DPP-1 to 4 Maths

NTSE-STAGE-I WORK SHOP DAILY PRACTICE PROBLEMS SESSION– 2011-12 Subject : Mathematics 1.

2.

Topic : Number System & Algebra

The sum of the digits of a number 10n – 1 is 3798. The value of n is : (A) 422 (B) 431 (C) 501

(B) 5 1

6.

1

(C) 7

(D) Infinitely many

1

If

(B) 1

2048 =

2x ,

2187 = 3 y and

(A) 1 5.

(D) 673

If 2x = 3y = 6–z, then  x  y  z  is equal to :   (A) 0

4.

Class : VIII

If 9  (n  2)2 is a real number, then the number of integral values of n is : (A) 3

3.

DPP No. 01

(C) 3125 =

(B) 9

3 2

(D) –

1 2

5 z then value of x + y – z is :

(C) 13

(D) 23

Factors of x2 – y2 – z2 – 2yz are : (A) (x + y + z) and (x – y – z) (C) (x – y + z) and (x + y + z)

(B) (x + y – z) and (x – y – z) (D) (x + y – z) and (x + y + z)

If 4x – 5z = 16 and xz = 12, 64x3 – 125z3 = (A) 14512 (B) 15676

(C) 25833

(D) 15616

7.

Factors of x2 + ax + b are (x – 7) and (x + 9) then the value of a and b is : (A) a = 2, b = – 63 (B) a = –2, b = 63 (C) a = –2, b = – 63 (D) a = 2, b = 63

8.

In a piggy bank the number of 25 paise coins are five times the number of 50 paise coins. If there are 120 coins, find the amount in the bank ? (A) Rs. 25 (B) Rs. 10 (C) Rs. 35 (D) Rs. 40

9.

When expanded, the number of zeros in 100010 is : (A) 13 (B) 30 (C) 4

10.

The smallest number exactly divisible by 1 (A) 15/2

11.

(A)

12.

1 1 5

1 32 2

(A) 193

(B)

,b=

(C) 15

(D) None of the above

lies between the numbers :

1 1 and 3 2

If a =

1 1 and 1 is 4 2

(B) 15/4

The number

(D) 10

1 32 2

1 1 and 2 2

(C)

1 1 and 4 3

(D)

1 1 and 5 4

then the value of a3 + b3 is :

(B) 194

(C) 198

(D) 196

13.

14.

If n = 1 + x where x is the product of four consecutive positive integers, then which of the following is/are true ? a. n is odd b. n is prime c. n is a perfect square (A) a and c only (B) a and b only (C) a only (D) None of these If u, v and w are the digits of decimal system, then the rational number represented by 0.uwuvuvuvuv.......is (A) (100 uw + 99 uv)/99 (C) (99uw + uv)/9900

(B) (99uw + uv)/980 (D) (9uw + 99uv)/900

15.

The number of 2-digit numbers, greater than 10, divisible by 2 and 5 but not by 4 or 25 is : (A) 2 (B) 3 (C) 5 (D) 12

16.

113 + 213 + 313 + .....+ 6013 is divisible by : (A) 61 (B) 63

(B) 65

(D) 60

17.

If the difference of (1025 – 7) and (1024 + x) is divisible by 3 then x is equal to (A) 3 (B) 2 (C) 6 (D) 1

18.

What is the unit’s digit of 1781 + 2781 + 3781 + ........ + 9781 ? (A) 1 (B) 3 (C) 5

(D) 7

The number of prime factors of (3 × 5)12 (2 × 7)10 (10)25 is : (A) 47 (B) 60 (C) 72

(D) None of these

One of the factors of the expression (2a + 5b)3 + (2a – 5b)3 would be – (A) 4a (B) 10b (C) 2a + 5b

(D) 2a – 5b

19. 20. 21.

22.

The LCM of (16 – x2) and (x2 + x– 6) is : (A) (x – 3) (x + 3) (4 – x2) (C) 4(4 – x2) (x + 3)

(B) (4 – x2) (x – 3) (D) None of these

GCD of (x2 – 4) and (x2 + x – 6) is : (A) x + 2 (B) x – 2

(C) x2 – 2

(D) (x2 – 4)

23.

Find the HCF and LCM of the polynomials (x2 – 5x + 6) and (x2 – 7x + 10) : (A) (x – 2), (x – 2) (x – 3) (x – 5) (B) (x – 2), (x – 2) (x – 3) (C) (x – 3), (x – 2) (x – 3) (x – 5) (D) (x – 2), (x – 2) (x – 3) (x – 5)2

24.

If 3 is a prime number is – 3 a prime number : (A) Yes (B) No

(C) Can’t say

(D) None of these

What is the unit digit of (52)97 × (43)72 : (A) 2 (B) 6

(C) 8

(D) 4

25. 26.

Smallest two digit number which is a perfect square and perfect cube both : (A) 16 (B) 32 (C) 64 (D) 81

27.

What is the square root of 9 + 4 5 : (A) 2 +

28.

29.

5

(B) 4 +

5

(C) 5 + 2

(D) 7 +

2

A hundred and twenty digit number is formed by writing the first x natural numbers in front of each other as 1 2 3 4 5 6 7 8 9 10 11 12.......... Find the remainder when this number is divided by 4. (A) 0 (B) 1 (C) 2 (D) 3

x

y  xy is true only when :

(A) x > 0, y > 0

(B) x > 0, y < 0

(C) x < 0, y > 0

(D) All of these

30.

