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ARMY PUBLIC SCHOOL,AHMEDNAGAR QUESTION BANK FOR CLASS X MATHEMATICS
ARMY PUBLIC SCHOOL,AHMEDNAGAR
QUESTION BANK FOR CLASS X
MATHEMATICS
SECTION A
MCQ
25 MCQ FROM EACH CHAPTER
CHAPTER 2
POLYNOMIALS
1. If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is (a) 10 (b) -10 (c) 5 (d) -5
2. Given that two of the zeroes of the cubic poly-nomial ax3 + bx² + cx + d are 0, the third zero is
3. If one of the zeroes of the quadratic polynomial (k – 1) x² + kx + 1 is – 3, then the value of k is
4. A quadratic polynomial, whose zeroes are -3 and 4, is (a) x²- x + 12 (b) x² + x + 12
(c) (d) 2x² + 2x – 24
5. If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and -3, then (a) a = -7, b = -1 (b) a = 5, b = -1 (c) a = 2, b = -6 (d) a – 0, b = -6
6. The number of polynomials having zeroes as -2 and 5 is (a) 1 (b) 2 (c) 3 (d) more than 3
7. Given that one of the zeroes of the cubic polynomial ax3 + bx² + cx + d is zero, the product of the other two zeroes is
8. If one of the zeroes of the cubic polynomial x3 + ax² + bx + c is -1, then the product of the other two zeroes is (a) b – a + 1 (b) b – a – 1 (c) a – b + 1 (d) a – b – 1
9. The zeroes of the quadratic polynomial x2 + 99x + 127 are (a) both positive (b) both negative
(c) one positive and one negative (d) both equal
10. The zeroes of the quadratic polynomial x² + kx + k, k? 0, (a) cannot both be positive (b) cannot both be negative (c) are always unequal (d) are always equal
11. If the zeroes of the quadratic polynomial ax² + bx + c, c # 0 are equal, then (a) c and a have opposite signs (b) c and b have opposite signs (c) c and a have the same sign (d) c and b have the same sign
12. If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it (a) has no linear term and the constant term is negative. (b) has no linear term and the constant term is positive. (c) can have a linear term but the constant term is negative. (d) can have a linear term but the constant term is positive.
13. Which of the following is not the graph of quadratic polynomial?
14. The number of polynomials having zeroes as 4 and 7 is (a) 2 (b) 3 (c) 4 (d) more than 4
15. A quadratic polynomial, whose zeores are -4 and -5, is (a) x²-9x + 20 (b) x² + 9x + 20 (c) x²-9x- 20 (d) x² + 9x- 20
16. The zeroes of the quadratic polynomial x² + 1750x + 175000 are (a) both negative (b) one positive and one negative (c) both positive (d) both equal
17. The zeroes of the quadratic polynomial x² – 15x + 50 are (a) both negative (b) one positive and one negative (c) both positive (d) both equal
18. The zeroes of the quadratic polynomial 3x² – 48 are (a) both negative (b) one positive and one negative (c) both positive (d) both equal
19. The zeroes of the quadratic polynomial x² – 18x + 81 are (a) both negative (b) one positive and one negative (c) both positive and unequal (d) both equal and positive
20. The zeroes of the quadratic polynomial x² + px + p, p ≠ 0 are (a) both equal (b) both cannot be positive (c) both unequal (d) both cannot be negative
21. If one of the zeroes of the quadratic polynomial (p – l)x² + px + 1 is -3, then the value of p
is
22. If the zeroes of the quadratic polynomial Ax² + Bx + C, C # 0 are equal, then (a) A and B have the same sign (b) A and C have the same sign (c) B and C have the same sign (d) A and C have opposite signs
23. If x3 + 1 is divided by x² + 5, then the possible degree of quotient is (a) 0 (b) 1 (c) 2 (d) 3
24. If x3 + 11 is divided by x² – 3, then the possible degree of remainder is (a) 0 (b) 1 (c) 2 (d) less than 2
25. If x4 + 3x² + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are: (a) 3, 0 (b) 4, 1 (c) 3, 1 (d) 4, 0
CHAPTER 3
LINEAR EQUATIONS IN TWO VARIABLES
1. A pair of linear equations a1x + b1y + c1 = 0; a2x + b2y + c2 = 0 is said to be inconsistent, if
2. Graphically, the pair of equations 7x – y = 5; 21x – 3y = 10 represents two lines which are (a) intersecting at one point (b) parallel (c) intersecting at two points (d) coincident
3. The pair of equations 3x – 5y = 7 and – 6x + 10y = 7 have (a) a unique solution (b) infinitely many solutions (c) no solution (d) two solutions
