)} represents an identity function, then the value of a and b are respectively
(1) (8, 6) (2) (8, 8) (3) (6, 8) (4) (6, 6) Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}. A function f: A → B given by f = {(1, 4), (2, 8), (3, 9), (4, 10)} is a
(1) Many-one function (2) Identity function (3) One-to-one function (4) Into function If f(x) = 2x² and g(x) = 1/(3x), then f o g is
(1) 3/(2x²) (2) 2/(3x²) (3) 2/(9x²) (4) 1/(6x²) If f: A → B is a bijective function and if n(B) = 7, then n(A) is equal to
(1) 7 (2) 49 (3) 1 (4) 14 Let f and g be two functions given by f = {(0, 1), (2, 0), (3, -4), (4, 2), (5, 7)}, g = {(0, 2), (1, 0), (2, 4), (-4, 2), (7, 0)} then the range of f o g is
(1) {0, 2, 3, 4, 5} (2) {-4, 1, 0, 2, 7} (3) {1, 2, 3, 4, 5} (4) {0, 1, 2} Let f(x) = √(1 + x²) then
(1) f(xy) = f(x).f(y) (2) f(xy) ≥ f(x).f(y) (3) f(xy) ≤ f(x).f(y) (4) None of these If g = {(1, 1), (2, 3), (3, 5), (4, 7)} is a function given by g(x) = αx + β then the values of α and β are
(1) (-1, 2) (2) (2, -1) (3) (-1, -2) (4) (1, 2) f(x) = (x+1)³ - (x-1)³ represents a function which is
(1) linear (2) cubic (3) reciprocal (4) quadratic
2. Numbers and Sequences
Multiple choice questions
Euclid's division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy.
(1) 1 < r < b (2) 0 < r < b (3) 0 ≤ r < b (4) 0 < r ≤ b Using Euclid's division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are
(1) 0, 1, 8 (2) 1, 4, 8 (3) 0, 1, 3 (4) 1, 3, 5 If the HCF of 65 and 117 is expressible in the form of 65m - 117, then the value of m is
(1) 4 (2) 2 (3) 1 (4) 3 The sum of the exponents of the prime factors
in the prime factorization of 1729 is (1) 1 (2) 2 (3) 3 (4) 4 The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
(1) 2025 (2) 5220 (3) 5025 (4) 2520 7^(4k) ≡ ___ (mod 100)
(1) 1 (2) 2 (3) 3 (4) 4 Given F1 = 1, F2 = 3 and Fn = Fn-1 + Fn-2 then F5 is
(1) 3 (2) 5 (3) 8 (4) 11 The f
irst term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.? (1) 4551 (2) 10091 (3) 7881 (4) 13531 If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is
(1) 0 (2) 6 (3) 7 (4) 13 An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is
(1) 16 m (2) 62 m (3) 31 m (4) 31/2 m In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?
(1) 6 (2) 7 (3) 8 (4) 9 If A = 2^65 and B = 2^64 + 2^63 + 2^62 + ... + 2^0 which of the following is true?
(1) B is 2^64 more than A (2) A and B are equal (3) B is larger than A by 1 (4) A is larger than B by 1 The next term of the sequence 3/16, 1/8, 1/12, 1/18, ...