165 + 215 is divisible by : (A) 31 (B) 27

(C) 13

(D) 33

31.

xy is a number that is divided by ab where xy < ab and gives a result 0. xy xy xy.......then ab equals : (A) 11 (B) 33 (C) 99 (D) 66

32.

The product of a natural number and the number written by the same digits in the reverse order is 2430. Find the numbers : (A) 54 and 45 (B) 56 and 65 (C) 53 and 35 (D) 85 and 58

33.

What is the unit digit of (173)45 × (152)77 × (777)999 : (A) 2 (B) 4 (C) 8

(D) 6

Which of these is greater 200300 or 300200 or 400150 : (A) 200300 (B) 300200 (C) 400150

(D) Can’t say

34. 35.

How many pairs of natural numbers are there the difference of whose squares is 45. (A) 1 (B) 2 (C) 3 (D) 4

36.

Find the least value of a + b, if 23a57b6 is divisible by 33: (A) 4 (B) 1 (C) 10

(D) 6

37.

4 bells toll together at 9 : 00 AM. They toll after 7, 8, 11, and 12 seconds respectively. How many times will they toll together again in the next 3 hr : (A) 3 (B) 4 (C) 5 (D) 6

38.

Find the value of a if pqa = (2p + q)2 – (2p – q)2 : (A) 6 (B) 7 (C) 8

39. 40.

41.

2

If a – 2b = 15 and ab = 11 find the value of a + 4b : (A) 269 (B) 267 (C) 259

(D) 279

Simplify : (y – 1) (y + 1) (y2 + 1) (y4 + 1) (A) y8 – 1 (B) y6 – 1

(D) None of these

Find the value of 49x2 – 56xy + 16y2 when x = (A) 2

42.

(B) 3

Factorize : p2 + pq +

p q  (A)    1 2 2  43.

(D) 10

2

2

(C) y7 – 1

1 1 and y = : 7 2 (C) 4

(D) 1

q2 + 1 + 2p + q 4

p  (B)   q  1 2  

Find the value of 473 + 293 – 763 : (A) 0 (B) 301764

2

q   (C)  p   1 2  

(C) 310764

2

(D) None of these

(D) – 310764

44.

If p + q + r = 1 and pq + qr + pr = – 1 and pqr = – 1, find the value of p3 + q3 + r3 : (A) 0 (B) 1 (C) 2 (D) – 1

45.

Find the value of 27x3 + 8y3 if 3x + 2y = 20 and xy = (A) 4770

(B) 7440

14 : 9

(C) 7470

(D) 4740

NTSE-STAGE-I WORK SHOP DAILY PRACTICE PROBLEMS SESSION– 2011-12 Subject : Mathematics 1.

Topic : Geometry

DPP No. 02

Class : VIII

What is the value of  d in the given figure ? (A) 107.5º

A aa d D

(B) 120º (C) 200º

B

b b

55º

C

(D) 117.5º 2.

Two sides of a triangle are 20 m and 40 m, find the maximum length of the third side, if angles are in the ratio of 1 : 2 : 3 (A) 20.5 m

3.

(B) 20

5m

(C) 25 m

(D) 22 m

In given figure if AB || DF, AD || FG, BAC = 65º, ACB = 55º then FGH is : (A) 120º (B) 125º (C) 115º (D) 140º

4.

ABC is a right angled triangle, where B = 90º. CD and AE are medians. If AE = x and CD = y then, correct statement is : A (A) x2 + y2 = AC2 (B) x2 + y2 = 2AC2 3 (C) x + y = AC2 2 2

5

(D) x2 + y2 = 4 AC2 5.

D

x

2

y

B

E

C

In the adjoining figure ABCD is a parallelogram, then the measure of x is : (A) 45º (B) 60º (C) 90º (D) 135º

6.

In fig. ABCD is a parallelogram. P and Q are mid points of the sides AB and CD, respectively. Then PRQS is : (A) parallelogram (B) trapezium (C) rectangle (D) none of these

7.

In the diagram two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other. Find the length of the common chord. (A) 2 3 cm (B) 4 3 cm (C) 4 2 cm (D) 8 cm

8.

Three wires of length 1, 2, 3 form a triangle surmounted by another circular wire, If 3 is the diameter and 3 = 21, then the angle between 1 and 3 will be : (A) 30o (B) 60o (C) 45o (D) 90o

9.

ABCD is a rhombus with  ABC = 56º, then the  ACD will be – (A) 56º (B) 62º (C) 124º

10.

(D) 34º

PQ is a chord of a circle. The tangent XR at X on the circle cuts PQ produced at R. If XR = 12 cm, PQ = x cm, QR = x – 2 cm, then x in cm is : (A) 6

X 12

(B) 7

x– 2

x P

Q

R

(C) 10 (D) 14

11.

How many tangents can be drawn, if two circle contact to each other externally (A) zero (B) two (C) four (D) three

12.

In the adjoining figure, chord ED is parallel to the diameter AC of the circle with centre ‘O’. If CBE = 65º then the measured of DEC is equal to.

(A) 35º 13.

14.