4. If a pair of linear equations is consistent, then the lines will be (a) always coincident (b) parallel (c) always intersecting (d) intersecting or coincident
5. The pair of equations x = 0 and x = 5 has (a) no solution (b) unique/one solution (c) two solutions (d) infinitely many solutions
6. The pair of equation x = – 4 and y = – 5 graphically represents lines which are (a) intersecting at (- 5, – 4) (b) intersecting at (- 4, – 5)
(c) intersecting at (5, 4) (d) intersecting at (4, 5)
7. For what value of k, do the equations 2x – 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines
8. If the lines given by 2x + ky = 1 and 3x – 5y = 7 are parallel, then the value of k is
9. One equation of a pair of dependent linear equations is 2x + 5y = 3. The second equation will be (a) 2x + 5y = 6 (b) 3x + 5y = 3 (c) -10x – 25y + 15 = 0 (d) 10x + 25y = 15
10. If x = a, y = b is the solution of the equations x + y = 5 and 2x – 3y = 4, then the values of a and b are respectively (a) 6, -1 (b) 2, 3 (c) 1, 4 (d) 19/5, 6/5
11. The graph of x = -2 is a line parallel to the (a) x-axis (b) y-axis (c) both x- and y-axis (d) none of these
12. The graph of y = 4x is a line (a) parallel to x-axis
(b) parallel to y-axis (c) perpendicular to y-axis (d) passing through the origin
13. The graph of y = 5 is a line parallel to the (a) x-axis (b) y-axis (c) both axis (d) none of these
14. Two equations in two variables taken together are called (a) linear equations (b) quadratic equations (c) simultaneous equations (d) none of these
15. If am bl then the system of equations ax + by = c, lx + my = n, has (a) a unique solution (b) no solution (c) infinitely many solutions (d) none of these
16. If in the equation x + 2y = 10, the value of y is 6, then the value of x will be (a) -2 (b) 2 (c) 4 (d) 5
17. The graph of the equation 2x + 3y = 5 is a (a) vertical line (b) straight line (c) horizontal line (d) none of these
18. The value of k, for which equations 3x + 5y = 0 and kx + lOy = 0 has a non-zero solution is (a) 6 (b) 0 (c) 2 (d) 5
19. The value of k, for which the system of equations x + (k + l)y = 5 and (k + l)x + 9y = 8k – 1 has infinitely many solutions is (a) 2 (b) 3 (c) 4 (d) 5
20. The value of k for which the equations (3k + l)x + 3y = 2; (k2 + l)x + (k – 2)y = 5 has no solution, then k is equal to (a) 2 (b) 3 (c) 1 (d) -1
21. The pair of equations x = a and y = b graphically represents lines which are (a) parallel (b) intersecting at (b, a) (c) coincident (d) intersecting at (a, b)
22. Asha has only ₹1 and ₹2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ₹75, then the number of ₹1 and ₹2 coins are, respectively (a) 35 and 15 (b) 15 and 35 (c) 35 and 20 (d) 25 and 25
23. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages of the son and the father are, respectively (a) 4 and 24 (b) 5 and 30 (c) 6 and 36 (d) 3 and 24
24. The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is (a) 27 (b) 72
(c) 45 (d) 36
25. The pair of linear equations 2x + 3y = 5 and 4x + 6y= 10 is (a) inconsistent (b) consistent (c) dependent consistent (d) none of these
CHAPTER 4
QUADRATIC EQUATIONS
1. Which of the following is not a quadratic equation (a) x² + 3x – 5 = 0 (b) x² + x3 + 2 = 0 (c) 3 + x + x² = 0 (d) x² – 9 = 0
2. The quadratic equation has degree (a) 0 (b) 1 (c) 2 (d) 3
3. The cubic equation has degree (a) 1 (b) 2 (c) 3 (d) 4
4. A bi-quadratic equation has degree (a) 1 (b) 2 (c) 3 (d) 4
5. The polynomial equation x (x + 1) + 8 = (x + 2) {x – 2) is (a) linear equation (b) quadratic equation (c) cubic equation (d) bi-quadratic equation
6. The equation (x – 2)² + 1 = 2x – 3 is a (a) linear equation (b) quadratic equation (c) cubic equation (d) bi-quadratic equation
7. The roots of the quadratic equation 6x² – x – 2 = 0 are
8. The quadratic equation whose roots are 1 and (a) 2x² + x – 1 = 0 (b) 2x² – x – 1 = 0 (c) 2x² + x + 1 = 0 (d) 2x² – x + 1 = 0
9. The quadratic equation whose one rational root is 3 + √2 is (a) x² – 7x + 5 = 0 (b) x² + 7x + 6 = 0 (c) x² – 7x + 6 = 0 (d) x² – 6x + 7 = 0
