**ORDERING OF SENTENCES**

- What is the geometric means of the observations 125, 729, 1331?
- 495
- 1485
- 2221
- None of these

- Examples of data are given below:
- Information on households collected by an investigator by door-to-door visits.
- Data on the percentage of literates, sex-wise, for the different districts of a state collected from records of the census of India.

- General Information about families, collected by telephonic interviews.

Which one of the following in respect of the above is correct?

- I and II are primary data
- I and III are primary data
- II and III are primary data
- I, II and III are primary data

- Which one of the following can be obtained from a historgam?
- Mean
- Median
- Mode
- None of these

- The median of three positive integers, no two of which are equal, is 5. What is the least possible value of arithmetic means of these integers?
- 2
- 3
- 4
- No such least possible value exists

- Consider the following pairs of numbers:
- (8, 12) II. (9, 11) III. (6, 24)

Which pairs of number have the same harmonic means?

- I and II
- II and III
- I and III
- I, II and IIII

- If 27 × (81)
^{2n+3}– 3^{m}= 0, then what is m equal to?- 2n + 5
- 5n + 6
- 8n + 3
- 8n + 15

- There are four numbers forming a GP in which the third term is greater than the first by 9 and the second term is greater than the fourth by 18. What is the first term?
- 2
- 3
- – 2
- – 3

- What is the value of [log
_{13}(10)]/[log_{169}(10)]?- 1/2
- 2
- 1
- log
_{10}13

- A boy travels a distance of 8 km at the rate of 4 km/h, 6 km at the rate of 3 km/h and 4 km at the rate of 2 km/h. What is the average speed for the entire journey?
- 2 km/h
- 3 km/h
- 4 km/h
- 6 km/h

- Which one of the following is not correct in respect of the sets A and B?

- If 0 < θ< Φ< 90°, then which one of the following is correct?
- (sin θ+ cos θ)2 > 2
- (sin
^{2}θ+ cos^{2}Φ) ≤ 2 - (sin
^{2}θ+ cos^{2}Φ) < 2 - (sin
^{2}θ+ cos^{2}Φ) > 2

- For what value of θ is (sin θ+ cosecθ ) = 2.5 where 0 <θ ≤ 90°?
- 30°
- 45°
- 60°
- 90°

- The angles of a triangle are in AP and the greatest angle is double the least. What is the ratio of angles in the Indian measure?
- 2 : 3 : 4
- 1 : 2 : 3
- 3 : 3 : 6
- 4 : 5 : 7

- The length of the shadow of a person s cm tall when the angle of elevation of the sun is α is p cm. It is q cm when the angle of elevation of the sun is β. Which one of the following is correct when β = 3α ?

- If cot θ= 2xy/x
^{2}-y^{2},then what is cosθ equal to?

- The value of cosec
^{2}θ– 2 + sin^{2}θis always- less than zero
- non-negative
- zero
- 1

- If tan θ=p/q ,then what is p sec θ-q cosec θ/p sec θ+q cosec θ equal to?

- p –q/p+ q
- q
^{2}-p^{2}/ q^{2}+p^{2} - p
^{2}– q^{2}/q^{2}+p^{2} - 1

- What is the value of sin
^{3}60° cot 30° – 2 sec^{2 }45° + 3 cos 60° tan 45° – tan2 60°?- 35/8
- – 35/8
- –11/8
- 11/8

- If 0 < x < 45° and 45° < y < 90°, then which one of the following is correct?
- sin x = sin y
- sin x < sin y
- sin x > xin y
- sin x ≤ sin y

- The difference of the two angles in degree measure is 1 and their sum in circular measure is also I. What are the angles in circular measure?

- None of the above

- is satisfied by which one of the following values of θ?
- π/2
- π/3
- π/4
- π/6

- Consider the following

Which of the statements given above is/are correct?