(B) 55º

(C) 37.5º

(D) 25º

Two circles of radii 20 cm and 37 cm intersect in A and B. If O1 and O2 are their centres and AB = 24 cm, then the distance O1O2 is equal to (A) 44 cm (B) 51 cm (C) 40 ½ cm (D) 45 cm 9 If one of the interior angles of a regular polygon is to be equal to   times of one of the interior angles 8 of a regular hexagon, then the interior sides of the polygon is : (A) 7 (B) 8 (C) 4 (D) 5

15.

Suppose the triangle ABC has an obtuse angle at C and let D be the midpoint of side AC. Suppose E is on BC such that the segment DE is parallel to AB. Consider the following three statements. (i) E is the midpoint of BC (ii) The length of DE is half the length of AB (iii) DE bisects the altitude from C to AB (A) only (i) is true (B) only (i) and (ii) are true (C) only (i) and (iii) are true (D) all three are true.

16.

The straight lines AB and CD intersect one another at the point O. If  AOC +  COB +  BOD = 274°, then  AOD = (A) 86° (B) 90° (C) 94° (D) 137°

17.

There are four lines in a plane no two of which are parallel. The maximum number of points in which they can intersect is : (A) 4 (B) 5 (C) 6 (D) 7 Each interior angle of a regular polygon is 135°. The number of sides of the polygon is : (A) 6 (B) 8 (C) 5 (D) 9

19.

20. 21.

A polygon has 27 diagonals. The number of sides of the polygon is : (A) 9 (B) 10 (C) 11

(A) 24° (B) 22° (C) 20° (D) 10°

B

5y

4y E

9y D

C

22.

(D) 12

How many degrees are there in an angle which equals one-fifth of its supplement? (A) 15° (B) 30° (C) 75° (D) 150° From the adjoining figure the value of y is : F A

O

18.

In fig. OE is the bisector of AOB and OF is the angle bisector of AOC, then the value of EOF is : F

A E

O

C

23.

B

(A) 90° (B) 180° (C) 270° (D) None of these In figure, AB || CD and EF || DQ. Determine PDQ, AED and DEF.

Q F P o

34 C

D 78o

A

(A) 68°, 68°, 34°

(B) 78°, 34°, 68°

E

B

(C) 68°, 34°, 68°

(D) 102°, 34°, 68°

24.

The sum of the two angles in a triangle is 95° and their difference is 25°. Then the angles of the triangle is (A) 75°, 50°, 55° (B) 85°, 65°, 30° (C) 50°, 45°, 85° (D) 60°, 35°, 85°

25.

In the figure find x if AB || CD|| EF . (A) 45° (C) 60°

26.

A

(B) 55° (D) 70°

B x° 25° E

F

150°

C

What value of x will make AOB a straight line ?

D

C B

2x + 30°

2x – 50°

(A) 30° 27.

29. 30.

31.

O

A

(C) 49°

(D) None of these

In figure, AP and BQ are bisectors of XAY and UBA respectively. Find the value of x for which l || m :

(A) 10 28.

(B) 50°

(B) 20

(C)

20 3

(D)

10 3

In a rectangular close box the number of pairs of parallel planes is : (A) 3 (B) 5 (C) 2 (D) 6 The sum of the interior angles of a regular polygon is twice the sum of its exterior angles. The polygon is : (A) An octagon (B) A nonagon (C) A decagon (D) A hexagon In the given figure AB || CD,  ABE = 130°,  BED = 20° and  EDC = y°, then the value of y is :

(A) 150° (B) 110° (C) 170° (D) 140° n coplanar straight lines meet at a point. The angles between consecutive lines are x°, 2x°, , nx°. The value of n in order that the minimum angle be 24°, is : (A) 3 (B) 4 (C) 5 (D) 6

32.

33.

34. 35.

36.

37.

38.

39.

ABCDE is a regular pentagon. Alternate vertices are joined to make a five-pointed star ACEBDA. The sum of the 5 vertical angles of this star is : (A) 1 right angle (B) 2 right angles (C) 270° (D) 300° In the pentagon, sum of the angles marked is :

(A) 360° (B) 540° (C) 720° (D) 1260° For a triangle ABC, the true statement is : (A) AC2 = AB2 + BC2 (B) AC = AB + BC (C) AC > AB + BC (D) AC < AB + BC In a ABC, the sides AB and AC have been produced to D and E. Bisectors of  CBD and  BCE meet at O. If  A = 64°, then  BOC = (A) 52° (B) 58° (C) 26° (D) 112° The distance between the tops of two trees 20 m and 28 m high is 17 m. The horizontal distance between the trees is : (A) 11 m (B) 31 m (C) 15 m (D) 9 m In an equilateral triangle ABC, if AD  BC, then : (A) 2AB2 = 3 AD2 (B) 4 AB2 = 3 AD2 (C) 3 AB2 = 4 AD2

(D) 3 AB2 = 2 AD2

The hypotenuse of a right angled triangle is 25 cm. The other two sides are such that one is 5 cm longer than the other. Their lengths (in cm) are : (A) 10, 15 (B) 20, 25 (C) 15, 20 (D) 25, 30 From the adjoining figure the value of x is : (A) 60 (B) 75 (C) 90 (D) 120

40.

In the adjoining figure AM  BC and AN is the bisector of BAC. If B = 70° and C = 35° then MAN is : (A) 17.5° (B) 27.5° (C) 37.5° (D) 47.5°

41.