10. The equation 2x² + kx + 3 = 0 has two equal roots, then the value of k is (a) ±√6 (b) ± 4 (c) ±3√2 (d) ±2√6
11. The roots of the quadratic equation , x ≠ 0 are.
12. The roots of the quadratic equation 2x² – 2√2x + 1 = 0 are
13. The sum of the roots of the quadratic equation 3×2 – 9x + 5 = 0 is (a) 3 (b) 6 (c) -3 (d) 2
14. If the roots of ax2 + bx + c = 0 are in the ratio m : n, then (a) mna² = (m + n) c² (b) mnb² = (m + n) ac (c) mn b² = (m + n)² ac (d) mnb² = (m – n)² ac
15. If one root of the equation x² + px + 12 = 0 is 4, while the equation x² + px + q = 0 has equal roots, the value of q is
16. a and p are the roots of 4x² + 3x + 7 = 0, then the value of is
17. If a, p are the roots of the equation (x – a) (x – b) + c = 0, then the roots of the equation (x – a) (x – P) = c are (a) a, b (b) a, c (c) b, c (d) none of these
18. Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are (a) 9,1 (b) -9,1 (c) 9, -1 (d) -9, -1
19. If a and p are the roots of the equation 2x² – 3x – 6 = 0. The equation whose roots
are and is (a) 6x² – 3x + 2 = 0 (b) 6x² + 3x – 2 = 0 (c) 6x² – 3x – 2 = 0 (d) x² + 3x-2 = 0
20. If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then (a) P = 0 (b) p = -2 (c) p = ±2 (d) p = 2
21. If one root of the quadratic equation 2x² + kx – 6 = 0 is 2, the value of k is (a) 1
(b) -1 (c) 2 (d) -2
22. The roots of the quadratic equation
(a) a, b (b) -a, b (c) a, -b (d) -a, -b
23. The roots of the equation 7x² + x – 1 = 0 are (a) real and distinct (b) real and equal (c) not real (d) none of these
24. The equation 12x² + 4kx + 3 = 0 has real and equal roots, if (a) k = ±3 (b) k = ±9 (c) k = 4 (d) k = ±2
25. If -5 is a root of the quadratic equation 2x² + px – 15 = 0, then (a) p = 3 (b) p = 5 (c) p = 7 (d) p = 1
CHAPTER 5
ARITHMETIC PROGRESSIONS 1. The nth term of an A.P. is given by an = 3 + 4n. The common difference is (a) 7 (b) 3 (c) 4 (d) 1
2. If p, q, r and s are in A.P. then r – q is (a) s – p (b) s – q (c) s – r (d) none of these
3. If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are (a) 2, 4, 6 (b) 1, 5, 3 (c) 2, 8, 4 (d) 2, 3, 4
4. The (n – 1)th term of an A.P. is given by 7,12,17, 22,… is (a) 5n + 2 (b) 5n + 3 (c) 5n – 5 (d) 5n – 3
5. The nth term of an A.P. 5, 2, -1, -4, -7 … is (a) 2n + 5 (b) 2n – 5 (c) 8 – 3n (d) 3n – 8
6. The 10th term from the end of the A.P. -5, -10, -15,…, -1000 is (a) -955 (b) -945
(c) -950 (d) -965
7. Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4 (a) 262 (b) 272 (c) 282 (d) 292
8. The sum of all two digit odd numbers is (a) 2575 (b) 2475 (c) 2524 (d) 2425
9. The sum of first n odd natural numbers is (a) 2n² (b) 2n + 1 (c) 2n – 1 (d) n²
10. If (p + q)th term of an A.P. is m and (p – q)tn term is n, then pth term is
11. If a, b, c are in A.P. then is equal to
12. The number of multiples lie between n and n² which are divisible by n is (a) n + 1 (b) n
(c) n – 1 (d) n – 2
13. If a, b, c, d, e are in A.P., then the value of a – 4b + 6c – 4d + e is (a) 0 (b) 1 (c) -1. (d) 2
14. The next term of the sequence
15. nth term of the sequence a, a + d, a + 2d,… is (a) a + nd (b) a – (n – 1)d (c) a + (n – 1)d (d) n + nd
16. The 10th term from the end of the A.P. 4, 9,14, …, 254 is (a) 209 (b) 205 (c) 214 (d) 213
17. If 2x, x + 10, 3x + 2 are in A.P., then x is equal to (a) 0 (b) 2 (c) 4 (d) 6
18. The sum of all odd integers between 2 and 100 divisible by 3 is (a) 17 (b) 867
(c) 876 (d) 786
19. If the numbers a, b, c, d, e form an A.P., then the value of a – 4b + 6c – 4d + e is (a) 0 (b) 1 (c) -1 (d) 2
20. If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then 18th term is (a) 18 (b) 9 (c) 77 (d) 0
21. If p, q, r are in AP, then p3 + r3 – 8q3 is equal to (a) 4pqr (b) -6pqr (c) 2pqr (d) 8pqr
22. In an AP, if a = 3.5, d = 0, n = 101, then a will be [NCERT Exemplar Problems] (a) 0 (b) 3.5 (c) 103.5 (d) 104.5
23. The list of numbers -10, -6, -2, 2, … is [NCERT Exemplar Problems] (а) an AP with d = -16 (b) an AP with d = 4 (c) an AP with d = -4 (d) not an AP
24. Two APs have the same common difference. . The first term of one of these is -1 and that of the other is -8. Then the difference between their 4th terms is [NCERT Exemplar Problems] (a) -1 (b) -8 (c) 7 (d) -9
25. In an AP, if d = -2, n = 5 and an = 0, the value of a is (a) 10 (b) 5 (c) -8 (d) 8
CHAPTER 6
TRIANGLES 1. O is a point on side PQ of a APQR such that PO = QO = RO, then (a) RS² = PR × QR (b) PR² + QR² = PQ² (c) QR² = QO² + RO² (d) PO² + RO² = PR²
2. In ABC, DE || AB. If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to (a) 7.5 cm (b) 3 cm (c) 4.5 cm (d) 6 cm
3. AABC is an equilateral A of side a. Its area will be…
4. In a square of side 10 cm, its diagonal = … (a) 15 cm (b) 10√2 cm (c) 20 cm (d) 12 cm
5. In a rectangle Length = 8 cm, Breadth = 6 cm. Then its diagonal = … (a) 9 cm (b) 14 cm (c) 10 cm (d) 12 cm
6. In a rhombus if d1 = 16 cm, d2 = 12 cm, its area will be… (a) 16 × 12 cm² (b) 96 cm² (c) 8 × 6 cm² (d) 144 cm²
7. In a rhombus if d1 = 16 cm, d2 = 12 cm, then the length of the side of the rhombus is (a) 8 cm (b) 9 cm (c) 10 cm (d) 12 cm
8. If in two As ABC and DEF, , then (a) ∆ABC ~ ∆DEF (b) ∆ABC ~ ∆EDF (c) ∆ABC ~ ∆EFD (d) ∆ABC ~ ∆DFE
9. It is given that ∆ABC ~ ∆DEF and . Then is equal to (а) 5 (b) 25
(c)
(d)
10. In ∠BAC = 90° and AD ⊥ BC. A Then
(а) BD.CD = BC² (б) AB.AC = BC² (c) BD.CD = AD² (d) AB.AC = AD²
11. D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then, length of DE (in cm) is (a) 2.5 (b) 3 (c) 5 (d) 6
12. If ΔABC ~ ΔDEF and ΔABC is not similar to ΔDEF then which of the following is not true? (a) BC.EF = AC.FD (b) AB.ED = AC.DE (c) BC.DE = AB.EE (d) BC.DE = AB.FD
