MATH

If you are preparing for Defence Exam, then here you can practice Percentage Questions MCQ Mathematics which can help in your preparation.   Question 1: Shyam’s monthly income is Rs. 12,000. He saves Rs. 1200. Find the percent of his savings and his expenditure. (A) 20%,80% (B) 10%, 90% (C) 80%, 20% (D) 90%, 10%   Question 2: Due to increase of 30% in the price of a color TV, the sale is reduced by 40%. What will be the percentage change in income? (A) 6% increase (B) 10% increase (C) 16% increase (D) 22% increase   Question 3: What percent of 2/7 is 1/35? (A) 2.5% (B) 10% (C) 25% (D) 90%   Question 4: The population of a town is 176400. It increases annually at the rate of 5% per annum. What will be its population after 2 years? (A) 194780 (B) 194688 (C) 194546 (D) 194481   Question 5: In 2010, the population of a town is 1,50,000. If it is increased by 10% in the next year. Find the population in 2011 (A) 1,65,000 (B) 1,70,000 (C) 1,75,000 (D) 1,80,000 Percentage Questions MCQ Question 6: If x% of y is 100 and y% of z is 200, then the relation between x and z is (A) z = 4x (B) z = x/2 (C) z = 2x (D) z = x/4 Question 7: If 12% of an amount is Rs. 1080, then the amount is (A) Rs. 6500 (B) Rs. 8500 (C) Rs. 9000 (D) Rs. 9500   Question 8: 15% of the total number of biscuits in a jar is 30. The total number of biscuits is (A) 50 (B) 150 (C) 200 (D) 250 Question 9: A number when increased by 12% gives 224. What is the number? (A) 200 (B) 210 (C) 232 (D) 242 Question 10: What percent of 3% in 5%? (A) 45% (B) 55% (C) 60% (D) 65% Percentage Questions MCQ Question 11: Find the total amount, if 12% of it is Rs. 1080 . (A) Rs. 9,000 (B) Rs. 10,000 (C) Rs. 17,000 (D) Rs. 25,000   Question 12: If 75% of a number is added to 75, then the result is the number itself. Find the number (A) 55 (B) 65 (C) 300 (D) 350   Question 13: After spending 40% on machinery, 25% on building, 15% on raw material and 5% on furniture, a small scale industry owner had a balance of Rs. 1,30,500. Total money with him (in rupees) wa (A) 7,21,200 (B) 7,37,450 (C) 7,54,650 (D) 8,70,000   Question 14: In an examination 35% of students passed and 455 failed. Total number of students appeared for the examination is (A) 500 (B) 600 (C) 700 (D) 800   Question 15: Value of 28% of 450 + 45% of 280 is (A) 150 (B) 157 (C) 252 (D) 224 Percentage Questions MCQ Question 16: If 20% of pure acid is in 8 litres of a solution. How many litres of pure acid is in that solution? (A) 1.2 (B) 1.6 (C) 1.8 (D) 2.2   Question 17: A man invested 1/3 of his capital at 7%; 1/4 at 8% and the remainder at 10%. If his annual income is Rs. 561 find the capital. (A) Rs. 5,200 (B) Rs. 5,400 (C) Rs. 6,200 (D) Rs. 6,600 Question 18: 1100 boys and 700 girls are examined in a test. 42%of the boys and 30%of the girls pass. Find the % of the fail. (A) 52.5% (B) 62.67% (C) 66% (D) 75%   Question 19: A refrigerator is purchased for Rs. 14,355, including sales tax. If the actual cost price of the refrigerator is Rs. 13,050, find the rate of sales tax. (A) 8% (B) 9% (C) 10% (D) 11%   Question 20: A person spends 30% of his earnings on groceries, 10% on children’s school fee, 5% on transportation and 20% on rent. If he earns an amount of Rs. 50,000 then his savings is (A) Rs. 15,500 (B) Rs. 16,500 (C) Rs. 17,500 (D) Rs. 18,500 Percentage Questions MCQ, Percentage Questions MCQ, Percentage Questions MCQ Percentage Questions MCQ Mathematics – For Defence Answer Key: – Question No. Answer Question No. Answer Question 1 B Question 11 A Question 2 D Question 12 C Question 3 B Question 13 D Question 4 D Question 14 C Question 5 A Question 15 C Question 6 C Question 16 B Question 7 C Question 17 D Question 8 C Question 18 B Question 9 A Question 19 C Question 10 C Question 20 C Find More Questions: – Math Questions (Set 1) Math Questions (Set 2) Math Questions (Set 3) Math Questions (Set 4) Math Questions (Set 5) Math Questions (Set 6) Math Questions (Set 7) Math Questions (Set 8) Math Questions (Set 9)

