CDS (I) 2026 — Elementary Mathematics (Full Question Paper)

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AlgebraArithmeticNumber SystemGeometryStatisticsTrigonometryMensurationData Sufficiency

Questions 1–10

1.
Algebra

If p + q + r = 0, then what is z^p²qr × z^q²rp × z^r²pq equal to?

(a)1
(b)z
(c)z²
(d)z³

2.
Algebra

What is the value of k for which (k² – 5k + 4)x² + (k² – 3k – 4)x + (k² – 4k) = 0 is an identity?

(a)-1
(b)0
(c)1
(d)4

3.
Algebra

If a²b²+c² = b²c²+a² = c²a²+b², then what is the value of a⁴ + b⁴ + c⁴ equal to?

(a)a^2b² + b^2c² + c^2a²
(b)2(a^2b² + b^2c² + c^2a²)
(c)3(a^2b² + b^2c² + c^2a²)
(d)4(a^2b² + b^2c² + c^2a²)

4.
Algebra

If 1/x = 1/p + 1/q, then what is pqp²-q² × [x+px-p – x+qx-q] equal to?

(a)-2
(b)-1
(c)1
(d)2

5.
Number System

Let P = 5⁵ × 15¹⁵ × 25²⁵ × 35³⁵ and Q = 10¹⁰ × 20²⁰ × 30³⁰ × 40⁴⁰. What is the number of consecutive zeros at the end of the sum (P + Q)?

(a)100
(b)65
(c)50
(d)Zero

6.
Algebra

If (x – 5) is the HCF of x² – x – p and x² – qx – 10, then what is the value of (p + q)?

(a)-23
(b)-17
(c)17
(d)23

7.
Algebra

The LCM and HCF of two polynomials p(x) and q(x) are (x + a)(x³ – a³) and (x² – ax + a²), respectively. If p(x) = x⁴ + a^2x² + a⁴, then what is q(x) equal to?

(a)x⁴ – 2a^2x² + a⁴
(b)x⁴ + 2a^2x² + a⁴
(c)x² – a²
(d)x⁴ – a^2x² + a⁴

8.
Algebra

Which of the following expressions can divide both the polynomials x³ + 2x² – 5x + 2 and x³ + 4x² + x – 6 exactly?

I.x – 1
II.x + 1
III.x + 2

Select the correct answer using the code given below:

(a)I and II only
(b)II and III only
(c)I and III only
(d)I only

9.
Arithmetic

Eight men and 24 women can finish a piece of work in one day while 12 men and 18 women can also finish it in one day. What is the time taken by 24 men and 72 women to finish the work?

(a)13 of a day
(b)23 of a day
(c)3 days
(d)92 days

10.
Algebra

For what integral value of k, the system of equations kx – 5y + 6 = 0 and 4(k – 1)y – 12x + 3 = 0 has no solution?

(a)4
(b)3
(c)1
(d)No such value exists

Questions 11–20

11.
Number System

Seven times a two-digit positive number is equal to four times the number obtained by reversing the order of the digits. How many such two-digit numbers are there?

(a)1
(b)4
(c)6
(d)8

12.
Arithmetic

In what duration of time will ₹3300 become ₹3399 at 12% per annum interest compounded quarterly?

(a)3 months
(b)6 months
(c)9 months
(d)1 year

13.
Algebra

If x varies directly as y, then which of the following is/are correct?

I.(x² + y²) varies directly as y².
II.x³y⁴ varies directly as y.

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

14.
Arithmetic

X can do a piece of work in 4 days and Y can do the same piece of work in 6 days. Which of the following statements is/are correct?

I.If X and Y work alternately starting with X, then the piece of work will be finished on the fifth day.
II.If X and Y work alternately starting with Y, then the piece of work will be finished in less than 5 days.

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

15.
Arithmetic

12 men working 8 hours a day can completely build a wall of length 100 m, breadth 20 cm and height 5 m in 10 days. How many days will 16 men working 10 hours a day require to build a wall of length 200 m, breadth 60 cm and height 5 m?

(a)18
(b)24
(c)27
(d)36

16.
Arithmetic

A train P starts from station X for station Y and another train Q starts from station Y for station X at the same time. After passing each other, P takes 4 hours to reach Y and Q takes 1 hour to reach X. If the average speed of P is 60 km/h, then what is the average speed of Q?