13. If in two triangles DEF and PQR, ZD = ZQ and ZR = ZE, then which of the following is not true?
14. If ΔABC ~ ΔPQR, then is (a) 9 (b) 3 (c) 1/3 (d) 1/9
15. If ΔABC ~ ΔQRP, , AB = 18 cm and BC = 15 cm, then PR is equal to (a) 10 cm (b) 12 cm
(c) cm (d) 8 cm
16. If in triangles ABC and DEF, , then they will be similar, if (a) ∠B = ∠E (b) ∠A = ∠D (c) ∠B = ∠D (d) ∠A = ∠F
17. In the given figure, and ∠ADC = 70° ∠BAC =
(a) 70° (b) 50° (c) 80° (d) 60°
18. In given figure, AD = 3 cm, AE = 5 cm, BD = 4 cm, CE = 4 cm, CF = 2 cm, BF = 2.5 cm, then
(a) DE || BC (b) DF || AC (c) EF || AB (d) none of these
19. If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true? [NCERT Exemplar Problems] (a) BC . EF = AC . FD (b) AB . EF = AC . DE (c) BC . DE = AB . EF (d) BC . DE = AB . FD
20. If in two triangles ABC and PQR, , then [NCERT Exemplar Problems] (a) ΔPQR ~ ΔCAB (b) ΔPQR ~ ΔABC (c) ΔCBA ~ ΔPQR (d) ΔBCA ~ ΔPQR
21. Match the column:
(a) 1 → A, 2 → B, 3 → C, 4→ D (b) 1 → D, 2 → A, 3 → C, 4 → B (c) 1 → B, 2 → A, 3 → C, 4 → D (d) 1 → C, 2 → B, 3 → D, 4 → A.
22. In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are [NCERT Exemplar Problems] (a) congruent but not similar (b) similar but not congruent (c) neither congruent nor similar (d) congruent as well as similar
23. If in triangles ABC and DEF, then they will be similar, when [NCERT Exemplar Problems]
(a) ∠B = ∠E (b) ∠A = ∠D (c) ∠B = ∠D (d) ∠A = ∠F
24. ABC and BDE are two equilateral triangles such that D is mid-point of BC. Ratio of the areas of triangles ABC and BDE is (a) 2 : 1 (b) 1:4 (c) 1:2 (d) 4:1
25. Sides of two similar triangles are in the ratio 3 : 7. Areas of these triangles are in the ratio (a) 9 : 35 (b) 9 : 49 (c) 49 : 9 (d) 9 : 42
CHAPTER 7
COORDINATE GEOMETRY 1. The distance of the point P(2, 3) from the x-axis is (a) 2 (b) 3 (c) 1 (d) 5
2. The distance between the point P(1, 4) and Q(4, 0) is (a) 4 (b) 5 (c) 6 (d) 3√3
3. The points (-5, 1), (1, p) and (4, -2) are collinear if the value of p is (a) 3 (b) 2 (c) 1 (d) -1
4. The area of the triangle ABC with the vertices A(-5, 7), B(-4, -5) and C(4, 5) is (a) 63 (b) 35 (c) 53 (d) 36
5. The distance of the point (α, β) from the origin is (a) α + β (b) α² + β² (c) |α| + |β| (d)
6. The area of the triangle whose vertices are A(1, 2), B(-2, 3) and C(-3, -4) is (a) 11
(b) 22 (c) 33 (d) 21
7. The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are (a) (3, 3) (b) (- 3, 3) (c) (3, – 3) (d) (-3,-3)
8. The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio (a) 3 : 4 (b) 3 : 2 (c) 2 : 3 (d) 4 : 3
9. The distance between A (a + b, a – b) and B(a – b, -a – b) is
10. If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of ‘a’ is (a) 12 (b) -6 (c) -12 (d) -4
11. If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is (a) -7 or -1 (b) -7 or 1 (c) 7 or 1 (d) 7 or -1
12. The points (1,1), (-2, 7) and (3, -3) are (a) vertices of an equilateral triangle (b) collinear
(c) vertices of an isosceles triangle (d) none of these
13. The coordinates of the centroid of a triangle whose vertices are (0, 6), (8,12) and (8, 0) is (a) (4, 6) (b) (16, 6) (c) (8, 6) (d) (16/3, 6)
14. Two vertices of a triangle are (3, – 5) and (- 7,4). If its centroid is (2, -1), then the third vertex is (a) (10, 2) (b) (-10,2) (c) (10,-2) (d) (-10,-2)
15. The area of the triangle formed by the points A(-1.5, 3), B(6, -2) and C(-3, 4) is (a) 0 (b) 1 (c) 2 (d) 3/2
16. If the points P(1, 2), B(0, 0) and C(a, b) are collinear, then (a) 2a = b (b) a = -b (c) a = 2b (d) a = b
17. A triangle with vertices (4, 0), (- 1, – 1) and (3, 5) is a/an (a) equilateral triangle (b) right-angled triangle (c) isosceles right-angled triangle (d) none of these
18. The points (- 4, 0), (4, 0) and (0, 3) are the vertices of a/an [NCERT Exemplar Problems] (a) right triangle (b) isosceles triangle (c) equilateral triangle (d) scalene triangle
19. A circle drawn with origin as the centre passes through , . The point which does not lie in the interior of the circle is [NCERT Exemplar Problems]
20. If the distance between the points(4, p) and (1, 0) is 5 units, then the value of p is [NCERT Exemplar Problems] (a) 4 only (b) ± 4 (c) -4 only (d) 0
