Pioneer’s · A circle placed against a right angled triangle centred at O is the 14 cm radius. What is the radius of the smaller circle placed in the remaining gap? (a) 7( 2 1)

Pioneer’s Aspire Scholarship Exam

10th CBSE Examination Centre: Pioneer Education, Sector – 40-D

Name: _______________________________________Father Name:_________________________________

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General Instructions:

The question paper contains 90 multiple choice questions.

There are two sections in the question paper

Section: A– MATHEMATICS (1 to 45)

Section: B– SCIENCE (46 to 90)

Each right answer carries 4 marks and − 1 for every wrong answer.

The Maximum marks are 360 and Maximum Time 2.00 hrs.

Give your response in the OMR Sheet provided with the Question Paper.

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Section-A {Mathematics}

1. If the roots of the equation a2 x2 – kx + 9 = 0 are real and unequal, then the value of k must be

(a) lesser than – 6a (b) greater than 6a (c) between – 6a and 6a (d) None of these

2. The quadratic equation, whose roots are negative of the roots of the equation 23x 8x 3 0

4, is

(a) 24x 8x 3 0

3 (b) 24

x 8x 3 03

(c) 23x 8x 3 0

4 (d) 23

x 8x 3 04

3. In Fig. O is the centre of the circle and BC = AO. Which of the

following relationship between x and y is correct?

(a) x = 3 y always (b) x = 2 y always

(c) x = 4 y always (d) x = 2 y or x = 3 y

4. In Fig. O is the centre of the circle and AB = AC, If AC = 12 cm and

AE = 8 cm, then AD is equal to

(a) 27 cm (b) 24 cm

(c) 18 cm (d) 10 cm

5. One of the sides of a triangle is divided into line-segments of lengths 6 cm and 8 cm by the point of

tangency of the in-circle. If the radius of the in-circle is 4 cm, then the length of the shortest side of the

triangle is

(a) 12 cm (b) 13 cm (c) 15 cm (d) 16 cm

6. PT is a tangent-segment to a circle from an external point P and PAB is a secant of the circle intersecting

the circle at points A and B. If PA = 3 cm and PT = 6 cm, then AB is equal to

(a) 15 cm (b) 9 cm (c) 12 cm (d) 6 cm

7. A person on tour has Rs 360 for his expenses. If he extends his tour for 4 days, he has to cut down his

daily expenses by Rs 3. Find the original duration of the tour.

(a) 24 days (b) 20 days (c) 25 days (d) 22 days

8. If the numbers a, b, c, d, e form an A.P., then find the value of a – 4b + 6c – 4d + e.

(a) 1 (b) –1 (c) 0 (d)2

9. In an A.P., the sum of first n terms is 23n 5n

2 2. Find its 25th term.

(a) 76 (b) 72 (c) 78 (d) 74




10. At the foot of a mountain the elevation of its summit is 450; after ascending 1000 m towards the

mountain up a slope of 300 inclination, the elevation is found to be 600. Find the height of the mountain.

(a) 1.464km (b) 1.366km (c) 1.480km (d) 1.268km

11. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find

the value of p.

(a) p = 3 (b) p = –7 (c) p = 7 (d) p = 9

12. Find the area of the quadrilateral ABCD whose vertices are respectively A(1, 1), B(7, – 3) C(12, 2) and

D(7, 21).

(a) 132 sq. units (b) 134 sq. units (c) 179 sq. units (d) 130 sq. units

13. The digits of a positive integer, having three digits are in A.P. and their sum is 15. The number obtained

by reversing the digits is 594 less than the original number. Find the number.

(a) 573 (b) 852 (c) 258 (d) 582

14. If the given circle has a radius of 4, what is the

perimeter of the inscribed equilateral triangle?

(a) 6 2 (b) 6 3

(c) 12 2 (d) 12 3

15. Given two intersecting chords, find x.

(a) 200 (b) 400

(c) 600 (d) 800

16. In the figure, ABC is a right triangle, BDC is an equilateral triangle, E and F are the midpoints of AC and

BD respectively. Then x =

(a) a/2 (b) a

(c) 2a (d) 2/3a

17. Let ABCDE be a regular pentagon, then P + Q + R + S + T =?

(a) π

2 (b) π

(c) 3π

2 (d) 2π




18. If the area of the equilateral OAB shown in figure is 9 3 sq. units, then what are the coordinates of

point A?