Mathematics is a crucial subject in the NDA (National Defence Academy) exam and requires a strong understanding of concepts and formulas. To excel in the mathematics section of the NDA exam, it is essential to have a solid grasp of the important formulas. In this article, we will provide a comprehensive list of important formulas for NDA Mathematics that will help you in your preparation for the NDA Exam 2023. 1. Algebra Formulas: – Quadratic Formula: The solutions for the quadratic equation ax^2 + bx + c = 0 can be found using the formula x = (-b ± √(b^2 – 4ac)) / 2a. – Binomial Theorem: (a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + … + nCn * a^0 * b^n, where nCk represents the binomial coefficient. – Arithmetic Progression (AP) Formulas: The nth term of an AP is given by tn = a + (n – 1)d, where a is the first term and d is the common difference. 2. Trigonometry Formulas: – Pythagorean Identities: sin^2θ + cos^2θ = 1 and tan^2θ + 1 = sec^2θ. – Sine and Cosine Rules: In a triangle ABC, the sine rule states that a/sinA = b/sinB = c/sinC, and the cosine rule states that c^2 = a^2 + b^2 – 2abcosC. – Trigonometric Identities: Some important identities include sin(A ± B) = sinAcosB ± cosAsinB, cos(A ± B) = cosAcosB ∓ sinAsinB, and tan(A ± B) = (tanA ± tanB) / (1 ∓ tanAtanB). 3. Geometry Formulas: – Area of Triangle: The area of a triangle can be calculated using the formula 1/2 * base * height or Heron’s formula: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter and a, b, c are the lengths of the sides. – Perimeter and Area of a Circle: The perimeter of a circle is given by 2πr, and the area is given by πr^2, where r is the radius. – Volume and Surface Area of 3D Shapes: Formulas for volume and surface area of shapes like cubes, cylinders, spheres, and cones should be memorized. 4. Calculus Formulas: – Derivative Rules: Important derivative rules include the power rule (d/dx[x^n] = nx^(n-1)), product rule (d/dx[uv] = u’v + uv’), and chain rule (d/dx[f(g(x))] = f'(g(x))g'(x)). – Integration Formulas: Some common integration formulas include ∫kdx = kx + C (where k is a constant), ∫x^n dx = (x^(n+1))/(n+1) + C (for n ≠ -1), and ∫e^xdx = e^x + C. In the NDA Mathematics section, understanding and applying formulas correctly is crucial for solving problems efficiently. By familiarizing yourself with these important formulas and practicing their application, you will enhance your mathematical skills and boost your chances

1. A survey shows that 63% of Indians like milk and 76% like butter. If x% of the Indians like both milk and butter, then find the value of x. (a) x lies b/w [38,64] (b) x lies b/w [39,63] (c) x lies b/w [37,63] (d) None of these 2. If, A={a,b,c}, then what is the number of proper subsets of A? (a) 5 (b) 6 (c) 7 (d) 8 3. In a certain town 25% of families own a cell phone, 15% of families own a scooter and 65% of families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is- a. 10,000 b. 20,000 c. 30,000 d. 40,000 4. If a is positive and if A and G are the arithmetic mean and the geometric mean