Two sides of a triangle are 7 and 10 units. Which of the following length can be the length of the third side? (A) 19 cm (B) 17 cm (C) 13 cm (D) 3 cm

42.

In the adjoining figure, BD and CD are angle bisectors of  ABC and  ACE respectively. Then, which of the following is true ?

(A) D = 43.

1 A 2

x  y 2

(D) All of the above

The angles ABC and BDC are right angles, If AD = 9 cm and DC = 16 cm and AB = 15 cm, then the length of BD is :

(A) 12 cm 44.

(B) x +y =A +D (C) D =

(B) 16 cm

(C) 15 cm

(D) 25 cm

In figure, if QT  PR, TQR = 40° and SPR = 30°, then (x, y) = : P

T y

x R S (C) (50°, 70°)

Q (A) (50°, 80°) 45.

(B) (80°, 50°)

(D) (70°, 50°)

As shown in the figure, AB = AC. D and E are points on AC and AB respectively such that AD = ED = EC = BC. Then BEC : EDC =

A

D E

B (A) 3 : 2

(B) 1 : 3

C (C) 2 : 3

(D) 3 : 1

46.

In the given figure,  ABC = 90° and BM is a median, AB = 8 cm and BC = 6 cm. Then length of BM is equal to :

(A) 3 cm

(B) 4 cm

(C) 5 cm

(D) 7 cm

47.

A man goes to a garden and runs in the following manner. From the starting point, he goes west 25 m, then due north 60 m, then due east 80 m and finally due south 12 m. The distance between the starting point and the finishing point is : (A) 177 m (B) 103 m (C) 83 m (D) 73 m

48.

If ABC is a triangle right angled at B and M,N are the mid-points of AB and BC, then 4 (AN2 + CM2) = (A) 4 AC2

49.

(B) 5 AC2

1 B 2

1 (C) 90   C 2 (D) None of these

1 A 2

(C) 180 –

O

1 2

3 4

B

C

1 A 2

(B) 90 

1 A 2

(D) 180 

1 A 2

If a right angled triangle is with sides a, b and hypotenuse c, and altitude drawn on the hypotenuse is h, then. (A) h2 = ab

52.

(D) 6 AC2

In the adjoining figure BO, CO are angle bisectors of external angles of ABC, Then BOC is : (A) 90 –

51.

5 AC2 4

In the figure, the bisectors of B and C meet at O. Then BOC is : A 1 (A) 90   A 2 (B) 90 

50.

(C)

(B)

1 h

2



1 a

2



1 b2

(C) h2 = a2 + b2

In figure LM | | AB, AL = x – 3, AC = 2x, BM = x – 2, BC = 2x + 3, then x = : (A) 9 (B) 6 (C) 3 (D) 12

(D) h = a + b

53.

If PQRS is a square and SRT is an equilateral triangle then TQR =

(A) 5°

(B)10°

(C) 15°

(D) 20°

54.

The number of triangles with any three of the lengths 1, 4, 6 and 8 cm as sides is : (A) 4 (B) 1 (C) 2 (D) 0

55.

The figure formed by joining the consecutive mid-points of any rhombus is always : (A) A square (B) A rhombus (C) A rectangle (D) None of these

56.

AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, find the radius of the circle. (A) 16 cm (B) 25 cm (C) 9 cm (D) 13 cm

57.

Two circles of radii 10 cm and 8 cm intersect and the length of the common chord is 12 cm. Find the distance between their centres. (A) 13 cm (B) 13.29 cm (C) 16.29 cm (D) 16 cm

58.

A circle is divided into three parts in the ratio of 3 : 4 : 5. Find the angles of the triangle formed by joining the point of division : (A) 45°, 60°, 75° (B) 60°, 60°, 60° (C) 45°, 45°, 90° (D) None of these

59.

Find the value of X.

60.

(A) 78°

(B) 102°

(C) 90°

(D) 42°

Find the value of y. (A) 72°

(B) 102°

(C) 45°

(D) 78°

NTSE-STAGE-I WORK SHOP DAILY PRACTICE PROBLEMS SESSION– 2011-12 Subject : Mathematics

Topic : Mensuration & Statistics

DPP No. 03

Class : VIII

1.

The area of a square and a rectangle is same. If the side of the square is 40cm. and breadth of the rectangle is 25 cm. The length of the rectangle will be(A) 54 (B) 64 (C) 46 (D) 45

2.

A dice is thrown. The outcomes of prime number is (A) 4 (B) 3 (C) 2

3.

(D) 1

In the given pie chart, the marks obtained by a student in Hindi, English, Maths, Social Science and Science is shown. If the student scores total 540 marks then the marks obtained in Maths exceeded marks in Hindi by -

Ma

65º 90º

80º

Science

ths

Socia l

55º 70º En g

(A) 15 4.

di Hin

(C) 25

(D) 30

A cuboid has sides 5cm, 2cm, 5cm. The required number of cuboids to make it a cube is(A) 15

5.

(B) 20

lis h

(B) 20

(C) 25

(D) 30

A tank is filled by a tap at the rate of 60 litre per minute. If the volume of the tank is 108m3, the total time to fill the tank completely is. (A) 20hrs.

6.

8. 9.

10.

11.

(C) 30hrs.

(D) 35 hrs.

The length of a rectangle is 40cm. If the length of the diagonal is 41 cm, the perimeter of rectangle is(A) 96Cm

7.