(a) 3, 3 (b) 3, 3 /2

(c) 3,3 3 (d) 2, 3

19. For what value of k, the vertices (2, 1), (3, 3) and (5, k) form an equilateral triangle?

(a) 4 (b) 2 (c) 3/4 (d) No such value exist

20. The nature of the roots of the quadratic equation (b – c)x2 + 2(c – a)x + (a – b) = 0

(a) real and equal (b) imaginary

(c) real and distinct (d) Cannot be determined

21. If the equations ax2 + bx + c = 0 and x2 + 2x + 9 = 0 have a common root and a, b and c are real numbers,

the ratio a : b : c is

(a) 2 : 1 : 9 (b) 1 : 2 : 9 (c) 9 : 2 : 1 (d) 1 : 9 : 2

22. If x1, x2, x3, ….., xn are in AP, then the value of 1 2 2 3 3 4 n 1 n

1 1 1 1....

x x x x x x x x is

(a) 1 n

n 1

x x (b)

2 n 1

n 1

x x (c)

1 n

n

x x (d) None of the above

23. What will be the common difference of the arithmetic progression, whose sum of first m terms is given

by 2(m2 + 3m)?

(a) 4 (b) 8 (c) 2 (d) can’t be determined

24. A circle placed against a right angled triangle centred at O is the 14 cm radius. What is the radius of the

smaller circle placed in the remaining gap?

(a) 7( 2 1) (b) 14( 2 1)

(c) 27( 2 1) (d) 214( 2 1)

25. In the figure shown, two identical circles of radius 12 cm each are drawn with centres C and C’ with AB

and BD being their respective tangents at A and D. If BE is their common tangent and AB BD, the

length of BD is equal to

(a) 12( 2 1) (b) 12( 2 1)

(c) 12 2 (d) 24




26. Two poles at points A and B stand on a horizontal place. C and D are two points between them. The

angle of elevation of the top of the poles as observed from point C are 300 , 600 and from point D are 600

and 450. If CD = 30 m, then AB is equal to

(a) 15(4 3) (b) 15( 3 3) (c) 15(4 3) (d) None of these

27. The ratio of the perimeter of an equilateral triangle having an altitude equal to the radius of a circle, to

the perimeter of an equilateral triangle inscribed in the circle is :

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

28. The base of an isosceles triangle is 6 cm and one of the equal sides is 12 cm. The radius of the circle

through the vertices of the triangle is:

(a)8 15

5 (b) 4 3 (c)3 5 (d) none of these

29. In solving a problem that reduces to a quadratic equation one student makes a mistake only in the

constant term of the equation and obtains 8 and 2 for the roots. Another student makes a mistake only

in the coefficient of the first degree term and finds –9 and –1 for the roots. The correct equation was:

(a) x2 –10x + 9 = 0 (b) x2 + 10x + 9 = 0 (c) x2 – 10x + 16 = 0 (d) x2 – 8x –9 = 0

30. A and B together can do a job in 2 days; B and C can do it in four days; and A and C in 22

5 days. The

number of days required for A to do the job alone is:

(a) 1 (b) 3 (c) 6 (d) 12

31. A train, an hour after starting, meets with an accident which detains it a half hour, after which it

proceeds at 3

4of its former rate and arrives 3

1

2hours late. Had the accident happened 90 km farther

along the line, it would have arrived only 3 hours late. The length of the trip in km was:

(a) 400 (b) 465 (c) 600 (d) 540

32. If the 3 consecutive vertices of a square are (–1, 4), (–3, 0) and (1, –2). Which of the following can be its

fourth vertex?

(a) (3, 2) (b) (2, 3) (c) (–3, 2) (d) (1, 2)

33. A student cuts off two circles of radii r1 and r2 from a sheet of thick paper. He keeps these two in a

vertical position in contact with each other at a point P, Now, he keeps a rod of moderate thickness on

the top points A, B of the two circles. If r1 r2, then for any values of r1 and r2 the angle APB is equal to

(a) 30° (b) 60° (c) 90° (d) 120°.