(a)72 km/h
(b)80 km/h
(c)96 km/h
(d)120 km/h

17.
Arithmetic

Without stoppages, a train travels at an average speed of 60 km/h and with stoppages it covers the same distance at an average speed of 48 km/h. How many minutes per hour does the train stop?

(a)10 minutes
(b)12 minutes
(c)15 minutes
(d)20 minutes

18.
Arithmetic

A person goes downstream at x km/h and upstream at y km/h by the same boat. What is the ratio of speed of boat in still water to speed of water?

(a)x/y
(b)y/x
(c)x+yx-y
(d)x-yx+y

19.
Algebra

Let Q = x² + bx + c. If the sum of the roots is equal to product of the roots of the equation Q = 0, then which of the following statements is/are correct?

I.Q can be a perfect square.
II.Q is positive for all real values of x.

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

20.
Arithmetic

The ratio of the present age of X to that of Y is 4 : 5. k (less than 10) years ago, this ratio was 1 : 2. How many values of k are possible if the ages are expressed in complete years?

(a)1
(b)2
(c)3
(d)More than 3

Questions 21–30

21.
Number System

27²⁷ – 9⁴⁰ – 3⁷⁹ is divisible by how many natural numbers less than 10?

(a)1
(b)2
(c)3
(d)More than 3

22.
Number System

If the HCF of p and q (p > q) is G, then which of the following statements is/are correct?

I.HCF of p and (p + q) is G
II.HCF of p, (p – q) is G

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

23.
Number System

The HCF and LCM of two numbers p and q are 44 and 4620 respectively. When p is divided by 55, the quotient is 4 and remainder is 0. What is the value of q?

(a)770
(b)924
(c)1155
(d)2310

24.
Number System

Let N be the greatest number that will divide 600, 631 and 724, leaving the same remainder. What is the value of N?

(a)41
(b)37
(c)33
(d)31

25.
Number System

What is the LCM of 3.6, 0.009, 0.27?

(a)5.4
(b)10.8
(c)16.2
(d)21.6

26.
Number System

What is the greatest possible speed at which a person can walk 13.3 km and 20.9 km so that the time (in hours) required in each case is a whole number?

(a)1.7 km/h
(b)1.9 km/h
(c)2.1 km/h
(d)2.3 km/h

27.
Number System

What is the sum of all the divisors of 256?

(a)511
(b)510
(c)256
(d)255

28.
Number System

Consider the following statements:

I.Two consecutive natural numbers are always co-prime.
II.If m and n are relatively prime, then m × n is always even.

Which of the statements given above is/are correct?

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

29.
Algebra

If log₁₀(80) = p, log₁₀(45) = q and log₁₀(216) = r, then what is log₁₀(384) equal to?

(a)p + q + r
(b)p – q + r
(c)p – q – r
(d)p + q – r

30.
Number System

What is the digit in the unit place of the number 1¹ × 3³ × 5⁵ × 7⁷ × 9⁹?

(a)1
(b)3
(c)5
(d)7

Questions 31–40

31.
Number System

Let P = N² where N is an odd integer. What is the remainder when P is divided by 8?

(a)1
(b)3
(c)5
(d)Cannot be determined due to insufficient data

32.
Arithmetic

A reduction of 10% in the price of sugar enables a person to buy 6.2 kg more for ₹2790. What is the reduced price per kilogram?

(a)₹50
(b)₹48
(c)₹45
(d)₹42

33.
Arithmetic

A single discount which is equivalent to a series of discounts p %, p2 %, p4 % is 31.6%. What is the value of p?

(a)24%
(b)20%
(c)18%
(d)16%

34.
Algebra

A locomotive engine can go 40 km/hr. Its speed gets reduced by a quantity that varies directly as the square root of the number of wagons attached. It is known that its speed becomes 16 km/hr if 36 wagons are attached. What is the smallest number of wagons with which the engine is unable to move?

(a)100
(b)81
(c)64
(d)49

35.
Algebra

Two numbers P and Q are such that P : Q = x : y. If 1 is added to both the numbers, the ratio becomes 7 : 10. If 3 is added to both the numbers, the ratio becomes 3 : 4. What is (x + y) : (x – y) equal to?

(a)-5
(b)-3
(c)3
(d)Cannot be determined due to insufficient data

36.
Geometry

ABC is a triangle right-angled at C. A semicircle is drawn on AB as diameter. Let P be any point on AC produced such that AP = AB = 10 cm. Further, B and P are joined. If BC = 8 cm, then what is BP equal to?