of the roots of x^2 – 2ax + a^2 =0 respectively, then a. A = G b. A = 2G c. 2A = G d. A2 = G 5. Suppose that two persons A and B solve the equation x2 +ax + b = 0. While solving commits a mistake in commits a mistake in the coefficient of x was taken as 15 in place of –9 and finds the roots as –7 and –2. Then the equation is- a. x^2 + 9x + 14 = 0 b. x^2 – 9x + 14 = 0 c. x^2 + 9x – 14 = 0 d. x^2 – 9x – 14 = 0 6. If x2 +2x + n > 10 for all real numbers x, then which of the following conditions is true? a. n < 11 b. n = 10 c. n = 11 d. n > 11 7. If the sum of the 12th and 22nd terms of an A.P is 100, then the sum of the first 33 terms of the A.P. is- a. 1700 b. 1650 c. 3300 d. 3400 8. The number of ways in which 5 ladies and 7 gentlemen can be seated at a round table so that no two ladies sit together, is a. 3.5X(720)^2 b. 7(360)^2 c. 7(720)^2 d. 720 9. All the words that can be formed using alphabets A, H, L, U, and R are written as in a dictionary (no alphabet is repeated). Then the rank of the word RAHUL is a. 70 b. 71 c. 72 d. 74 10. A matrix that is symmetric and skew-symmetric is a. Orthogonal matrix b. Idempotent matrix c. Null matrix d. None of these 11. Given that the drawn ball from U2 is white, the probability that the head appeared on the coin is a. 17/23 b. 11/23 c. 15/23 d. 12/23 12. A fair coin is tossed a fixed number of times. If the probability of getting exactly 3 heads equals the probability of getting exactly 5 heads, then the probability of getting exactly one head is- a. 1/64 b. 1/32 c. 1/16 d. 1/8 13. If sinx = sin 15° + sin 45°, where 0° < x < 90°, then x is equal to a. 45° b. 54° c. 60° d. 75° 14. If O is at the origin, OA is along the negative x-axis and (–40, 9) is a point on OB, then the value of sin AOB is a. 5/16 b. 9/40 c. 9/41 d. 19/41 15. The equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest value, is a. y = 2x b. y = x + 1 c. x + 2y = 5 d. y = 3x – 1 16. If a line with y-intercept 2, is perpendicular to the line 3x – 2y = 6, then its x-intercept is – a. 1 b. 2 c. –4 d. 3 17. If the lines ax + ky + 10 = 0, bx + (k + l)y + 10 = 0 and cx + (k + 2)y + 10 = 0 are concurrent, then- a. a,b, c are in G.P. b. a, b, c are in H.P. c. a, b, c are in A.P. d. (a + b)2 = c 58. 18. A line passes through the point of intersection of the lines 100x + 50y –1= 0 and 75x + 25y + 3 = 0 and makes equal intercepts on the axes. Its equation is a. 25x + 25y – 1= 0 b. 5x – 5y + 3 = 0 c. 25x + 25y – 4 = 0 d. 25x – 25y + 6 = 0 19. The circumcentre of the triangle with vertices (0, 30), (4, 0), and (30, 0) is a. (10, 10) b. (10, 12) c. (12, 12) d. (17, 17) 20. The lines (a+2b)x +(a–3b)y = a – b for different values of a and b pass through the fixed point whose coordinates are . a. (2/5,2/5) b. (3/5,3/5) c. (1/5,1/5) d. (2/5,3/5)

1. Suppose cos A is given. If only one value of cos (A/2) is possible, then A must be (a) An odd multiple of 90° (b) A multiple of 90° (c) An odd multiple of 180° (d) A multiple of 180° 2. If cos α + cos β + cos γ = 0, where 0 < α ≤ π/2, 0 < β ≤ π/2, 0 < γ ≤ π/2, then what is the value of sin α + sin β + sin γ? (a) 0 (b) 3 (c) 5√2/2 (d) 3√2/2 3. The maximum value of sin (x + π/5) + cos (x + π/5), where x ∈ (0, π/2), is attained at (a) π/20 (b) π/15 (c) π/10 (d) π/2 4. What is the distance between the points which divide the line segment joining (4, 3) and (5, 7) internally and externally in the ratio 2 : 3? (a) 12√17/5 (b) 13√17/5 (c) √17/5 (d) 6√17/5 5. What is the angle between the straight lines (m2 – mn) y = (mn + n2) x + n3 and (mn + m2) y = (mn – n2) x + m3, where m > n? (a) tan-1 (2mn/m2 + n2) (b) tan-1 (4m2n2/m4 – n4) (c) tan-1 (4m2n2/m4 + n4) (d) 45° 6. What is the equation of the straight line cutting off an intercept 2 from the negative direction of y-y-axis and inclined at 30° with the positive direction of x-axis? (a) x – 2 √3 y – 3√2 = 0 (b) x + 2 √3 y – 3√2 = 0 (c) x + √3 y – 2√3 = 0 (d) x – √3 y – 2√3 = 0 7. What is the equation of the line passing through the point of intersection of the lines x + 2y – 3 = 0 and 2x – y + 5 = 0 and parallel to the line y – x + 10 = 0? (a) 7x – 7y + 18 = 0 (b) 5x – 7y + 18 = 0 (c) 5x – 5y + 18 = 0 (d) x – y + 5 = 0 8. Consider the following statements: 1. The length p of the perpendicular from the origin to the line ax + by = c satisfies the relation p2 = c2/a2 + b2. 2. The length p of the perpendicular from the origin to the line x/a + y/b = 1 satisfies the relation 1/p2 = 1/a2 + 1/b2. 3. The length p of the perpendicular from the origin to the line y = mx + c satisfies the relation 1/p2 = 1 + m2 + c2/c2. Which of the above is/are correct? (a) 1, 2 and 3 (b) 1 only (c) 1 and 2 only (d) 2 only 9. What is the equation of the ellipse whose vertices are (± 5, 0) and foci are at (± 4, 0)? (a) x2/25 + y2/9 = 1 (b) x2/16 + y2/9 = 1 (c) x2/25 + y2/16 = 1 (d) x2/9 + y2/25 = 1 10. What is the equation of the straight line passing through the point (2, 3) and making an intercept on the positive y-axis equal to twice its intercept on the positive x-axis? (a) 2x + y = 5 (b) 2x + y = 7 (c) x + 2y = 7 (d) 2x – y = 1 11. Let the coordinates of the points A, B, C be (1, 8, 4), (0, – 11, 4) and (2, – 3, 1) respectively. What are the coordinates of the point D which is the foot of the perpendicular from A on BC? (a) (3, 4, -2) (b) (4, -2, 5) (c) (4, 5, -2) (d) (2, 4, 5) 12. What is the equation of the plane passing through the points (- 2, 6, – 6), (- 3, 10, – 9) and (- 5, 0, – 6)? (a) 2x – y – 2z = 2 (b) 2x + y + 3z = 3 (c) x + y + z = 6 (d) x – y – z = 3 13. A sphere of constant radius r through the origin intersects the coordinate axes in A, B and C. What is the locus of the centroid of the triangle ABC? (a) x2 + y2 + z2 = r2 (b) x2 + y2 + z2 = 4r2 (c) 9 (x2 + y2 + z2) = 4r2 (d) 3(x2 + y2 + z2) = 2r2 14. The coordinates of the vertices P, Q and R of a triangle PQR are (1, -1, 1), (3, -2, 2) and (0, 2, 6) respectively. If ∠RQP = θ, then what is ∠PRQ equal to? (a) 30° + θ (b) 45° – θ (c) 60° – θ (d) 90° – θ 15. The perpendiculars that fall from any point or the straight line 2x + 11y = 5 upon the two straight lines 24x + 7y = 20 and 4x – 3y = 2 are (a) 12 and 4 respectively (b) 11 and 5 respectively (c) Equal to each other (d) Not equal to each other 16. The equation of the line, when the portion of it intercepted between the axes is divided by the point (2, 3) in the ratio of 3 : 2, is (a) Either x + y = 4 or 9x + y = 12 (b) Either x + y = 5 or 4x + 9y = 30 (c) Either x + y = 4 or x + 9y = 120 (d) Either x + y = 5 or 9x + 4 y = 30 17. What is the distance between the straight lines 3x + 4y = 9 and 6x + 8y = 15? (a) 3/2 (b) 3/10 (c) 6 (d) 5 18. What is the equation to the sphere whose centre is at (- 2, 3, 4) and radius is 6 units? (a) x2 + y2 + z2 + 4x – 6y – 8z = 7 (b) x2