34. If a and are roots of the equation x2+2x+ 1 = 0, then the equation whose roots are 1

and 1

is a

(a) x2+1

2x +

1

2 = 0 (b) x2+x +

1

2 = 0 (c) x2+

1

2x+ 1 = 0 (d) x2 + 2x +1 = 0.

35. In the figure, O is the centre of circle; BCO = m°, BAC = n°. Then

(a) m + n = 90° (b) m + n = 180°

(c) 2m + n = 180° (d) m + 2n = 180°.

36. In this figure the centre of the circle is O. AB BC, ADOE is a straight line, AP AD , and AB has a

length twice the radius. Then:

(a) AP2 = PB.AB (b) AP . DO PB . AD

(c) 2AB AD . DE (d) AB. AD OB . AO

37. John ordered 4 pairs of black socks and some additional pairs of blue socks. The price of the black socks

per pair was twice that of the blue. When the order was filled, it was found that the number of pairs of

the two colours had been interchanged. This increased the bill by 50% .The ratio of the number of pairs

of black socks to the number of pairs of blue socks in the original order was:

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

38. A point is selected at random inside an equilateral triangle. From this point perpendiculars are dropped

to each side. The sum of these perpendiculars is:

(a) least when the point is the centre of gravity of the triangle

(b) greater than the altitude of the triangle

(c) equal to the altitude of the triangle

(d) one-half the sum of the sides of the triangle

39. The hypotenuse of an isosceles right-angled triangle is q. If we describe equilateral triangles (outwards)

on all its 3 sides, then the total area of the re-entrant hexagon thus obtained is

(a) q2( 3 +2) (b)

2q 2 3 1

4 (b)

2q 4 3 1

4 (d)

2q 5 3 2

4

40. An insect climbs up a 10 metre high pole. It climbs up 3 metres in the first minute but slips down 2

metres in the second minute, again climbs up 3 metres in the third minute and slips down 2 metres in




the fourth minute and so on. It reaches the top of the pole in

(a) 15 minutes (b) 17 minutes (c) 19 minutes (d) 20 minutes.

41. If α,β are the zeroes of the polynomial f(x) = 2x2 + 5x + k satisfying the relation 2 2 21α β αβ ,

4then

find the value of k for this to be possible.

(a) k = –1 (b) k = 1 (c) k = –2 (d) k = 2

42. If –4 is a root of the quadratic equation x2 + px + 4 = 0 and the quadratic equation x2 + px + k = 0 has

equal roots, find the value of k.

(a) 4

9 (b)

9

4 (c)

9

4 (d)

4

9

43. Which term of the sequence 4, 9, 14, 19, … is 124?

(a) 25th term (b) 24th term (c) 20th term (d) none of these

44. Which term of the arithmetic progression 5, 15, 25, …will be 130 more than its 31st term?

(a) 43rd term (b) 44th term (c) 45th term (d) 46th term

45. If 2x, x + 10, 3x + 2 are in A.P. , find the value of x.

(a) x = 4 (b) x = 2 (c) x = 6 (d) x = 8




Section-B {Science}

46. Which of the following changes occur when you walk out of bright sunshine into a poorly lit

room?

(a) the pupil becomes larger (b) the lens becomes thicker

(c) the ciliary muscle relaxes (d) the pupil becomes smaller

47. After testing the eyes of a child, the optician has prescribed the following lenses for his

spectacles: Left eye : + 2.00 D Right eye : + 2.25 D

The child is suffering from the defect of vision called :

(a) short-sightedness (b) long-sightedness (c) cataract (d) presbyopia

48. With both eyes open, a person’s field of view is about :

(a) 900 (b) 1500 (c) 1800 (d) 3600

49. The day is longer on the earth by about 4 minutes because :

(a) the earth is round in shape (b) the earth rotates on its axis

(c) the earth revolves around the sun (d) the earth has atmosphere

50. The bluish colour of water in deep sea is due to

(a) the presence of algae and other plants found in water

(b) reflection of sky in water

(c) scattering of light

(d) absorption of light by the sea

51. Which of the following statements is correct regarding the propagation of light of different

colours of white light in air?