(a)4√5 cm
(b)9 cm
(c)10 cm
(d)5√5 cm

37.
Statistics

All possible groups of 3 distinct numbers from among A, B, C, D and E are formed. If the aggregate of sums of numbers of each group is 120, then what is the arithmetic mean of A, B, C, D and E?

(a)4
(b)5
(c)10
(d)20

38.
Statistics

The arithmetic mean of 100 observations is 50. If 10 is added to each observation then what will be the new arithmetic mean?

(a)50
(b)55
(c)60
(d)65

39.
Statistics

The sum of the deviations of a set of n numbers x₁, x₂, x₃, …, x_n measured from 15 is -90 and the sum of the deviations of the same numbers measured from -3 is 54. What is the arithmetic mean?

(a)3.25
(b)3.50
(c)3.75
(d)4.25

40.
Statistics

The numbers 59, 53, 51, 43, 36, (8x + 1), (x² + 1), 13, 12, 9, 7, 3 are written in descending order and their median is 25. What is/are the values of x?

(a)-12 only
(b)4 only
(c)-12, 4
(d)12, -4

Questions 41–50

41.
Trigonometry

If cos θ1 – sin θ + cos θ1 + sin θ = 4, then which one of the following is a value of (tan² θ + cot² θ)?

(a)5/3
(b)10/3
(c)4
(d)5

42.
Trigonometry

For 0 < θ < π/2, consider the following:

I.(tan⁴ θ + tan⁶ θ)(cot⁴ θ + cot⁶ θ) = sec² θ cosec² θ
II.tan θ + sin θtan θ – sin θ = cot² θ (sec θ + 1)²

Which of the above is/are identities?

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

43.
Trigonometry

If 3sinθ + 4cosθ = 5, then what is a value of 4tanθ + 3cotθ?

(a)7
(b)8
(c)9
(d)10

44.
Trigonometry

At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be 5/6. On walking 70 m towards the tower, the tangent of the angle of elevation of the top of the tower is found to be 9/8. What is the height of the tower?

(a)225 m
(b)270 m
(c)300 m
(d)330 m

45.
Trigonometry

Two persons are on diametrically opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30° and 60° respectively. If the height of the tower is 100 m, what is the approximate distance between the two persons?

(a)220 m
(b)225 m
(c)230 m
(d)235 m

46.
Geometry

In a cyclic quadrilateral ABCD, the diagonal AC bisects the angle C. Which of the following statements is/are correct?

I.∠ABD = ∠ADB
II.The diagonal BD is parallel to the tangent of the circle at A

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

47.
Mensuration

Let x be the length of a diagonal of a face of a cube and y be the length of a diagonal of the cube. If x + y = (5 + 2√6) units, then what is the total surface area of the cube?

(a)6(x + y)
(b)6xy
(c)3(x + y)
(d)3xy

48.
Geometry

ABC is a triangle in which AB = AC and D is any point on BC. Which of the following statements is/are correct?

I.AB² – AD² = CD × BD
II.BC² + BD² – DC² = 2BD × BC

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

49.
Geometry

ABC is a triangle right-angled at B with sides BC = a, CA = b and AB = c. Let p be the length of the perpendicular from B to AC. Which of the following statements is/are correct?

I.p = ac√a²+c²
II.pb = ac

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

50.
Geometry

ABC is an equilateral triangle. Let PQRS be a square inscribed in it such that P is on AB and Q is on AC. Which of the following is/are correct?

I.AP : PB = 4 : 3
II.√3AB = (2 + √3)PQ

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

Questions 51–60

51.
Mensuration

The perimeter of a right-angled isosceles triangle is 20 units. If α is the area of the triangle, then

(a)15 < α < 16
(b)16 < α < 17
(c)17 < α < 18
(d)18 < α < 19

52.
Geometry

Let O be the centre of a circle. Let A, B and C lie on the circle such that ∠ABC = 153°. What is the value of ∠AOC?

(a)54°
(b)52°
(c)39°
(d)27°

53.
Geometry

In a quadrilateral ABCD, the diagonals intersect at O. Let the area of the triangle ABD be p. If AO : OC = m : n, then what is the area of the triangle BCD?

(a)npm
(b)mpn
(c)n² pm²
(d)m² pn²

54.
Geometry

Let ABCD be a parallelogram and E be the midpoint of BC. The diagonal BD and line segment AE intersects at F. If BF = 2.4 cm, then what is BD equal to?