NDA MATHS QUESTIONS 1.Consider a question and two statements : Question :Is 3x + 2y positive? Statement-I : x3 = -29.8 Statement-II : y = 3x Which one of the following is correct in respect of the question and the statements? – (a) Statement-I alone is sufficient toanswer the question (b) Statement-II alone is sufficient toanswer the question (c) Both Statement-I and Statement-IIare together sufficient to answerthe question (d) Both Statement-I and Statement-IIare not sufficient to answer thequestion 2. Consider a question and two statements : Question :Does the equation ax2 + bx + c = 0have real roots of opposite sign? Statement-I : The discriminant D> 0 Statement-II : c/a> Which one of the following is correct in respect of the question and the statements? (a) Statement-1 alone is sufficient toanswer the question (b) Statement-Il alone is sufficient toanswer the question le) (c)Both Statement-I and Statement-IIare together sufficient to answerthe question (d) Both Statement- and Statement-IIare not sufficient to answer the question 3. Consider a question and two stateme Question :Is a? + b 2 + c2-ab-bc-ca (a, b, c are distinct real numbers) alwayspositive? Statement-I :a>b>C Statement-II : a+b+c=0 Which one of the following is correct in respect of the question and the statements? (a) Statement-1 alone is required toanswer the question (b) Statement-II alone is required toanswer the question (c) Both Statement-I and Statement-IIare required to answer the question (d)Neither Statement-1. nor Statement-II is required to answer thequestion 4. Consider a question and two statements : Question :Is y always greater than** + y (x + y+0)?x2 + y2 Statement-I : *>y Statement-II : x2 + y2 > 2xy Which one of the following is correct in respect of the question and the statements? (a)Statement-l alone is required toanswer the question (b) Statement-Il alone is required toanswer the question (c) Both Statement-I and Statement-IIare required to answer the question (d) Neither Statement-I nor Statement-II is required to answer the question 5.Sudhir purchased a chair with three consecutive discounts of 20%, 12.5% and 5%. The actual deduction will be? (a)25.35% (b)30.33% (c)31.35% (d)33.50% 6.To mainain 8 cows for 60 days, a milkman has to spend Rs. 6,400. To maintain 5 cows for n days, he has to spend Rs. 4,800. What is the value of n ? (a)68 days (b)70 days (c)72 days (d)74 days 7.A student has to secure 40% of marks to pass an examination. He gets only 45 marks and fails by 5 marks. The maximum marks are (a)120 (b)125 (c)130 (d)135 8.Five years ago, Ram was three times as old as Shyam. Four years from now, Ram will be only twice as old as Shyam. What is the present age of Ram ? (a)28 years (b)30 years (c)32 years (d)34 years 9.A boy went to his school at a speed of 12 km/hr and returned to his house at a speed of 8 km/hr. If he has taken 50 minutes for the whole journey, whatwas the total distance walked? (a)2 km (b)4 km (c)6 km (d)8 km 10.There are 350 boys in the first three standards. The ratio of the number of boys in first and second standards is 2 : 3, while that of boys in second and third standards is 4 : 5. What is the total number of boys in first and third standards? (a)210 (b)220 (c)230 (d)240 11.There are 8 lines in a plane, no two of which are parallel. What is the maximum number of points at which they can intersects? (a)28 (b)26 (c)24 (d)22 12.An arc of a circle subtends an angle π at the centre . If the length of the arc is 22 cm , then what is the radius of the circle? (a)9 cm (b)7 cm (c)5 cm (d)3 cm 13.The diagonals of a rhombus are of length 20 cm and 48 cm. What is the length of a side of the rhombus? (a)26 cm (b)29 cm (c)36 cm (d)39 cm 14.A hollow cube is formed by joining six identical squares. A rectangular cello tape of length 4 cm and breadth 0.5 cm is