(a) Red light moves fastest

(b) Blue light moves faster than green light

(c) All the colours of the white light move with the same speed

(d) Yellow light moves with the mean speed as that of the red and the violet light

52. A beam of light is incident through the holes on side A

and emerges out of the holes on the other face of the

box as shown in the figure. Which of the following

could be inside the box?

(a) Concave lens (b) Rectangular glass slab

(c) Prism (d) Convex lens




53. A 10 mm long awl pin is placed vertically in front of a concave mirror. A 5 mm long image of the

awl pin is formed at 30 cm in front of the mirror. The focal length of this mirror is

(a) – 30 cm (b) –20 cm (c) – 40 cm (d) – 60 cm

54. In the concave reflector of a torch, the bulb is placed :

(a) between the pole and focus of reflector (b) at the focus of reflector

(c) between focus and centre of curvature of reflector (d) at the centre of curvature of reflector

55. In order to obtain a magnification of, –0.6 (minus 0.6) with a concave mirror, the object must be

placed :

(a) at the focus (b) between pole and focus

(c) between focus and centre of curvature (d) beyond the centre of curvature

56. A spherical mirror and a spherical lens each have a focal length of, – 15 cm. The mirror and the

lens are likely to be:

(a) both concave. (b) both convex.

(c) the mirror is concave but the lens is convex. (d) the mirror is convex but the lens is concave.

57. The refractive index of glass with respect to air is 3

2 and the refractive index of water with

respect to air is 4

3. The refractive index of glass with respect to water will be :

(a) 1.525 (b) 1.225 (c) 1.425 (d) 1.125

58. In the soap micelles

(a) the ionic end of soap is on the surface of the cluster while the carbon chain is in the in terior

of the cluster.

(b) ionic end of soap is in the interior of the cluster and the carbon chain is out of the cluster.

(c) both ionic end and carbon chain are in the interior of the cluster

(d) both ionic end and carbon chain are on the exterior of the cluster

59. The heteroatoms present in CH3 – CH2 – O – CH2 – CH2 Cl are

(i) oxygen (ii) carbon (iii) hydrogen (iv) chlorine

(a) (i) and (ii) (b) (ii) and (iii) (c) (iii) and (iv) (d) (i) and (iv)

60. Neopentane and Isopentane are

(a) allotropes (b) isobars (c) isomers (d) homologues

61. Which of the following gas is known as illuminating gas?

(a) Ethane (b) Ethene (c) Ethyne (d) Propane




62. Which of the following pairs are members of a homologous series?

(a) CH3OCH3; CH3CH2-OH (b) CH3–CHO; CH3CH2CHO

(c) CH3CH2COOH; CH3COOCH3 (d) (CH3)2CH–OH; CH3CH2CH2–OH

63. Which of the following are the characteristics of isotopes of an element?

(i) Isotopes of an element have same atomic masses

(ii) Isotopes of an element have same atomic number

(iii) Isotopes of an element show same physical properties

(iv) Isotopes of an element show same chemical properties

(a) (i), (iii) and (iv) (b) (ii), (iii) and (iv) (c) (ii) and (iii) (d) (ii) and (iv)

64. Which of the following statement (s) about the Modern Periodic Table are incorrect

(i) The elements in the Modern Periodic Table are arranged on the basis of their decreasing

atomic number

(ii) The elements in the Modern Periodic Table are arranged on the basis of their increasing

atomic masses

(iii) Isotopes are placed in adjoining group (s) in the Periodic Table

(iv) The elements in the Modern Periodic Table are arranged on the basis of their increasing

atomic number

(a) (i) only (b) (i), (ii) and (iii) (c) (i), (ii) and (iv) (d) (iv)only

65. Atomic number of the element which is surrounded by elements with atomic numbers 17, 34, 36

and 53 in the Modern Period Table is

(a) 18 (b) 52 (c) 37 (d) 35

66. The correct sequence of atomic radii is

(a) Na > Mg > Al > Si (b) Al > Si > Na > Mg (c) Si > Al > Mg > Na (d) Si > Al > Na > Mg