21. The points (2, 5), (4, – 1) and (6, – 7) are vertices of an/a (a) isosceles triangle (b) equilateral triangle (c) right-angled triangle (d) none of these
22. If the segment joining the points (a, b) and (c, d) subtends a right angle at the origin, then (a) ac – bd = 0 (b) ac + bd = 0 (c) ab + cd = 0 (d) ab – cd= 0
23. AOBC is a rectangle whose three vertices are A(0, 3), 0(0, 0) and B(5, 0). The length of its diagonal is [NCERT Exemplar Problems] (a) 5 (b) 3 (c) √34 (d) 4
24. The perimeter of a triangle with vertices (0,4), (0, 0) and (3, 0) is [NCERT Exemplar Problems] (a) 5 (b) 12
(c) 11 (d) 7 + √5
25. If the distance between the points (4, p) and (1, 0) is 5 units, then the value of p is [NCERT Exemplar Problems] (a) 4 only (b) ±4 (c) -4 only (d) 0
CHAPTER 15
PROBABILITY Question 1. The probability of getting exactly one head in tossing a pair of coins is (a) 0 (b) 1 (c) 1/3 (d)1/2
Question 2. The probability of getting a spade card from a well shuffled deck of 52 cards is
Probability MCQ Class 10 Question 3. The probability of getting less than 3 in a single throw of a die is
Probability Class 10 MCQ Question 4. The total number of events of throwing 10 coins simultaneously is (a) 1024 (b) 512 (c) 100 (d) 10
MCQ Of Probability For Class 10 Question 5. Which of the following can be the probability of an event? (a) – 0.4 (b) 1.004
(c)
(d)
Probability MCQs With Answers Pdf Question 6. Three coins are tossed simultaneously. The probability of getting all heads is
Probability MCQ Question 7. One card is drawn from a well shuffled deck of 52 cards. The probability of getting a king of red colour is
MCQ Questions For Class 10 Maths With Answers Question 8. One card is drawn from a well shuffled deck of 52 playing cards. The probability of getting a non-face card is
9. The chance of throwing 5 with an ordinary die is
MCQ Questions For Class 10 Maths Question 10. The letters of the word SOCIETY are placed at random in a row. The probability of getting a vowel is
Probability Questions And Answers Pdf Question 11. Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out from the bag at random. The probability that the number on the card taken out is an even number, is
Maths MCQ For Class 10 Question 12. The total events to throw three dice simultaneously is (a) 6 (b) 18 (c) 81 (d) 216
10 Class Maths MCQ With Answers Question 13. The probability of getting a consonant from the word MAHIR is
Probability Multiple Choice Questions Question 14. A girl calculates that the probability of her winning
the first prize in a lottery is . If 6,000 tickets are sold, how many tickets has she bought? (a) 400 (b) 750 (c) 480 (d) 240
Multiple Choice Questions On Probability Question 15. A card is drawn from a well shuffled deck of 52 cards. The probability of a seven of spade is
Probability Multiple Choice Questions And Answers Question 16. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. The probability that a red ball drawn is
Probability MCQ Pdf Question 17. A child has a die whose six faces show the letters as given below:
A B C D E F
The die is thrown once. The probability of getting a ‘D’ is
Probability Multiple Choice Questions And Answers Pdf Question 18. One card is drawn from a well-shuffled deck of 52 cards. The probability that the card will not be an ace is
Probability Multiple Choice Questions Pdf Question 19. A lot consists of 144 ball pens of which 20 ae defective and the others are good. Tanu will buy a pen if it is good but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. The probability that she will buy that pen is
Multiple Choice Probability Questions Question 20. A ticket is drawn at random from a bag containing tickets numbered from 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is
Probability Questions Multiple Choice Question 21. Which of the following cannot be the probability of an event? [Delhi 2011] (a) 1.5
(b) (c) 25% (d) 0.3
Basic Probability Multiple Choice Questions Pdf Question 22. A coin is tossed twice. The probability of getting both heads is [Foreign 2013]
Probability MCQs With Answers Question 23. A fair dice is rolled. Probability of getting a number x such that 1 ≤ x ≤ 6, is (a) 0 (b) > 1 (c) between 0 and 1 (d) 1