based for joining each pair of edges. What is the total area of cello tape used? (a)12 square cm (b)20 square cm (c)24 square cm (d)36 square cm 15.If, A = {x : x is a multiple of 7}B = {x : x is a multiple of 5}C = {x : x is a multiple of 35}then which one of the following is a null set ? (a)(A – B) ∪ C (b)(A – B) – C (c)(A ∩ B) ∩ C (d)(A ∩B) – C 16.Kx + 3y + 1 = 02x + y + 3 = 0The pair of linear equations given above will intersect each other, if (a)K = 6 (b)K ≠ 6 (c)K = 0 (d)K ≠ 0 17.The number of prime numbers which are less then 100 is (a)20 (b)25 (c)30 (d)35 18.If the equations given below have a common root x2 – px + q = 0x2 + qx – p = 0then which one of the following is correct? (a) p – q = 0 (b) p + q – 2 = 0 (c) p + q – 1 = 0 (d) p – q – 1 = 0 19.710 – 510 is divisible by (a)5 (b)7 (c)9 (d)11 20.Which of the points P(5, -1), Q( 3, -2 ) and R(1, 1) lie in the solution of the system of inequations x + y ≤ 4 and x – y ≥ 2 ? (a)P and Q (b)Q and R (c)P and R (d)P, Q and R

Q1. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is:(a) 7(b) 14(c) 21(d) 28 Q2. An urn contains lottery tickets numbered from 1 to 100. If a ticket is selected at random, then the probability that it is a perfect square is?(a) 0.1(b) 0.08(c) 0.09(d) 0.01 Q3. If the probability of winning a game is 0.3, the probability of losing it is?(a) 1.3(b) 1(c) 0.7(d) 0.1 Q4. The total number of events of throwing 10 coins simultaneously is(a) 1024(b) 512(c) 100(d) 10 Q5. If the probability of an event is P, the probability of its complementary event will be:(a) P – 1(b) P(c) 1 – p(d) 1 – 1/p Q6. If P(A) denotes the probability of an event then:(a) P(A) < 0 (b) P(A) > 0(b) 0 = P(A) = 1(c) -1 = P(A) = 0(d) 1 = P(A) = 1 Q7. An event is very unlikely to happen. Its probability is closest to:(a) 0.0001(b) 0.001(c) 0.01(d) 0.1 Q8. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is:(a) 4(b) 13(c) 48(d) 51 Q9. A girl calculate that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?(a) 40(b) 240(c) 480(d) 750 Q10. 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 Q11. The median of first 10 prime numbers is(a) 11(b) 12(c) 13(d) none of these Q12. The measure of central tendency which is given by the x-coordinate of the point of intersection of the ‘more than’ ogive and ‘less than’ ogive is –(a) Mean(b) Median(c) Mode(d) None of these Q13. While computing mean of a grouped data, we assume that the frequencies are(a) centered at the lower limits of the classes(b) centered at the upper limits of the classes(c) centered at the class marks of the classes(d) evenly distributed over all the classes Q14. The mean of the first 10 natural numbers is(a) 5(b) 6(c) 4.5(d) 5.5Q15. Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is(a) 48(b) 49(c) 50(d) 60 Q6. The marks obtained by 9 students in Mathematics are 59, 46, 30, 23, 27, 44, 52, 40 and 29. The median of the data is(a) 30(b) 35(c) 29(d) 40 Q17. The wickets taken by a bowler in 10 cricket matches are 2, 6, 4, 5, 0, 3, 1, 3, 2, 3. The mode of the data is(a) 1(b) 2(c) 3(d) 4 Q18. The mean and the median of a distribution are 45.9 and 46 respectively. The mode will be(a) 45(b) 47(c) 48(d) 46.2 Q19. Mode is the(a) middle most frequent value(b) least frequent value(c) maximum frequent value(d) none of these Q20. While computing mean of grouped data, we assume that the frequencies are all the classes(a) evenly distributed over(b) centred at the classmarks of the classes(c) centred at the upper limits of the classes(d) centred at the lower limits of the classes