solutions- ntse 2014 stage - i

7/23/2019 Solutions- Ntse 2014 Stage - i

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NTSE 2014 STAGE – I (DELHI STATE)

(Held on 2nd

November 2014)

QUESTION PAPER WITH HINTS & SOLUTIONS

MENTAL ABILITY TEST

1. If 1

9of a number is 4 more than its

1

10, then number is:

(1) 300 (2) 260(3) 460 (4) 360

1. 4

Sol.1 1

x x 49 10

x4

90

x = 360

2. If x% of x is 25, x will be:(1) 50 (2) 40(3) 60 (4) 500

2. 1Sol. x% of x = 25

x2 = 2500x = 50

3. If 3

5of a Cistern is filled in 1 minute, how much more time will be required to fill rest of it:

(1) 30 seconds (2) 40 seconds

(3) 36 seconds (4) 24 seconds3. 2

Sol.60 x

3 2

5 5

x = 40 seconds

4. A train overtakes a person walking at 1 m/s in 5 seconds. If the speed of train is 65 m/s.Then what is the length of the train:(1) 400 m (2) 300 m(3) 320 m (4) 450 m

4. 3Sol. L = 64 x 5

320 m

5. The mean weight of 21 students is 21 kg. If a student weighing 21 kg is removed from thegroup then what is the mean weight of remaining students:(1) 19 kg (2) 21 kg(3) 20 kg (4) None of these

5. 2

Sol. mean =21 21 21

21kg20




6. If n n 12 2 4 , then the value of 4n will be?(1) 1 (2) 27(3) 8 (4) 64

6. 4

Sol. n n 12 2 4

n 12 1 4

2

2n

= 8n = 34n = 64

7. For what value of k do the equation 3 k 1 4y 24 and 15x + 20 y = 8 (k + 13) have

infinite solution?(1) 2 (2) 1(3) 4 (4) 3

7. 1

Sol.

3 k 1 4 24

15 20 8 k 13

k 1 1

5 5

k = 2

8. The price of an article is increased by 25%. By what percentage must its consumption bedecreased so that the expenditure on it remains unchanged?

(1)1

33 %3

(2) 25%

(3) 20% (4) 10%8. 3Sol. 1.25 p x xq = pq

1.25x = 1

x =1

1.25=

40.8

5

required decrease = (1–0.8) x 100 =20%

9. Value of

4 1

1 10 23 2

21

52

(1) 0 (2) –1(3) 1 (4) 2

9. 1

Sol.

4 11 10 2

3 221

52

=4 1

1 53 2

29

2

=4 5

12 2

23




=12 5

18 2

=3 5

12 2

= 0

10. If (y + 2) is a factor of y2 + my + 14, then value of m is:(1) 7 (2) 2

(3) 9 (4) 1410. 3Sol. f (–2) = 0

(-2)2 + m (-2) + 14 = 04 – 2m + 14 = 02m = 18m = 9

11. The average of first 81 natural numbers is:(1) 40 (2) 40.5(3) 41 (4) 42

11. 3

Sol. mean =81 82

412 81

12. A sum of money at simple interest amounts to Rs 815 in 3 years and Rs 854 in 4 years. Thesum is:(1) 700 (2) 698(3) 679 (4) 689

12. 2

Sol.3 P R

815 P100

--- (1)

P 4 R854 P

100

--- (2)

PR 854 P

100 4

Using this in (1)

854 P3 815 P

4

2562 – 3P = 3260 – 4PP = 3260 – 2562 = Rs 698

13. A person climbs up a pole of 90 metres high, in every minute he climbs 15 meter but slipsdown 12 metres. How much time he will take to reach at the top:(1) 30 minutes (2) 29 minutes(3) 24 minutes (4) 26 minutes

13. 4Sol. In every minute he climbs 3m. So, in 25 minute he climbs 75m. Next minute he reached the

top. So total time = 26 minutes.

Directions (For Question no 14 – 18): In a school total number of students are 1260. FollowingPie diagram represents different mode of transport used by students with the help of Pie Chart. Answer the Questions.




14. Number of students who come to school by car:(1) 315 (2) 430(3) 310 (4) 415

14. 1

Sol.90

1260360

= 315

15. What is the ratio of number of students comes to school by scooter and car:(1) 8:9 (2) 7:9(3) 7:5 (4) 1:2

15. 2Sol. Ratio = 7 : 9

16. Number of total students who come to school by on their feet and by bus:(1) 689 (2) 710(3) 700 (4) 640

16. 3

Sol.80 120

1260360

=20

126036

= 700

17. Number of students who do not come to school by bus:(1) 300 (2) 420

(3) 460 (4) 84017. 4

Sol.240

1260360

=2

12603

= 840

18. By how much percentage number of students who comes to school by car is more thanthose who comes by their feet:(1) 13.5 (2) 11.5(3) 12.5 (4) 10.5

18. 3Sol. By car = 90o

On feet = 80o

90 =x

80100

x =9000

80= 112.5Required percentage = 12.5%



19. A purse contains a certain number of coins of denominations Rs 1 and 50 paise. The totalvalue of the coins (in rupees) is 14 less than total number of coins. Find the number of 50paise coins:(1) 22 (2) 28(3) 12 (4) 18

19. 2Sol. Let the bag contains ‘x’ Rs 1 coins and ‘y’ 50 p coins

y

x x y 142 y

142

y = 28

20. 5 5 5 5 5 ?