is (1) 1/24 (2) 1/27 (3) 2/3 (4) 1/81 If the sequence t1, t2, t3, ... are in A.P. then the sequence t6, t12, t18, ... is
(1) a Geometric Progression (2) an Arithmetic Progression (3) neither an Arithmetic Progression nor a Geometric Progression (4) a constant sequence The value of (1³ + 2³ + 3³ + ... + 15³) - (1 + 2 + 3 + ... + 15) is
(1) 14400 (2) 14200 (3) 14280 (4) 14520
3. Algebra
Multiple choice questions
A system of three linear equations in three variables is inconsistent if their planes
(1) intersect only at a point (2) intersect in a line (3) coincides with each other (4) do not intersect The solution of the system x + y - 3z = -6, -7y + 7z = 7, 3z = 9 is (Note: corrected obvious typo in source from 3x to 3z)
(1) x = 1, y = 2, z = 3 (2) x = -1, y = 2, z = 3 (3) x = -1, y = -2, z = 3 (4) x = 1, y = -2, z = 3
If (x - 6) is the HCF of x² - 2x - 24 and x² - kx - 6 then the value of k is
(1) 3 (2) 5 (3) 6 (4) 8 (3y - 3)/y ÷ (7y - 7)/3y² is
(1) 9y/7 (2) 9y³/(21y - 21) (3) (21y² - 42y + 21)/3y³ (4) 7(y² - 2y + 1)/y² y² + 1/y² is not equal to
(1) (y⁴ + 1)/y² (2) (y - 1/y)² + 2 (3) (y + 1/y)² - 2 (4) (y + 1/y)² x/(x² - 25) - 8/(x² + 6x + 5) gives
(1) (x² - 7x + 40) / ((x - 5)(x + 5)) (2) (x² + 7x + 40) / ((x - 5)(x + 5)(x + 1)) (3) (x² - 7x + 40) / ((x² - 25)(x + 1)) (4) (x² + 10) / ((x² - 25)(x + 1)) The square root of (256x⁸y⁴z¹⁰) / (25x⁶y⁶z⁶) is equal to
(1) 16/5 |x²z⁴ / y²| (2) 16 |y² / x²z⁴| (3) 16/5 |y / xz²| (4) 16/5 |xz² / y| Which of the following should be added to make x⁴ + 64 a perfect square
(1) 4x² (2) 16x² (3) 8x² (4) -8x² The solution of (2x - 1)² = 9 is equal to
(1) -1 (2) 2 (3) -1, 2 (4) None of these The values of a and b if 4x⁴ - 24x³ + 76x² + ax + b is a perfect square are
(1) 100, 120 (2) 10, 12 (3) -120, 100 (4) 12, 10 If the roots of the equation q²x² + p²x + r² = 0 are the squares of the roots of the equation qx² + px + r = 0, then q, p, r are in
(1) A.P (2) G.P (3) Both A.P and G.P (4) none of these Graph of a linear polynomial is a
(1) straight line (2) circle (3) parabola (4) hyperbola The number of points of intersection of the quadratic polynomial x² + 4x + 4 with the X axis is
(1) 0 (2) 1 (3) 0 or 1 (4) 2 For the given matrix A = [1 3 5 7; 2 4 6 8; 9 11 13 15] the order of the matrix A^T is
(1) 2 x 3 (2) 3 x 2 (3) 3 x 4 (4) 4 x 3 If A is a 2 x 3 matrix and B is a 3 x 4 matrix, how many columns does AB have
(1) 3 (2) 4 (3) 2 (4) 5 If number of columns and rows are not equal in a matrix then it is said to be a
(1) diagonal matrix (2) rectangular matrix (3) square matrix (4) identity matrix Transpose of a column matrix is
(1) unit matrix (2) diagonal matrix (3) column matrix (4) row matrix Find the matrix X if 2X + [1 3; 5 7] = [5 7; 9 5]
(1) [-2 -2; 2 -1] (2) [2 2; 2 -1] (3) [1 2; 2 2] (4) [2 1; 2 2] Which of the following can be calculated from the given matrices A = [1 2; 3 4; 5 6] and B = [1 2 3; 4 5 6; 7 8 9]?
(i) A² (ii) B² (iii) AB (iv) BA (1) (i) and (ii) only (2) (ii) and (iii) only (3) (ii) and (iv) only (4) all of these If A = [1 2 3; 3 2 1], B = [1 0; 2 -1; 0 2] and C = [0 1; -2 5]. Which of the following statements are correct?