(B) 25 hrs.

(B) 98Cm

(C) 100Cm

(D) 102Cm

In an examination marks obtained in mathematics by fifteen students are follows :19, 25, 23, 20, 09, 20,15, 10, 05, 16, 25, 20, 24,12, 20 Median of obtained marks is(A)16 (B)19 (C) 20 (D)10 What is the mode of the following data 1, 1,2, 3, 4, 3, 4, 2, 1, 2, 2, 4, (A) 1 (B) 2 (C) 3 (D) 4 Which of the following triplet is pythagorean : (A) (2, 3, 4) (B) (1, 2, 3) (C) (3, 4, 5) (D) (4, 5, 6) The number of lines of symmetry in a parallelogram is : (A) 0 (B) 4 (C) 6

(D) 8

Volume of the greatest cone which can be cut from the cube of side 3 cm, is– (A) 9 cm3

(B)

9  cm3 4

(C) 3 cm3

(D)

9  cm3 2

12.

A box tied by a ribbon, as shown in the figure, is to klbe presented as a gift.After allowing an additional length of 10 cm. for the knot, length of the ribbon required is–

(A)140 cm 13.

14.

15.

(B) 150 cm

(C) 70 cm

If the length of a cuboid is decreased by 50% then its volume is decreased by–

1 (A) 33 % (B) 75% (C) 50% (D) None of these 2 If V and C stand respectively for the volume and curved surface area of a cylinder with radius r of base then– (A) VC = r (B) 2V = Cr (C) 2C = Vr (D) 2r = VC If the length of a rectangle is increased by 10% and area is unchanged then the corresponding breadth must be decreased by– 1 % (B) 10% (C) 11% 11 If radius of circle is 2m then the area of shaded portion will be

1 (D) 11 % 9

(A) (4 – ) m2

(D) (4 – 4) m2

(A) 9 16.

(D) 80 cm

(B) 2(4 – ) m2

(C) 4(4 – ) m2

17.

In a scalene triangle ABC, AD BE and CF are medians which intersect at point G, then G is called (A) Centroid (B) Incentre (C) Otho centre (D) None of these

18.

How many cubes of edge 5cm. can be ..... off form a cube of edge 20cm. (A) 4 (B) 16 (C) 64 (D) 100

19.

The lateral (Cuved) surface are of a cone is 220 square cm and its slant height 10 cm. Its total surface area is (A) 119  cm2

20.

(B) 490  cm2

(C) 269  cm2

(D) None of these

(C) 54 m2

(D) None of these

Area of triangle RST is :

T 12 m Q

3m R

4m

S

P (A) 6 m2

(B) 72 m2

21.

Surabhi scored an 88 on her last test. Her scores before the last test were 95, 89, 90 and 93. What score must Surabhi make on the next test in order to receive a mean score of 90 ? (A) 85 (B) 88 (C) 90 (D) 91

22.

The number of pairs of parallel planes that a regular hexagonal prism posses is (A) 3 (B) 4 (C) 5 (D) 6

23.

In ABC, AB = 20, AC = 14 and BC = 12. If sides AB and AC are doubled while BC remains the same. then the area of the triangle : (A) will be double (B) will be eight times (C) will be four times (D) will be zero

24.

If the area of three adjacet faces of a cuboid is a, b and c. Then find its volume. C A

(A) abc

(B)

B

(C) a2 b2 c2

abc

(D) a + b + c

25.

The perimeter of the base of a cylinder is as same as the perimeter of a square whose one side is 11 cm. If the volume is 98, the height of the cylinder will be. (A) 2 cm (B) 3 cm (C) 1 cm (D) 4 cm

26.

When two cube of side 12 cm are joined end to end to form a cuboid then the total surface area of cuboid is. (A) 1740 cm2 (B) 1640 cm2 (C) 1540 cm2 (D) 1440 cm2

27.

In the figure, ABCD is a parallelogram and PBQR is a rectangle R

Q C

D

A

P

B

If AP : PB = 1 : 2 = PD : DR, what is the ratio of the area of ABCD to the area of PBQR ? (A) 1 : 2 28.

(B) 2 : 1

(C) 1 : 1

(D) 2 : 3

A square board side 10 centimeters, standing vertically, is tilted to the left so that the bottom-right corner is raised 6 centimeters from the ground

6 cm

By what distance is the top-left corner lowered from its original position ? (A) 1 cm

(B) 2 cm

(C) 3 cm

(D) 0.5 cm

29.

From one corner of a square of side 8 centimeters, a small square of side 1 centimeter is cut off. What is the perimeter of the remaining figure ? (A) 28 cm (B) 30 cm (C) 32 cm (D) 34 cm

30.

In the figure, ABCD is a square, HGF is a semicircle and HE, FE are quarter-circles. G

D

C F

H

A

B

E 2cm

What is the area of the shaded part ? (A) 4 sq. cm 31.

(B) 2 sq. cm

(C)

1  sq. cm 2

(D)  sq. cm

In the figure, O is the centre of the circle and OABC is rectangle : C

B

A O 3cm 2cm

What is the length of AC ? (A) 4 cm (B) 4.5 cm 32.

(C) 5 cm

In the figure below, ABCD is a rectangle and E is the midpoint of AB :

D

A

33.