24. The sum of the probabilities of all elementary events of an experiment is p, then (a) 0 < p < 1 (b) 0 ≤ p < 1 (c) p = 1 (d) p = 0
25. If an event cannot occur, then its probability is [NCERT Exemplar Problems] (a) 1
(b)
(c) (d) 0
SECTION B
CHAPTER 2
POLYNOMIALS 1. Find all the zeros of the polynomial 2x4 – 11x3 – 16x2 + 55x + 30 if two of its zeros are √5, −√5. 2. Find all the zeroes of the polynomials 4x4 + 14x3 – 38x3 – 28x + 60 if two of its zeroes are √2 & √2
3. Find all the zeros of the polynomial x4 – 7x3 + 7x2 + 35x – 60, if two of its zeros are √5 and −√5. 4. Find all the zeroes of polynomial x4 – 4x3 – 35x2 + 12x + 96 if two of its zeroes are √3 and −√3. 5. If one zero of the polynomial p(x) = 2x2 – 4kx + 6x – 7 is the negative of other find the zeros of x2 – kx – 1. 6. Find all the zeros of the polynomial 2x4 + 4x3 – 22x2 – 32x + 48 if two of its zeros are 2√2 and −2√2. 7. Find all the zeroes of the polynomial x4 – 9x3 + 27x2 – 33x + 14, if two of its zeroes are 3 ± √2. 8. If two zeros of the polynomial 2x4 – 12x3 – 52x2 + 276x – 70 are 2 ± √3 find the other zeros. 9. Obtain all the zeros of x4 – 8x3 +3 x2 + 72x-108 is two of its zeros are 2 and 3. 10. Find the zeros of the polynomial x4 – 5x3 – x2 + 35x – 42 if √7 & −√7 are the zeros of the polynomial. 11. Show that 3z + 10 is factor of 9z3 –27z2 -100z + 300. Find also the other factors.
12. If α and βare the roots of 2x2 – 4x + 1 = 0, frame the equation whose roots are 𝛂β&
β𝛂
13. Factorise 3x4 – 10x3 + 5x2 + 10x – 8
14. If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to x – a, find k and a. 15. If the two zeroes of the polynomial x4 – 8x3 + 20x2 – 20x + 7 are 3 ±√2, find other zeroes.
16. Obtain all the zeroes of 3x4 + 6x3 – 2x2 – 10x – 5 if two of its zeroes are
17. Find the zeroes of the polynomial f(x) = x3 – 6x2 + 11x – 6, if it is given that the product of its two zeroes is 6. 18. If the squared difference of the zeroes of the quadratic polynomial f(x) = x2 + kx + 30 is equal to 169, find the value of k & the zeroes. 19. If 2 and –2 are the zeroes of the polynomial p(x) = x4 – 5x3+ 2x2 + 20x – 24, find the other two zeroes. 20. Obtain all the zeroes of x3 – 7x + 6 if one of its zero is 2.
CHAPTER 3
LINEAREQUATIONS IN TWO
VARIABLES
1. If α and β are the zeros of x2 + 2x + 15, find the value of
2. 3. If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are inconsistence find k. 4. 24x + 23y = 117
23x + 24y = 118
5. One third of the perimeter of a rectangular garden, whose length is 6 m more than breadth is 28 m. Find the dimensions of the garden. 6. For what value of k, the following systems of equations have infinitely many solutions?
3x – 4y = 5 6x + (2k + 1)y = 10
7. For what value of k, with the following system of equations have infinitely many solutions?
4x + 5y = 7
(k + 2)x + 10y = 2k + 2
8. Two numbers are in ratio of 4 : 5. If 8 is subtracted from each of the numbers the ratio becomes 3 : 4. Find the numbers. 9. Solve the following
2x + 3y = 7
3x – 5y = 1
10. Find the value of P for which the system of end has no solution. (3p – 1) x + (p – 2)y = 3p + 1
2x – y + 1 = 0
11. If the sum of two consecutive odd integers is 20, find the numbers. 12. Find the equation of a straight line passing through (1, 2) and perpendicular to the line y = 7. 13. Solve the following system of equations:
3x – y = 7, 4x – 5y = 2
14. Solve for x and y
29x + 32y = 26
32x + 29y = 35
15. Solve for x & y : 99x + 101y = 4989
101x + 99y = 501
16. Check whether the system of linear equations 3x + 4y – 6 = 0 and 6x + 8y – 12 = 0 is consistent. 17. For what value of p, the system of equation has no solution. (p + 1) x + (p + 2) y = 10
8x + 10y = 5
18. Determine a and b for which the following system of equations has infinite no. of solutions
4x – (a – 4)y = 4b + 2
12x – (2a – 3)y = 3b + 1
19. Determine whether the following system of equation has a unique solution, no solutions or infinity many solutions. 3x – 7y = 5, 6x – 14y = 10
20. For what value of k, 3x+ 2y = 4 and 6x + (k + 2)y = 3k + 2 will have infinitely many solutions.
CHAPTER 4
QUDRATIC EQUATIONS 1. For what value of k, the quadratic equation kx2 – 2√3kx + 9 = 0 has equal roots?