- I only
- II only
- Both I and II
- Neither I nor II

- What is the angle subtended at the centre of a circle of radius 8 m after traversing 4π m along its circumference?
- π/3
- π/2
- 2 π/3
- 3 π/4

- If cot θ= 8/15, then what is the value of where θis a positive acute angle?
- 1/5
- 2/5
- 3/5
- 4/5

- In the figure given above, O is the centre of the circle ∠AOD = 106°. What is ∠BCD equal to?

- 53°
- 43°
- 40°
- 37°

- The quadrilateral formed by joining the mid-points of the sides AB, BC, CD, DA of a quadrilateral ABCD is

- a trapezium but not a parallelogram
- a quadrilateral but not a trapezium
- a parallelogram only
- a rhombus

- In the figure given above, ABCD is a square in which AO = AX. What is ∠XOB?

- 5°
- 25°
- 30°
- 45°

- In the figure AB is parallel to CD and BE is parallel to FH. What is ∠FHE equal to?

- 110°
- 120°
- 125°
- 130°

- In the figure given above, ∠AOB = 46°; AC and OB intersect each other at right angles. What is the measure of ∠OBC? (O is the centre of the circle)

- 44°
- 46°
- 67°
- 5°

- In the figure given above, O is the centre of the circle. The line UTV is a tangent to the circle at T, ∠VTR = 52° and triangle PTR is an isosceles traingle such that TP = TR. What is ∠x + ∠y + s equal to?

- 175°
- 208°
- 218°
- 250°

- What is the number of points in the plane of a triangle ABC which are at equal distance from the vertices of the triangle?
- 0
- 1
- 2
- 3

- The bisectors of the angles ABC and BCA of a triangle ABC meet in a point O. What is the angle at O facing the side BC?
- 90° – (A/2)
- 90° + (A/2)
- 90° – A
- 90° + A

- ABC is a triangle in which AB = AC. Let BC be produced to D. From a point E on the line AC let EF be a straight line such that EF is parallel to AB. Consider the quadrilateral ECDF thus formed. If ∠ABC = 65° and ∠EFD = 80°, then what is ∠FDC equal to
- 43°
- 41°
- 37°
- 35°

- ABC is a triangle and the perpendicular drawn from A meets BC in D. If AD
^{2}= BD.DC, then which one of the following is correct?- ABC must be an obtuse angled triangle
- ABC must be an acute angled triangle
- Either ∠B ≥ 45° or ∠C ≥ 45°
- AC
^{2}= AB^{2}+ BC^{2}

- Consider the following statements:
- Congruent triangles are similar.
- Similar trianlges are congruent.

- If the hypotenuse and a side of one right triangle are equal to the hypotenuse and a side of another right triangle respectively, then the two right triangles are congruent.

Which of the statement given above is/are correct?

- I only
- II only
- II and III
- I and III

- ABC is triangle. X is a point outside the triangle ABC such that CD = CX, where D is the point of intersection of BC and AX; and ∠BAX = ∠XACWhich one of the following is correct?
- Triangles ABD, ACX are similar
- ∠ABD < ∠ÐACD
- AC = CX
- ∠ADB > ∠DXC

- A point P moves such that its distance from two given points A and B are equal. Then what is the focus of the point P?
- A straight line which is the high right bisector of AB
- A circle with centre at A
- A circle with centre of B
- A straight line passing through either A or B

- In the figure given above, PT is a tangent to a circle of radius 6 cm. If P is at a distance of 10 cm from the centre O and PB = 5 cm, then what is the length of the chord BC?