E

B

(B) 5000

(C) 5020

(D) 5040

The rainfall (in centimetre) recorded in the month of June to December are 14, I5, 25, 20, 30,42 and 8.Then the average rainfall is: (A) 21

35.

C

If the area of the triangle EBC is 8 sq. cm, then what is the area of the trapezium AECD ? (A) 48 sq. cm (B) 32 sq. cm (C) 24 sq. cm (D) 16 sq. cm A wheel has a radius of 35 cm. How many revolution will it make to cover 11 km. (A) 4990

34.

(D) 5.5 cm

(B) 22

(C) 24

If the diagonals of a rhombus are 20 em. and 25 cm, what is its area ? (A) 100 cm2 (B) 150 cm2 (C) 200 cm2

(D) 26 (D) 250 cm2

36.

The area of a trapezium is 100 m2. If the sum of its parallel sides is 50m, then its height is equal to : (A) 4 m (B) 6 m (C) 8 m (D) 10 m

37.

If the radius of a sphere is halved then the ratio of their volumes is : (A) 1 : 8 (B) 8 : 1 (C) 8 : 3

(D) 3 : 8

38.

Find the arithmetic mean from the following table : x 4 5 6 7 8 f (Frequency) 3 2 3 5 2 (A) 5 (B) 6 (C) 7

21 1 (D) 8

39.

The average of 9 readings is 9 that of first 5 being 10 and of last 5 being 8. What is the fifth reading ? (A) 10 (B) 9 (C) 8 (D) 7

40.

The mean of 20 items of a data is 5 and if each item is multiplied by 3, then the mean will be : (A) 5 (B) 10 (C) 15 (D) 20

41.

The average age of two brothers is 13 It is increased by 11 years when their mother's age is also included. The age of the mother is : (A) 45 years (B) 46 years (C) 47 years (D) 48 years

42.

If a sphere and a cube have the same surface area then the ratio of diameter of sphere to edge of cube is : (A)

6 :

(B)



 :

6

(C) 2 : 1

(D) 1 : 2

43.

Area of square ABCD is 169 sq. em. E, F, G, H are mid points of AB, BC,CD and DA respectively. Area of quadrilateral EFGH is : (A) 84 sq. cm. (B) 84·5 sq. cm. (C) 85 sq. cm. (D) 85.5 sq. cm.

44.

Length of one diagonal of· a rhombus is10 cm and its area is 120 sq. cm. Length of each side of the rhombus is side of the rhombus is : (A) 12 cm. (B) 13 cm. (C) 14 cm. (D) 15 cm.

A 45.

D

20 cm

28 cm

B1 7

cm C

The area of the trapezium ABCD is : (A) 300 cm2 (B) 360 cm2 (C) 480 cm2 (D) None of these 46-50. Study the following table carafully and answer the questions given below. Export of Tea and coffee (in million kgs) Year Tea Coffee 1993-94 150 137 1994-95 147 138 1995-96 167 170 1996-97 169 180 1997-98 210 525 46. The approximate percentage by whih the export of coffee increased from 1996-97 to 1997-98 is : (A) 185 (B) 190 (C) 195 (D) 205 47.

The ratio of the export of coffee in 1994-95 to that in 1996-97 is : (A) 69 : 85 (B) 30 : 23 (C) 85 : 69

(D) 23 : 30

48.

The percentage increase in the export of tea in 1997-98 from that in 1993-94 is : (A) 20 (B) 35 (C) 40 (D) 90

49.

The percentage by which the export of tea fell in 1994-95 from that in the previous year is : (A) 1 (B) 2 (C) 3 (D) 4

50.

The ratio between export of coffee to tea in 1997-98 is : (A) 5 : 14 (B) 2 : 5 (C) 5 : 2

(D) 14 : 5

NTSE-STAGE-I WORK SHOP DAILY PRACTICE PROBLEMS SESSION– 2011-12 Subject : Mathematics

Topic : Commercial Mathematics

DPP No. 04

Class : VIII

1.

At an election where there are two candidates only, the candidate who gets 43% of the votes is rejected by a majority of 420 votes. Find the total number of votes recorded : (A) 3000 (B) 600 (C) 1200 (D) 2400

2.

Two numbers are respectively 20% and 35% more than a third. What percentage is the first of the second : (A)

200 % 3

(B)

400 % 9

(C)

800 % 9

(D)

200 % 9

3.

The population of town increases by 12% during first year and decreases by 10% during second year. If the present population is 50400, what it was 2 years ago : (A) 40000 (B) 50000 (C) 42000 (D) 40400

4.

If the price of a commodity be raised by 16 2 % , find how much percent must a householder reduce his 3 consumption of that commodity, so as not to increase his expenditure :

1 (A) 14 % 7

6 (B) 13 % 7

2 (C) 14 % 7

2 (D) 16 % 3

5.

The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was Rs 22. Find the amount of the bill : (A) Rs 1100 (B) Rs 200 (C) Rs 2200 (D) Data inadequate

6.

The number of seats in a cinema hall is increased by 25%. The price on a ticket is also increased by 20%. What is the effect on the revenue collected : (A) 45% increase (B) 49% increase (C) 50% increase (D) 52% increase

7.

A candidate scores 35% and fails by 40 marks, while another candidate who scores 60% marks, gets 35 marks more that the minimum required marks to pass the examination. Find the maximum marks for the examination: (A) 300 (B) 200 (C) 350 (D) 450

8.