2.
3. Solve for x : 2√3x2 – 2√2x – √3 = 0 4. For what value of k, the quadratic equation 5x2 – kx + 4 have equal roots. 5. If 2 is a root of the equation ax2 + ax + 2 = 0 and x2 – x – b = 0 then find a/b. 6. If x = 1/3 is a solution to the equation 3x2 – 2kx + 5 = 0 find k. 7. For what value of k the quadratic equation has equal roots? Hence find the roots of the equation, 2kx2 – 4(k – 2)x + 9
8. Find K for which the roots of quadratic equation are ( K – 9) x2 + 2(K – 9)x + 4 = 0 equal. 9. For what value of K, the quadratic equation has equal roots: (k + 2)x2 – 4kx + 4 = 0
10. For what value of P, the quadratic equation px(x – 4) + 64 = 6 has equal roots. p≠ 0. 11. Consider the polynomial P(x) = x2 – 6x + 9
(a) Find P(3) (b) Prove that the value of this polynomial cannot be negative numbers. (c) Find two numbers a and b such that P(a) = P(b). 12. Find the values of k for which the roots of the equation kx2 – 5x + k = 0 are real and equal. 13. Form the quadratic equation whose roots are 7 + √3 and 7 – √3. 14. If the equation (1 + m2) x2 + 2 mcx + (c2 – a2) = 0 has equal roots, prove that c2 = a2 (1 + m2) 15. y = x2 – 2x – 8 solve the equation
x2 – 2x – 15 = 0
16. If α and β are the roots of the equation 3x2 – 6x + 4 = 0, find the value of α2 + β2.
17.
18. Form the quadratic equation whose roots are
19. Find the sum and products of the roots of equation
20. The product of two consecutive even numbers is 168. Find them.
CHAPTER 5
ARITHMETIC PROGRESSIONS 1. In an A.P. the sum of n terms is given by Sn = n2 – 3n find the 30th term. 2. Find the sum of 1st 15 even natural numbers?
3. In an A.P. sum of n terms Sn = n3 + 3n, find the 20th term. 4. Find the middle term of the A.P. 5, 12, 19 …….215. 5. The sum of n terms given by Sn = n2 + 3n. Find 20th term. 6. Find the sum of 1st 30 natural numbers 7. Which term of the sequence 2, 5, 8, 11 …. is 128? 8. Find the sum of all the 3-digit numbers which leaves remainder 3 when divided by 4. 9. If sum of n terms of an A.P is Sn = n2 + 2 find the 4th term. 10. If pth term of an A.P. is q and qth term is P find the first term. 11. Find the number of 3 digit numbers that are divisible by 13. 12. Which term of the sequence 2, 5, 8, 11…..is 134?
13. An arithmetic sequence starts as 5, 9, 13, …… What is the next term? Is 2012 a term of this sequence? Why?
14. What is the least three digit number, which is a multiple of 6?
Find the sum of all three digit numbers which are multiples of 6. 15. Second and fourth terms of the following arithmetic sequence are missing. Find the numbers at these positions. 16.If the first term of an A.P is 5 and its 100th term is −292, then its 51st term is ……. (a) −142 (b) −149 (c) 155 (d) −145 17. Find the sum of the first 20 terms of A.P. in which 3rd term is 7 and 7th term is two more than thrice of its 3rd term. 18. Find the sum of all positive integers less than 298 which are multiplies of 9. 19. If 10 times the 10th term of an A.P. is equal to 20 times its 20th term, show that the 30th term f the A.P. is zero. 20. How many two digit numbers are divisible by 13?
CHAPTER 6
TRIANGLES
1. In figure PQ | | CD and PR | | CB. Prove that
2. If figure two triangles ABC and DBC are on the same base BC in which ∠A = ∠D = 90°. If CA and BD meet each other at E, show that AE × CE = BE × DE.
3. Find the perimeter of rhombus whose diagonals are 20 cm & 30 cm. 4. In figure P, Q,R are the points on OA,O B and OC respectively such that QP | | AB, QR | | BC. Show that AC | | PR .
5. In parallelogram ABCD, find the values of x and y.If X+Y=15,X-Y=5
6. Two triangles BAC and BDC are drawn as same base BC. Prove that AP × PC = DP × PB
7. In ∆ ABC, DE | | BC
AD = 8, DB = 6, AE = 4, find AC.
8. ∆ ABC ~ ∆ PQR. Their corresponding altitudes AD & PS are in ratio 2 : 3. If Area of the ∆ ABC is 20 cm2 find area of ∆ PQR
9. If ∆ ABC ~ ∆ DEF, BC = 6 cm, EF = 8 cm and area (∆ ABC) = 108 cm2 find area (∆ DEF)
10.
From the above figure find ∠MLN
11. In ∆ ABC, ∠B = 90°
BD ⊥ AC
Prove that AB2 = AC × AD
12. In figure , AB ⊥ BC, DE ⊥ AC and HG ⊥ AB. Prove that ∆ AGH ~ ∆ DEC
13. In quadrilateral PQRS, ∠Q = 90°. If PS2 = SR2 + QR2 + PQ2, find ∠PRS. 14. If ∆ XYZ ~ ∆ BMP, ∠Y = 120°, ∠B = 30° then find ∠P
15. In the given figure O is a point in the interior ∠POR = 90°. OP = 6 cm, OR = 8 cm. If the PQ = 24 cm, QR = 26 cm then that ∆ QPR is a right angled triangle.