(a)6.0 cm
(b)6.4 cm
(c)7.2 cm
(d)8.4 cm

55.
Geometry

ABC is a triangle right-angled at C. Let P be the midpoint of BC. If AP = 4√13 cm and AB = 20 cm, then what is the perimeter of the triangle ABC?

(a)40 cm
(b)48 cm
(c)50 cm
(d)60 cm

56.
Geometry

ABC is a triangle right-angled at B. Points M and N trisect BC. If AM = 6 cm and AN = 9 cm, then what is AC equal to?

(a)4√39 cm
(b)2√39 cm
(c)24 cm
(d)20 cm

57.
Geometry

ABC is a triangle right-angled at B. If AC = (p+q)/2 and BC = (p-q)/2, then which of the following statements is/are correct?

I.The value of AB is equal to the geometric mean of p and q.
II.The perimeter of the triangle is p(q + 1).

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

58.
Mensuration

A sphere of diameter 14 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 14 cm. If the sphere is completely submerged in water, then how much will the level of water rise?

(a)7/3 cm
(b)8/3 cm
(c)14/3 cm
(d)16/3 cm

59.
Geometry

ABCD is a quadrilateral with sides AB = 9 cm, BC = 40 cm, CD = 28 cm and DA = 15 cm and one of the diagonals AC = 41 cm. Which of the following statements is/are correct?

I.The vertices A, B, C and D of the quadrilateral lie on a circle.
II.The area of triangle ACD is 126 cm².

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

60.
Mensuration

The minute hand of a clock is 15 cm long and sweeps an area of 15π cm² on the dial of the clock. How much angle does it describe during this period?

(a)12°
(b)18°
(c)24°
(d)30°

Questions 61–70

61.
Mensuration

The diameter of a copper solid sphere is 6 cm. The sphere is melted and recast into a wire. If the diameter of the wire is 0.5 cm, then what is the length of the wire?

(a)5.24 m
(b)5.36 m
(c)5.76 m
(d)5.96 m

62.
Mensuration

A square and a rectangle have the same perimeter p and their areas differ by q units. What is the square of the difference between the length and breadth of the rectangle?

(a)1.5q
(b)2q
(c)2.5q
(d)4q

63.
Geometry

A triangle PQR is inscribed in a circle with its centre at O. A tangent PT is drawn at P such that ∠QPT = 36°. What is ∠POQ equal to?

(a)36°
(b)54°
(c)72°
(d)108°

64.
Geometry

ABCD is a cyclic quadrilateral. AB and DC are produced to meet at P. Which of the following statements is/are correct?

I.ΔPAD is similar to ΔPBC
II.∠PAD + ∠PDA = ∠PBC + ∠PCB

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

65.
Geometry

Let O be the centre of a circle. Let the chords AB = 10 cm and CD = 24 cm be two parallel chords of the circle. The two chords are on opposite side of the centre and the distance between them is 17 cm. Let P be the midpoint of AB and Q be the midpoint of CD. Further, the points O and A, the points O and C, the points A and C are joined. Which of the statements given below is/are correct?

I.Area of triangle OAP is equal to area of triangle OCQ.
II.Area of triangle OAC is equal to 102 cm².

Select the answer using the code given below:

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

66.
Mensuration

A metallic sheet of rectangular shape is 48 cm × 36 cm. From each corner a square of side x cm is cut off and an open box is made of the remaining sheet. If the box holds 5.12 litre of water, then what is the value of x?

(a)6 cm
(b)7.5 cm
(c)8 cm
(d)8.5 cm

67.
Geometry

Two triangles ABC right-angled at A and DBC right-angled at D are drawn such that AC and DB intersect at P. If AP = x, PC = y and BP = z, then what is (AC + BD) equal to?

(a)(xy + yz + zx)/z
(b)(xy + yz + zx + z²)/z
(c)(xy + yz + zx + y²)/y
(d)(xy + yz + zx + x²)/x

68.
Geometry

In a triangle ABC, AB = 18 cm, BC = 22 cm and AC = 15 cm. The bisector of ∠BAC intersects BC at D. What is (BD × DC) equal to?

(a)121 cm²
(b)120 cm²
(c)117 cm²
(d)96 cm²

69.
Mensuration

The volume of a cube is 8 cm³ and is equal to the volume of a cuboid of length x, breadth y and height z, where x, y and z are natural numbers (x > y > z). Let n be the number of such cuboids with different dimensions. What is the value of n?