What quantity of water should be added to reduce 6 litres of 50% acidic liquid to 20% acidic liquid : (A) 8 litres (B) 9 litres (C) 12 litres (D) 9.5 litres

9.

A reduction of 24% in the price of tea enables a person to buy 3 kg more for Rs 75. Find the original price of tea per kg : (A) Rs 6

16 19

(B) Rs 7

17 19

(C) Rs 6

(D) Rs 6

17 19

10.

The average height of 30 girls out of a class of 40 is 160 cm and that of the remaining girls is 156 cm. The average height of the whole class is : (A) 158 cm (B) 158.5 cm (C) 159 cm (D) 159.5 cm

11.

The average of 15 numbers is 50. The average of first 8 of these numbers is 52 and the last 8 of these numbers is 49. What is the 8th number. (A) 58 (B) 50 (C) 55 (D) 56

12.

A cricketer has completed 31 innings and his average is 18 runs. How many runs must he make in his next innings so as to raise his average to 22 : (A) 124 (B) 146 (C) 136 (D) 142

13.

5 years ago, the average of Ram and Shyam’s age was 20 years. Now the average age of Ram, Shyam and Mohan is 30 years. What will be Mohan’s age 10 years hence : (A) 45 years (B) 50 years (C) 49 years (D) 60 years

14.

A sum of money is to be divided among A, B and C in the ratio 2 : 3 : 7. If the total share of A and B together is Rs 1500 less than C, what is A’s share in it : (A) Rs 1000 (B) Rs 1500 (C) Rs 2000 (D) Data inadequate

15.

A horse is sold for Rs 1230 at a loss of 18%. What would have been gain or loss percent if it had been sold for Rs 1600 : 2 (A) 6 % loss 3

16.

2 (B) 6 % gain 3

1 (C) 6 % gain 3

(D) None of these

A customer asks for the production of x number of goods. The company produces y number of goods daily out of which z% are unfit for sale. The order will be completed in : (A)

100 x days y z – 1

(B)

x days 100 y z – 1

(C)

100 yz days x

(D)

100x days y(100 – z)

17.

The length and breadth of a square are increased by 30% and 20% respectively. The area of the rectangle so formed exceeds the area of the square by (A) 20% (B) 36% (C) 50% (D) 56%

18.

A man bought an article and sold it at a gain of 10%. If he had bought it at 20% less and sold it for Rs. 10 more, he would have made a profit of 40%. Find the C.P. of the article? (A) Rs. 500 (B) Rs. 600 (C) Rs. 400 (D) Rs. 550

19.

Some toffees are bought at the rate of 11 for Rs. 10 and the same number at the rate of 9 for Rs. 10. If the whole lot is sold at one rupee per toffee, find the gain or loss percent on the whole transaction. (A) Gain 2% (B) Gain 1% (C) Loss 2% (D) Loss 1%

20.

Jyoti and Meena run a ready-made garment shop. They mark the garments at such a price that even after allowing a discount of 12.5%, they make a profit of 10%. Find the marked price of a suit which costs them Rs. 1470. (A) Rs. 1848 (B) Rs. 1617 (C) Rs. 1798 (D) Rs. 1948

21.

Samir bought a shirt for Rs 336, including 12% sales tax and a necktie for Rs 110 including 10% sales tax. Find the printed price of the shirt and necktie together . (A) Rs. 450 (B) Rs. 600 (C) Rs. 400 (D) Rs. 500 1 4 Which is greatest in 33 % , and .35 ? 3 15

22.

1 (A) 33 % 3

23.

(B)

4 15

(C) 0.35

(D) all are equal

Three items are purchased at Rs. 450 each. One of them is sold at a loss of 10%. At what price should the other two be sold so as to gain 20% on the whole transaction? What is the gain % on these two items? (A) 40.5% (B) 31.5% (C) 35% (D) 45%

24.

2 The difference in simple interest and compound interest on a certain sum of money at 6 % per annum 3 for 3 years is Rs. 46. Determine the sum. (A) Rs 3375 (B) Rs. 3125 (C) Rs. 3525 (D) Rs. 3275

25.

Find the difference between the compound interest and simple interest, on a sum of Rs. 50,000 at 10% per annum for 2 years. (A) Rs. 400 (B) Rs. 450 (C) Rs. 600 (D) Rs 500

26.

In a mixture of 625 litres, milk and water are in the ratio of 13 : 12. What is the quantity of water in the mixture: (A) 300 (B) 180 (C) 350 (D) 325

27.

There is a sufficient food for 150 men for 15 days. After 10 days, 75 men leave the place. For how many days will the rest of the food last for the rest of the men : (A) 10 days (B) 8 days (C) 5 days (D) 15 days

28.

A can do a piece of work in 12 days. B is 60% more efficient than A. The number of days, it takes B to do the same piece of work, is : (A) 7

29.

1 days 2

(B) 6

1 days 4

(C) 8 days

(D) 6 days

xy (C) x  y

xy (D) x  y

The third proportional to x2 – y2 and x – y is : (A) x + y

(B) x – y

30.

A student walks from his house at 5 kmph and reaches his school 10 minutes late. If his speed had been 6 kmph he would have reached 15 minutes early. The distance of his school from his house is : (A) 2.5 km (B) 12.5 km (C) 5.5 km (D) 3.6 km

31.