(i) AB + C = [5 5; 5 5] (ii) BC = [0 1; 2 -3; -4 10] (iii) BA + C = [2 5; 3 0] (iv) (AB)C = [-8 20; -8 13] (1) (i) and (ii) only (2) (ii) and (iii) only (3) (iii) and (iv) only (4) all of these
4. Geometry
Multiple choice questions
If in triangles ABC and EDF, AB/DE = BC/FD then they will be similar, when
(1) Angle B = Angle E (2) Angle A = Angle D (3) Angle B = Angle D (4) Angle A = Angle F In Triangle LMN, Angle L = 60°, Angle M = 50°. If Triangle LMN ~ Triangle PQR then the value of Angle R is
(1) 40° (2) 70° (3) 30° (4) 110° If Triangle ABC is an isosceles triangle with Angle C = 90° and AC = 5 cm, then AB is
(1) 2.5 cm (2) 5 cm (3) 10 cm (4) 5√2 cm In a given figure ST || QR, PS = 2 cm and SQ = 3 cm. Then the ratio of the area of Triangle PQR to the area of Triangle PST is
(1) 25:4 (2) 25:7 (3) 25:11 (4) 25:13 The perimeters of two similar triangles Triangle ABC and Triangle PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then the length of AB is
(1) 6 2/3 cm (2) (10√6)/3 cm (3) 66 2/3 cm (4) 15 cm If in Triangle ABC, DE || BC. AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is
(1) 1.4 cm (2) 1.8 cm (3) 1.2 cm (4) 1.05 cm In a Triangle ABC, AD is the bisector of Angle BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. The length of the side AC is
(1) 6 cm (2) 4 cm (3) 3 cm (4) 8 cm In the adjacent figure Angle BAC = 90° and AD is perpendicular to BC then
(1) BD . CD = BC² (2) AB . AC = BC² (3) BD . CD = AD² (4) AB . AC = AD² Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?
(1) 13 m (2) 14 m (3) 15 m (4) 12.8 m In the given figure, PR = 26 cm, QR = 24 cm, Angle PAQ = 90°, PA = 6 cm and QA = 8 cm. Find Angle PQR
(1) 80° (2) 85° (3) 75° (4) 90° A tangent is perpendicular to the radius at the
(1) centre (2) point of contact (3) infinity (4) chord How many tangents can be drawn to the circle from an exterior point?
(1) one (2) two (3) infinite (4) zero The two tangents from an external points P to a circle with centre at O are PA and PB. If Angle APB = 70° then the value of Angle AOB is
(1) 100° (2) 110° (3) 120° (4) 130° In figure CP and CQ are tangents to a circle with centre at O. ARB is another tangent touching the circle at R. If CP = 11cm and BC = 7 cm, then the length of BR is
(1) 6 cm (2) 5 cm (3) 8 cm (4) 4 cm In figure if PR is tangent to the circle at P and O is the centre of the circle, then Angle POQ is
(1) 120° (2) 100° (3) 110° (4) 90°
5. Coordinate Geometry
Multiple choice questions
The area of triangle formed by the points (-5,0), (0,-5) and (5,0) is
(1) 0 sq.units (2) 25 sq.units (3) 5 sq.units (4) none of these A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y-axis. The path travelled by the man is
(1) x = 10 (2) y = 10 (3) x = 0 (4) y = 0 The straight line given by the equation x = 11 is
(1) parallel to X axis (2) parallel to Y axis (3) passing through the origin (4) passing through the point (0,11) If (5,7), (3,p) and (6,6) are collinear, then the value of p is
(1) 3 (2) 6 (3) 9 (4) 12 The point of intersection of 3x - y = 4 and x + y = 8 is
(1) (5,3) (2) (2,4) (3) (3,5) (4) (4,4) The slope of the line joining (12,3), (4,a) is 1/8. The value of
'a' is (1) 1 (2) 4 (3) -5 (4) 2 The slope of the line which is perpendicular to a line joining the points (0,0) and (-8,8) is
(1) -1 (2) 1 (3) 1/3 (4) -8 If slope of the line PQ is 1/√3 then slope of the perpendicular bisector of PQ is