(a)1
(b)2
(c)3
(d)More than 3

70.
Mensuration

Let x, y, z (all prime) be the length, breadth and height respectively of a cuboid with x > y > z. The volume of the cuboid is 30k³ cubic units, where k is a natural number. What is the total surface area of the cuboid?

(a)60 square units
(b)62 square units
(c)64 square units
(d)Cannot be determined due to insufficient data

Questions 71–80

71.
Data Sufficiency

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: A circle is inscribed in the equilateral triangle Δ. What is the radius of the circle?

Statement-I:Area of Δ is equal to 16√3 cm².
Statement-II:Perimeter of Δ is 24 cm.

Which one of the following is correct in respect of the above Question and the Statements?

(a)The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
(b)The Question can be answered by using either Statement alone
(c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d)The Question cannot be answered even by using both the Statements together

72.
Data Sufficiency

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: ABCD is a quadrilateral in which AD = BC. What is ∠ABC + ∠ADC equal to?

Statement-I:AB is parallel to DC
Statement-II:AD is not parallel to BC

Which one of the following is correct in respect of the above Question and the Statements?

(a)The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
(b)The Question can be answered by using either Statement alone
(c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d)The Question cannot be answered even by using both the Statements together

73.
Data Sufficiency

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: ABCD is a quadrilateral such that AC bisects ∠A and ∠C. Is AB/DC equal to AD/BC?

Statement-I:AB is parallel to DC
Statement-II:AD is parallel to BC

Which one of the following is correct in respect of the above Question and the Statements?

(a)The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
(b)The Question can be answered by using either Statement alone
(c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d)The Question can be answered even without using both the Statements

74.
Data Sufficiency

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: P, Q, R and S are respectively the midpoints of sides AB, BC, CD, DA of a rhombus ABCD. These points are joined to form a quadrilateral PQRS. Is the quadrilateral cyclic?

Statement-I:∠ABC = 120°
Statement-II:∠BCD = 60°

Which one of the following is correct in respect of the above Question and the Statements?

(a)The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
(b)The Question can be answered by using either Statement alone
(c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d)The Question can be answered even without using both the Statements

75.
Data Sufficiency

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: Two circles with radii p, q (p > q) in cm touch externally, where p, q are natural numbers and each greater than 1. What is the value of (p – q)?

Statement-I:The sum of their areas is 130π cm².
Statement-II:The distance between the centres of the two circles is 14 cm.

Which one of the following is correct in respect of the above Question and the Statements?

(a)The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
(b)The Question can be answered by using either Statement alone
(c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d)The Question cannot be answered even by using both the Statements together

76.
Data Sufficiency

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: Is rⁿ less than 1, where r is a real number and n is a natural number?

Statement-I:0 < r² < 1
Statement-II:0 < r³ < 2

Which one of the following is correct in respect of the above Question and the Statements?

(a)The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
(b)The Question can be answered by using either Statement alone
(c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d)The Question cannot be answered even by using both the Statements together

77.
Data Sufficiency

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: Is (p² + q²) always composite number, where p and q are different prime numbers?

Statement-I:(p – q) is an odd integer
Statement-II:(p + q) is an odd integer

Which one of the following is correct in respect of the above Question and the Statements?

(a)The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
(b)The Question can be answered by using either Statement alone
(c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d)The Question cannot be answered even by using both the Statements together

78.
Data Sufficiency

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: Is (0.5)ⁿ + (0.5)^-n always greater than 2, where n is an integer?

Statement-I:n is an even integer
Statement-II:n is negative

Which one of the following is correct in respect of the above Question and the Statements?

(a)The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
(b)The Question can be answered by using either Statement alone
(c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d)The Question can be answered even without using both the Statements

79.
Data Sufficiency

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: LCM of three numbers p, q and r (p > q > r > 0) is 30 and their HCF is 5. What is the product of the three numbers?

Statement-I:p = 15
Statement-II:q = 10

Which one of the following is correct in respect of the above Question and the Statements?

(a)The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
(b)The Question can be answered by using either Statement alone
(c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d)The Question can be answered even without using both the Statements

80.
Data Sufficiency

A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: Let XYZ be a 3-digit number and the difference between XYZ and ZYX is equal to PQR. Is (P + R) equal to Q?

Statement-I:P = 3
Statement-II:R = 6

Which one of the following is correct in respect of the above Question and the Statements?