Two trains start at the same time from Aligarh and Delhi and proceed towards each other at 36 kmph and 42 kmph respectively. When they meet, it is found that one train has travelled 48 km more than the other. The distance between the two stations (in km) is : (A) 624 (B) 636 (C) 544 (D) 460

32.

Renu rides at the rate of 10 km per hour but stops for 10 minutes to take rest at the end of every 15 km. How many hours will she take to cover 100 km. : (A) 10

(B) 11

(C) 12

(D) 11

1 6

33.

If a train 110 m long passes a telegraph pole in 3 seconds, then the time taken (in seconds) by it to cross a railway platform 165 m long, is : (A) 3 (B) 4 (C) 5 (D) 7.5

34.

A motor boat takes 2 hours to travel a distance of 9 km down the current and it takes 6 hours to travel the same distance against the current. The speed of the boat in still water and that of the current (in km/hr) respectively are : (A) 3, 1.5 (B) 3, 2 (C) 3.5,2.5 (D) 3, 1

35.

A and B can do a piece of work in 18 days; B and C in 24 days; C and A in 36 days. In how many days can they do it all working together ? (A) 12 (B) 13 (C) 16 (D) 26

36.

If 1 man or 2 women or 3 boys can do a piece of work in 44 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in : (A) 21 days (B) 24 days (C) 26 days (D) 33 days

37.

A and B working separately can do piece of work in 9 and 12 days respectively. If they work for a day alternately, beginning with A, in how many days, the work will be completed? (A) 10

1 days 2

(B) 10

1 days 4

(C) 10

2 days 3

(D) 10

1 days 3

38.

4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women finish it ? (A) 24 days (B) 32 days (C) 36 days (D) 40 days

39.

If

a 4 x 7  and  then 2ax – 3by = : b 3 y 5 ax  by (A) 116 : 31 (B) 19 : 37

(C) 11 : 43

(D) 18 : 35

40.

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train (in metres) is (A) 45 (B) 54 (C) 50 (D) 72

41.

A quantity x varies inversely as the square of y. Given that x = 4 when y = 3, the value of x when y = 6 is (A) 1 (B) 2 (C) 3 (D) 4

42.

A bag contains rupee, 50 paise and 25 paise coins in the ratio 5 : 7 : 9. If the total amount in the bag is Rs 430, find the numbers of coins of each kind : (A) 200, 280, 360 (B) 280, 200, 360 (C) 360, 280, 200 (D) 360, 200, 280

43.

10 men can cut 15 trees in 2 hours. If 2 men leave the job, how many trees will be cut in 3 hours : (A) 15 trees (B) 20 trees (C) 16 trees (D) 18 trees

44.

A, B and C can do a piece of work in 18, 27 and 12 days respectively. They work at it together, A stops the work after 6 days and B is called off 3 days before the work is done. In what time was the work finished : (A) 6 days

(B) 8 days

(C) 10 days

(D) 6

6 days 13

45.

If A : B = 2 : 3, B : C = 4 : 5, and C : D = 6 : 7 then A : B : C : D is : (A) 16 : 22 : 30 : 35 (B) 16 : 24 : 15 : 35 (C) 16 : 24 : 30 : 35 (D) 18 : 24 : 30 : 35

46.

In what time would a cistern be filled by three pipes whose diameters are 1 cm, 2 cm and 3 cm, respectively if largest alone fill it in 42 minutes, the amount of water flowing in by each pipe being proportional to the square of its diameter : (A) 27 min (B) 36 min (C) 18 min (D) 24 min

47.

A and B could together finish a job in p days. They worked together for q days and then A was called off. B finished the remaining work in r days. A will finish the work alone in : (A)

pr days r p  q

(B)

pq days r p  q

(C)

pq days r p  q

(D)

pr days pq

48.

If

ap  bq cr  ds  then which of the following is true : ap – bq cr – ds

(A) ap, bq, cr and ds are in proportion (C) Both A and B

49.

Walking at distance: (A) 12 min

(B) as, br, cq, and dp are in proportion (D) None of these

4 of his usual speed, a person is 6 min late to his office. Find his usual time to cover the 5

(B) 18 min

(C) 24 min

(D) Data inadequate

50.

A man covers a certain distance on scooter. Had he moved 4 km/hr faster, he would have taken 30 minutes less. If he had moved 3 km/hr. slower, he would have taken 30 min more. Find the original speed : (A) 24 km/hr (B) 20 km/hr (C) 28 km/hr (D) 18 km/hr

51.

The incomes of A and B are in the ratio 7 : 5 and their expenditures are in the ratio 5 : 3. If each saves Rs 1600, what are their incomes : (A) Rs 5600, Rs 4000 (B) Rs 7000, Rs 5000 (C) Rs 14000, Rs 10000(D) Rs 21000, Rs 15000

52.

A certain number of men can do a work in 45 days. If there were 4 men less it could be finished in 15 days more. How many men are there? (A) 28 men (B) 16 men (C) 24 men (D) 20 men

53.

A is 4 times as fast as B, and is therefore able to finish a work in 45 days less than B. Find the time in which they can do it working together : (A) 8 days (B) 20 days (C) 24 days (D) 12 days

54.

If x : y = 5 : 2 then (8x + 9y) : (8x + 2y) = (A) 22 : 29 (B) 26 : 61

(C) 29 : 22

(D) 61 : 26