(1) √3 (2) -√3 (3) 1/√3 (4) 0 If A is a point on the Y-axis whose ordinate is 8 and B is a point on the X-axis whose abscissae is 5 then the equation of the line AB is
(1) 8x + 5y = 40 (2) 8x - 5y = 40 (3) x = 8 (4) y = 5 The equation of a line passing through the origin and perpendicular to the line 7x - 3y + 4 = 0 is
(1) 7x - 3y + 4 = 0 (2) 3x - 7y + 4 = 0 (3) 3x + 7y = 0 (4) 7x - 3y = 0 Consider four straight lines
(i) l1: 3y = 4x + 5 (ii) l2: 4y = 3x - 1 (iii) l3: 4y + 3x = 7 (iv) l4: 4x + 3y = 2 Which of th e following statement is true? ( 1) l1 and l2 are perpendicular (2) l1 and l4 are parallel (3) l2 and l4 are perpendicular (4) l2 and l3 are parallel A straight line has equation 8y = 4x + 21. Which of the following is true
(1) The slope is 0.5 and the y intercept is 2.6 (2) The slope is 5 and the y intercept is 1.6 (3) The slope is 0.5 and the y intercept is 1.6 (4) The slope is 5 and the y intercept is 2.6 When proving
that a quadrilateral is a trapezium, it is necessary to show (1) Two sides are parallel. (2) Two parallel and two non-parallel sides. (3) Oppos ite sides are parallel. (4) All sides are of equal length. When proving that a quadrilateral is a parallelogram by using slopes you must find
(1) The slopes of two sides (2) The slopes of two pair of opposite sides (3) The lengths of all sides (4) Both the lengths and slopes of two sides (2, 1) is the point of intersection of two lines.
(1) x - y - 3 = 0; 3x - y - 7 = 0 (2) x + y = 3; 3x + y = 7 (3) 3x + y = 3; x + y = 7 (4) x + 3y - 3 = 0; x - y - 7 = 0
6. Trigonometry
Multiple choice questions
The value of sin²θ + 1/(1 + tan²θ) is equal to
(1) tan²θ (2) 1 (3) cot²θ (4) 0 tanθ cosec²θ - tanθ is equal to
(1) secθ (2) cot²θ (3) sinθ (4) cotθ If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to
(1) 9 (2) 7 (3) 5 (4) 3 If sin θ + cos θ = a and sec θ + cosec θ = b then the value of b(a² - 1) is equal to
(1) 2a (2) 3a (3) 0 (4) 2ab If 5x = sec θ and 5/x = tan θ, then x² - 1/x² is equal to
(1) 25 (2) 1/25 (3) 5 (4) 1 If sin θ = cos θ, then 2 tan²θ + sin²θ - 1 is equal to
(1) -3/2 (2) 3/2 (3) 2/3 (4) -2/3 If x = a tan θ and y = b sec θ then
(1) y²/b² - x²/a² = 1 (2) x²/a² - y²/b² = 1 (3) x²/a² + y²/b² = 1 (4) x²/a² - y²/b² = 0 (1 + tan θ + sec θ)(1 + cot θ - cosec θ) is equal to
(1) 0 (2) 1 (3) 2 (4) -1 If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p² - q² is equal to
(1) a² - b² (2) b² - a² (3) a² + b² (4) b - a If the ratio of the height of a tower and the length of its shadow is √3:1, then the angle of elevation of the sun has measure
(1) 45° (2) 30° (3) 90° (4) 60° The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point 'b' metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to
(1) √3b (2) b/3 (3) b/2 (4) b/√3 A tower is 60 m high. Its shadow is x metres shorter when the sun's altitude is 45° than when it has been 30°, then x is equal to
(1) 41.92 m (2) 43.92 m (3) 43 m (4) 45.6 m The angle of
depression of the top and bottom of 20 m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is (1) 20, 10√3 (2) 30, 5√3 (3) 20, 10 (4) 30, 10√3 Two persons are standing 'x' metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their f
eet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is (1) √2x (2) x/(2√2) (3) x/√2 (4) 2x The angle of elevation of a cloud from a point h metres above a lake is β. The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is
(1) h(1 + tan β) / (1 - tan β) (2) h(1 - tan β) / (1 + tan β) (3) h tan(45° - β) (4) none of these