- 8 cm
- 0 cm
- 4 cm
- 0 cm

- A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and radius 1 cm. What is the number of cones formed?
- 36
- 72
- 144
- 180

- In the triangle ABC, AB = 2 cm, BC = 3cm, and AC = 4 cm, D is the middle point of AC. If a square is constructed on the side BD, what is the area of the square?
- 5 cm
^{2} - 5 cm
^{2} - 35 cm
^{2} - None of these

- 5 cm
- From a cylindrical log whose height is equal to its diameter, the greatest possible sphere has been taken out. What is the fraction of the original log which is cut away?
- 1/2
- 1/3
- 1/4
- 2/3

- If a sphere of radius 10 cm is intersected by a plane at a distance 8 cm from its centre, what is the radius of the curve of intersection of the plane of the plane and the sphere?
- 8 cm
- 6 cm
- 5 cm
- 4 cm

- A cylindrical can of internal diameter 24 cm contains was. A solid sphere of radius 6 cm is completely immersed to water in the cylinder. The water level increases by
- 25 cm
- 5 cm
- 2 cm
- 3 cm

- A person rides a bicycle round a circular path of radius SC. The radius of the wheel of the bicycle is 50 cm. The cycle comes to the starting point for the first time in 1 h. What the number of revolutions of the wheel in 15 min?

- 20
- 25
- 30
- 35

- ABC is a straight right-angled at C. If p is the length of perpendicular from C to AB and a, b, c are the sides, the which one of the following is correct?

- pa = bc
- pb = ca
- pc = ab
- p2 = ab

- A bucket which is in the form of a frustum of a corner radii 3 and 5 unit and vertical height 6 unit. How may water can the bucket hold?

- 33 πcu unit
- 45 πcu unit
- 48π cu unit
- None of these

- How many litres of water (approximately) hemispherical container of radius 21 cm hold?

- 4 L
- 8 L
- 194 L
- 388 L

- PQRS is a diameter of a circle of radius 6 cm as shown in the figure above. The lengths PQ, QR and RS are equal. Semicircles are drawn on PQ and QS as diameters. What is the perimeter of the shaded region?

- 12 πcm
- 14 πcm
- 16 πcm
- 18π cm

- If the radius of the base and the height of a right circular cone are increased by 20% then what is the approximate percentage increase in volume?

- 60
- 68
- 73
- 75

- Seven semi-circular areas are removed from the rectangle ABCD as shown in the figure above. In which AB = 2 cm and AD = 0.5 cm. The radius of each semi-circle r, s, t, u, v is half of that of semi-circle p or q. What is the area of the remaining portion?

- (128 – 13 π)/128 cm
^{2} - (125 – 13 π)/125 cm
^{2} - (128 – 15 π)/128 cm
^{2} - None of these

- (128 – 13 π)/128 cm
- A wire is in the form of a circle of radius 42 cm. If it is bent into a square, then what is the side of the square?
- 66 cm
- 42 cm
- 36 cm
- 33 cm

- How many litres of water flow out of a pipe having an area of cross-section of 5 cm
^{2}in one minute. If the speed of water in the pipe is 30 cm/s?- 90 L
- 15 L
- 9 L
- 5 L

- A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. What is the volume of the solid so obtained?
- 50 πcm
^{3 } - 100 πcm
^{3} - 125π cm
^{3} - 150 πcm
^{3 }

- 50 πcm
- The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2 : 3. What is the ratio of their vertical heights?
- 5 : 6
- 6 : 5
- 9 : 5
- 5 : 9

- The paint in certain container is sufficient to paint an area equal to 5.875 m2. How many bricks of dimensions 12.5 cm ×10 × 7.5 cm can be painted out of this container?
- 225
- 180
- 150
- 100

- If p is an integer then every square integer is of the form
- 2p or (4p –1)
- 4p or (4p – 1)
- 3p or (3p + 1)
- 4p or (4p + 1)

- What least value must be given to Å so that the number 84705 Å 2 is divisible by 9?

- 0
- 1
- 2
- 3

- If x = then what is the value of x
^{3}+ 3bx – 2a?- 2a
^{3 } - –2a
^{3} - 1
- 0

- 2a
- If the roots of the equation are equal, then what is the value of m?
- 1
- ½
- 0
- – ½

- What is equal to?
- –3/4
- 1/4
- 3/4
- 0

- For two natural numbers m and n, let g
_{mn}denote the greatest common factor of m and n. Consider the following in respect of three natural numbers k, m and n. - g
_{m}(nk) = g(mn)k - g
_{mn}g_{nk}= g_{mk}

Which of the above is/are correct?