16. In ∆ ABC, DE | | BC. AD = 3 cm, DB = 6 cm, AE = 4 cm, find AC. Also find
17. From the given figure find ∠EDF
18. Two similar triangles with equal areas are congruent. Prove it.
19. In ∆ ABC, ∠C = 90°, CD ⊥ AB. Show that AC ∙ BC = CD ∙ AB
20. ∆ ABC ~ ∆ DEF. If area (ABC) = 64 sq cm, area(DEF) = 121 sq m., altitude AM = 16 cm find the altitude DN.
CHAPTER 7
COORDINATE GEOMETRY 1. Find the value of x for which the distance between the points P(x, −3) and Q(10, −9) is 10 units. 2. Find the relation between x and y if A(x, y), B(−2, 3) and C(4, −7) are collinear. 3. Find the co-ordinate of the centroid of triangle with co-ordinates (1, 3) (2, −2), (4, −6). 4. For what value of P, A(3, p) is equidistant from S(0, 4) & T(2, −3). 5. For what value of K, points (1, 3), (2, K) and (4, −2) are collinear? 6. From the figure, find the area of ∆ ABC
7. A point P(0, 3) is equidistant from the points A(4, P) and B(P, 3). Find the value of P. 8. The distance of the point (−2, 3) from X-axis is 5. Find the co-ordinate of the point on X-axis. 9. Find k for which the point p(k, 2) is equidistant from A (2, −3) and B(−3, 7) 10. If P(0, 2) is equidistant from A(4, −3) and B(x, 5) find x. 11. In what ratio does the point P(2, −5) divide the line segments joining A(−3, 5) and B(4, −9). 12. If the midpoint of line segment joining the points A(3, 5), B(K, 4) is P(x, y) and x + y = 8 find the value of K.
13. If the points (a, 1), (1, 2) and (0, b + 1) are collinear, then show that
14. The coordinates of the midpoint of the line segment joining the point (2a + 2, 3) and (4, 2b + 1) are (2a, 2b. Find the value of ‘a’ and ‘b’. 15. If A =(7, 5), B = (2, 4) and C = (6, 10), then show that AB = AC. 16. In what ratio does P(4, 6) divide the join of A(−2, 3) and B (6, 7). 17. Find the area of triangle formed by the points (−2, 3), (−7, 5) and (3, −5). 18. In what ratio is the line segment joining the points (−3, 2) and (6, 1) divided by the y-axis. 19. Find the coordinates of the point on x-axis equidistant from the points (2, 5) and (3, 4). 20. If the centroid of a triangle is at (1, 3) and two of its vertices are (−7, 6) and (8, 5), then find the third vertex of the triangle.
CHAPTER 15
PROBABILITY 1. A card in drawn randomly from a pack of 52 cards. Find the probability of getting a
(i) a black king
(ii) a face card 2. A card is drawn randomly from well shuffled pack of 52 cards. Find the probability that the drawn card is neither jack nor an ace. 3. Two dice are rolled. What is the probability of getting
(i) the sum of numbers on two dice is 11. (ii) odd numbers on both dice. 4. A box contains 30 cards from 1 to 30. A card is drawn random from the box. Find the probability that (i) It is divisible by 2 or 5
(ii) a prime number 5. Find the probability of getting 53 Tuesdays is a leap year. 6. Cards are marked with numbers from 2 to 101. They are mixed is a bag. A card is drawn random from the bag. Find the probability that the drawn card is
(i) a prime number (ii) a perfect square
7. A card is drawn from a well scuffled pack of 52 cards. Find the probability of getting (i) a black king (ii) a king or jack. 8. Consider the figure given below:
In the figure, two semi circles are drawn. O is the centre of the larger one. If we put a dot inside the larger semi circle by closing our eyes, what is the probability that the point is inside the smaller semi circle. 9. There are two boxes. Each one contains paper slips marked 1 to 10. If we take one slip from each box, what is the probability that both numbers are prime?
10. Two dice are rolled together. Find the probability that the two-digit number formed with the number turning up on their faces is multiple of 7 or 5. 11. A two digit number is formed with digits 3, 5 and 7. Find the probability that the number so formed is greater than 57. Repetition of the digits is not allowed. 12. A card is drawn from a well shuffled pack of 52 cards. Find the probability that it is an ace or spade. 13. An integer is chosen from the first twenty natural numbers. What is the probability that it is a prime number?
14. There are 7 defective items in a sample of 35 items. Find the probability that an item chosen at random is non-defective. 15. Three dice are thrown simultaneously. Find the probability of getting the same number on all the three dice. 16. Find the probability that a number selected at random from numbers 1 to 30 is a prime number when each of the given numbers is likely to be selected.
17. What is the probability of getting no head when two coins are tossed ?
18. The record of weather station shows that out of past 200 consecutive days, its weather forecasts were correct 125 times. What is the probability of getting a wrong prediction?
19. A bag contain 5 red, 6 black and 9 green balls. Find the probability that the ball drawn is black or red. 20. A card is drawn from a well Shuffled pack of playing cards. Find the probability of drawing face card.