(a)The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
(b)The Question can be answered by using either Statement alone
(c)The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d)The Question can be answered even without using both the Statements

Questions 81–90

For the next two (02) items that follow:

x⁴ + px³ + qx² + x + 6 is divisible by x² – x – 6.

81.
Algebra

What is the value of p?

(a)-2
(b)-1
(c)1
(d)2

82.
Algebra

What is the value of q?

(a)-7
(b)-5
(c)-3
(d)-1

For the next two (02) items that follow:

16(x⁴ + 1/x⁴) – 257 = 0

83.
Algebra

What is (x² + 1/x²) equal to?

(a)25/16
(b)21/16
(c)19/4
(d)17/4

84.
Algebra

What is (x³ + 1/x³) equal to?

(a)65/8
(b)63/8
(c)61/8
(d)59/8

For the next two (02) items that follow:

Let x = √6+√5√6-√5 and y = √6-√5√6+√5

85.
Algebra

What is (x² – y²) equal to?

(a)22√30
(b)44√30
(c)66√30
(d)88√30

86.
Algebra

What is (x² – xy + y²) equal to?

(a)487
(b)483
(c)481
(d)480

For the next two (02) items that follow:

X is an alloy of copper and zinc. Y is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of X and Y is found to contain 74% of copper, 16% of zinc and 10% of tin.

87.
Arithmetic

What is the percentage of copper in X?

(a)60%
(b)64%
(c)66%
(d)70%

88.
Arithmetic

What is the percentage of zinc in X?

(a)40%
(b)36%
(c)34%
(d)30%

For the next two (02) items that follow:

A person borrows a sum of ₹16,000 on simple interest at the beginning of a year. After 4 months, ₹24,000 more is borrowed at a rate of interest double the previous one. At the end of the year, the total interest on both the loans is ₹4800.

89.
Arithmetic

What is the initial rate of interest per annum?

(a)8%
(b)10%
(c)12%
(d)16%

90.
Arithmetic

What is the ratio of the interest on the first loan to the interest on the second loan?

(a)1 : 2
(b)2 : 3
(c)3 : 4
(d)4 : 5

Questions 91–100

For the next two (02) items that follow:

Let 12(tanθ + cotθ) = 25, where 45° < θ < 90°.

91.
Trigonometry

What is a value of (sinθ – cosθ)?

(a)-1/5
(b)-2/5
(c)1/5
(d)2/5

92.
Trigonometry

What is a value of (cosecθ + secθ)?

(a)4
(b)35/12
(c)25/12
(d)2

For the next two (02) items that follow:

cosecθ – sinθ = p³ and secθ – cosθ = q³

93.
Trigonometry

What is tanθ equal to?

(a)p/q
(b)q/p
(c)pq
(d)√pq

94.
Trigonometry

What is p^4q² + p^2q⁴ equal to?

(a)-2
(b)-1
(c)0
(d)1

For the next two (02) items that follow:

p sin² α + q cos² α = m and p cos² β + q sin² β = n

95.
Trigonometry

What is tan² α equal to?

(a)m-qp-m
(b)m-pq-m
(c)m-qm-p
(d)m-pm-q

96.
Trigonometry

What is cot² β equal to?

(a)n-qp-n
(b)n-pq-n
(c)n-pn-q
(d)n-qn-p

For the next two (02) items that follow:

p + q cotθ = 3cosecθ and q – p cotθ = 2cosecθ

97.
Trigonometry

What is p² + q² equal to?

(a)5
(b)7
(c)10
(d)13

98.
Trigonometry

What is tanθ equal to?

(a)2q+3p3q-2p
(b)2q-3p3q+2p
(c)3q+2p2q-3p
(d)3q-2p2q+3p

For the next two (02) items that follow:

p = sinθ1+cosθ+sinθ and q = 1+sinθ1+sinθ-cosθ

99.
Trigonometry

Which one of the following is correct?

(a)p – q = 0
(b)2pq – 1 = 0
(c)pq – 2 = 0
(d)pq – 1 = 0

100.
Trigonometry

What is (p + 1/q)(q + 1/p) equal to?

(a)1/2
(b)17/4
(c)9/2
(d)21/4

English-language questions transcribed from the official Combined Defence Services Examination (I), 2026 question booklet (KPRS-T-MTE), Series A, Elementary Mathematics. Hindi text omitted. Answer key not included.

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