- I only
- II only
- Both I and II
- Neither I nor II

- What is the value of k for which the system of equations x + 2y – 3 = 0 and 5x + ky + 7 = 0 has no solution?
- – 3/14
- –14/3
- 1/10
- 10

- If x + y + z = 0 then what is the value of

- 1/x2+y2+z2
- 1
- -1
- 0

- The length of a line segement AB is 2 unit. It is divided into two parts at the point C such that AC
^{2}= AB × CB. What is the length of CB?

- 3 + √5 unit
- 3 – √5 unit
- 2 – √5 unit
- √3 unit

- If pq + qr + rp = 0, then what is the value of

- 0
- 1
- -1
- 3

- If a = 1+x/2-x, the what is 1/a+1+2a+1/a2-1equal to?
- (1+x)(2+x)/2x-1
- (1-x)(2-x)/x-2
- (1+x)(2-x)/2x-1
- (1-x)(2-x)/2x+1

- The following table shows the percentage of male and female coffee drinkers and non-coffee drinkers in two Towns A and B.

Atributes __Town A__ __Town B__

Male Female Male Female

Coffee drinkers 40% 5% 25% 15%

Non-coffee drinkers 20% 35% 30% 30%

If the total population of the Towns A and B are 10000 and 20000 respectively, then what is the total number of female coffee drinkers in both towns?

- 8000
- 6000
- 3500
- 2500

- If (37)
^{x}= (0.037)^{y}= 10000, then what is the value of 1/x-1/y?- 1
- 2
- ½
- ¼

- If ax = by = cz and abc = 1, then what is xy + yz + zx equal
- xyz
- x + y + z
- 0
- 1

- When a polynomial is divided by alinear polynomial, then what is the remainder?
- Constant polynomial only
- Zero polynomial only
- Either constant o zero polynomial
- Liner polynomial

- What is the ratio of sum of squares of roots to the product of the roots of the equation 7x
^{2}+ 12x + 18 = 0?- 6 : 1
- –6 : 7
- – 6 : 1
- – 1 : 6

- If x = 2 + √3, then what is (x
^{2}+ x^{–2}) equal to?- 12
- 13
- 14
- 15

- Which one of the following statements is correct?
- Remainder theorem is a special case of factor theorem.
- Factor theorem is a special case of Remainder theorem.
- Factor theorem and Remainder theorem are two indepdent results
- None of the above

- When x
^{40 }+ 2 is divided by x^{4}+ 1, what is the remainder?- 1
- 2
- 3
- 4

- If the HCF of x
^{3}– 27 and x^{3}+ 4x^{2}+ 12x + k is quadratic polynomial, then what is the value of k?- 27
- 9
- 3
- – 3

- A number consists of two digits, whose sum is 10. If 18 is subtracted from the number, digits of the number are reversed. What is the product?
- 15
- 18
- 24
- 32

- What is the LCM of 3 (a
^{3}– b^{3}) and 11 (a^{4}– b^{4})?- 33(a
^{3 }– b^{3}) (a^{2}+ b^{2}) (a + b) - (a
^{3}– b^{3}) (a^{2}+ b^{2}) (a – b) - 33 (a – b) (a
^{2 }+ b^{2}– ab) (a^{3}– b^{3}) - 33 (a
^{3}– b^{3}) (a^{4}– b^{4})

- 33(a
- Students of a class are made to stand in rows. If one student is extra in a row, there would be two rows less. If one student is less is n a row, there would be three rows more. What is the number of students in the class?
- 65
- 55
- 60
- 50

- A railway ticket for a child costs half the full fare but the reservation charge is the same on half ticket as much as on full ticket. One reserved first class ticket for a journey between two stations is Rs. 362; one full and one half reserved first class tickets cost Rs. 554. What is reservations charge?
- 18
- 22
- 38
- 46