67. The element with electronic configuration 2, 8, 6 is

(a) metallic with valency 2 (b) non-metallic with valency 2

(c) metalloid with valency 2 (d) none of these

68. Which of the following hydroxides is most basic?

(a) Be(OH)2 (b) Ba(OH)2 (c) Ca(OH)2 (d) Mg(OH)2

69. Elements belonging to the same group have similar properties because

(a) they have similar electronic configuration of the outermost shell

(b) their atomic numbers go on increasing as we move down the group

(c) all of them are metallic elements

(d) none of the above




70. Which among the following is not the function of testes at puberty?

(i) formation of germ cells (ii) secretion of testosterone

(iii) development of placenta (iv) secretion of estrogen

(a) (i) and (ii) (b) (ii) and (iii) (c) (iii) and (iv) (d) (i) and (iv)

71. In figure, the parts A, B and C are sequentially

(a) cotyledon, plumule and radicle (b) plumule, radicle and cotyledon

(c) plumule, cotyledon and radicle (d) radicle, cotyledon and plumule

72. A duct coming from urinary bladder which carries sperms

(a) Vas deferens (b) Oviduct (c) Fallopian tube (d) Urethra

73. Sperm are produced in the

(a) seminiferous tubules (b) interstitial cells

(c) vas deferens (d) prostate gland

74. Placenta is the region, where

(a) foetus is supplied by maternal blood

(b) embryo is attached to mother by umbilical cord

(c) foetus receives maternal blood and nutrition

(d) embryo enclosed by membranes

75. Which one of the following is found in the human male but NOT in the female?

(a) Cowper’s gland (b) Rectal gland (c) Prostate gland (d) Bartholin’s gland

76. Focal length of a convex lens will be maximum for –

(a) blue light (b) yellow light (c) green light (d) red light

77. When a mirror is rotated through an angle θ , the refracted ray from it turns through an angle of –

(a) θ (b) θ/2 (c) 2θ (d) 0

78. A light ray is incident perpendicularly to one face to a 900

prism and is totally internally reflected at the glass-air

interface. If the angle of reflection is 450,

we conclude that the refractive index n –

(a) 1

n2

(b) n 2

(c) 1

n2

(d) n 2




79. A person using a lens as a simple microscope sees an –

(a) inverted virtual image (b) inverted real magnified image

(c) upright virtual image (d) upright real magnified image

80. The asexual process replaced by the sexual method is known as –

(a) Semigany (b) Amphimixis (c) Apospory (d) Apomixis

81. Which part of the ovary in mammals acts as an endocrine gland after ovulation –

(a) Vitelline membrane (b) Graffian follicles (c) Stroma (d) Germinal epithelium

82. Development of embryo in human body takes place in –

(a) ovary (b) oviduct (c) uterus (d) ostium

83. Which of the following statements is not true for ethane –

(a) It can be chlorinated with chlorine (b) It can be catalytically hydrogenated

(c) When oxidised produces CO2 and H2O (d) It is a homologous of isobutene

84. Ethyl bromide gives ethylene when reacted with –

(a) Ethyl alcohol (b) Dilute H2SO4 (c) Aqueous KOH (d) Alcoholic KOH

85. Which is the most reactive hydrocarbon in the following –

(a) Ethane (b) Ethyne (c) Ethene (d) Methane

86. The IUPAC name of the compound having the formula (CH3)3CCH=CH2 is –

(a) 3, 3, 3-trimethyl-1-propane (b) 1, 1, 1-trimethyl-1-1-butene

(c) 3,3-dimethyl-1-butene (d) 1,1-dimethyl-1,3-butene

87. The size of the following species increases in the order –

(a) Mg2+ < Na+ < F– < Al(b) F– < Al < Na+ > Mg2+ (c) Al < Mg < F– < Na+ (d) Na+ < Al < F– < Mg2+

88. Which one of the following oxides is neutral –

(a) CO (b) SnO2 (c) ZnO (d) SiO2

89. One important merit of modern periodic table is –

(a) it explains why element in the same group have the same chemical properties

(b) Hydrogen has been placed accurately

(c) Isobars have not been placed separately

(d) It is based on classifying elements according to their atomic masses

90. The elements belonging to IA to VII A and 0 groups are known as –

(a) alkali metals (b) representative elements

(c) transition elements (d) inner-transition elements

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Pioneer’s · A circle placed against a right angled triangle centred at O is the 14 cm radius. What is the radius of the smaller circle placed in the remaining gap? (a) 7( 2 1)