- Out of a group of swans 7/2 times the square root of the number are swimming in the pool while the two remaining are playing outside the pool. What is the total number of swans?
- 4
- 8
- 12
- 16

- If the ratio of x to y is 25 times the ratio of y to x, then what is the ratio of x to y?
- 1 : 5
- 5 : 1
- 25 : 1
- 1 : 25

- A milk vendor bought 28 L of milk at the cost of Rs. 8.50 per litre. After adding some water, he sold the mixture at the same price. If he gains 12.5%, how much water did he add?
- 5 L
- 5 L
- 5 L
- 5 L

- If m and n are two integers such that m = n
^{2 }-n, then (m^{2}– 2m) is always divisible by

- 9
- 16
- 24
- 48

- Which one is the largest among the following?
- 725
- 725
- 725
- 725

- 10% of the inhabitants of a certain city left that city. Later on 10% of the remaining inhabitants of that city again left the city. What is the remaining percentage of population of that city?
- 80%
- 4%
- 6%
- 81%

- If the rate of interest is 10% per annum and is compounded half yearly, the principal of Rs. 400 in 3/2 yr will amount to
- 463.00
- 463.05
- 463.15
- 463.20

- The number of workers in the employment guarantee scheme increased by 15 which resulted into an increase of 20%. What are the initial number of workers?
- 60
- 75
- 80
- 90

- Two men P and Q start from a place walking at 5 km at 6.5 km/h respectively. What is the time they will take to ?? 92 km apart if they walk in opposite directions?
- 2 h
- 4 h
- 6 h
- 8 h

- In an army camp ration is available for 100 soldier 10 days. After 2 days, 60 soldiers joined. Then for many more days will the remaining ration last?
- 7 days
- 6 days
- 5 days
- 4 days

- Two trains travel in the same direction at 50 km/h and 32 km/h respectively. A man in the slower train observes that 15 s elapse before the faster train completely passes him. What is the length of the faster train?
- 75 m
- 125 m
- 150 m
- 625/3 m

- A person walks a distance in 114 days, when he rests 9 h a day. How long will he take to walk twice the distance if he walks twice as fast and rests twice as long each day as before?
- 57 days
- 228 days
- 285 days
- 324 days

- If x : y = 1 : 3, y : z = 5: k, z : t = 2 : 5 and t : x + 3 :4, then what is the value of k?
- ½
- 1/3
- 2
- 3

- The number is √0.0001 is
- a rational number less than 0.01
- a rational number
- an irrational number
- neither a rational number nor an irrational number

- A person P started a business with a capital of Rs. 2525 and another person Q joined P after some months with a capital of Rs. 1200. Out of the total annual profit of Rs. 1644, P’s share was Rs. 1212. When did Q join as partners?
- After 2 months
- After 9 months
- After 4 months
- After 5 months

- The mess charges for 35 students for 24 days in Rs. 6300. In how many days will the mess charges be Rs. 3375 for 25 students?
- 12
- 15
- 18
- 21

- If a + b = 2m
^{2}, b + c = 6m, a + c = 2, where m is a real number and a ≤ b ≤ c, then which one of the following is correct?- 0 ≤ m ≤ 1/2
- – 1 ≤ m ≤ 0
- 1/3 ≤ m ≤ 1
- 1 < m ≤ 2

- What is the least number which when divided by 42, 72 and 84 leaves the remainders 25, 55 and 67 respectively?
- 521
- 512
- 504
- 487

- A trader sells two cycles at Rs. 1188 each and gains 10% on the first and loses 10% on the second. What is the profit or loss percent on the whole?
- 1% loss
- 1% gain
- No loss no gain
- 2% loss

- A person borrowed Rs. 7500 at 16% compound interest. How much does he have to pay at the end of 2 yr to clear the loan?
- 9900
- 10092
- 11000
- 11052

- P and Q can do a job in 2 days: Q and R can do it in 4 days; and P and R in 12/5 days. What is the number of days required for P alone to do the job?
- 5/2
- 3
- 14/5
- 6