(1)31

325 (2)32

315

(3) 25 5 (4) 625

20. 1

Sol.

31

325 5 5 5 5 5

21. 60% of 264 is same as(1) 10% of 44 (2) 15% of 1056(3) 30% of 132 (4) 12% of 144

21. 2

Sol.60

264100

= 158.415% of 1056 = 158.4

Directions (For Question no 22 – 25): refer following diagram:

Read the statement and choose the letter of the region which correctly represent the statement invenn diagram:

22. Students who took all three subjects i.e., Hindi, English and Sanskrit:(1) f (2) d(3) e (4) g

22. 4Sol. From figure

23. Students who took at least two subjects from Hindi, English and Sanskrit:(1) e, f and c (2) a, b and c(3) e, f, g and d (4) a, e, f and g


24. Students who did not take any of the three subjects:(1) d (2) h



(3) f (4) g24. 2Sol. From figure

25. Students who took Hindi and Sanskrit both only(1) d (2) e(3) f (4) g

25. 2

Sol. From figure

26. What number is opposite number 3, if four different position of a dice are as shown below:

(1) 6 (2) 4(3) 3 (4) 2

26. 2Sol. 2, 6, 1, 5 are adjacent to 3.

So, 4 is opposite.

27. Select the answer to substitute I and IV such that III and IV is related the same was as I isrelated to II:

(1) 1 (2) 2(3) 3 (4) 4

27. 1Sol. F is obtained by removing one line segment from E.

Similarly I is obtained by removing one line segment from L.

28. Which one will replace the question mark?

18 24 32

12 14 16

3 ? 4

72 112 128

(1) 1 (2) 2(3) 3 (4) 4

28. 3

Sol.18 12 32 16

72, 1283 4

24 14112

x

x = 3

Directions (For Question no 29 – 31): A cube of side 10 cm is coloured yellow and with a 2 cmwide black strip along all the side on all the face. The cube is cut into 125 smaller cube of equalsize:29. How many cubes have three black face each?

(1) 0 (2) 4(3) 8 (4) 16

29. 3



Sol.

Yellow

Black

Here n = 53 black faces on corners = 8

30. How many cubes have at least one face coloured?(1) 102 (2) 98(3) 89 (4) 76

30. 2Sol. 125 – 33 = 98

31. How many cubes are without any colour?(1) 0 (2) 14(3) 27 (4) 64

31. 3Sol. Without any colour = 33 = 27

32. Select the answer which has the same relationship to the third figure which is between thefirst two figures.

32. 2/3

Sol. In figure 2, ¬ is not correct and in figure 3 the ∆ is missing. So, no option iscompletely correct.


(1) 16 (2) 30(3) 36 (4) 40

33. 3Sol. (2 4 6 0) 4 8

6 2 10 8 4 22

4 14 12 10 4 36




(1) 18 (2) 30(3) 31 (4) 23

34. 3

Sol.3 27

152

9 8145

2

6 5631

2

Directions (For Question no 35 – 37): Consider a group comprising of 4 students – Rekha, Babita,Mamta, Neha who stand in a row. Rekha and Babita stand sixth and seventh from the left. Mamtaand Neha stand in the fourth and fifth position respectively from the right. When Babita and Mamtaexchange their positions, then Babita will be fifteenth from the left:

35. Originally Neha’s position from the left is

(1) 5th

(2) 13th

(3) 14th (4) 15th

35. 3

Sol. Rekha sixth from left

Babita seventh from left

Mamta fourth from right, fifteenth from left

Neha fifth from right

Number of students = 4 + 15 – 1 = 18

Neha’s position from left = 18 + 1 – 5 = 14th

36. After exchange of position between Babita and Mamta, Mamta’s position from the right is:(1) 5th (2) 10th

(3) 11th (4) 12th

36. 4Sol. Mamta’s position after exchange

= seventh from left= (18 + 1 - 7) from right= 12th from right

37. If Neha and Rekha exchange their positions between themselves, then after the exchange,Neha’s position from the left will be:(1) 6th (2) 10th

(3) 11th (4) 9th

37. 1Sol. Neha’s new position = 6th from left.

38. In a party, there are 7 people. They want to hand shake each other, then what is the number of total hand shakes(1) 56 (2) 21(3) 28 (4) 42

38. 2

Sol. Total number of handshakes =7 6

212

Directions (Question 39): In the following question, select a figure from amongst the four alternatives, which place in the blank space would complete the pattern:



39. Problem figure

Answer figure


40. Find out which of the answer figure (1), (2), (3) & (4) complete the given matrix?

Answer figure

40. 1Sol. In figure 2 only second arrow gets inverted, in figure 3 only first arrow gets inverted.

Directions (Question 41 - 43): In each of the following questions, choose the correct mirror imageof the given figure from amongst the four alternatives (1), (2), (3 and (4) given below.

41. Figure

41. 4.Sol. Lateral inversion



42.

B R I S K

42. 3Sol. Lateral inversion

43. Figure

43. 1Sol. Lateral inversion

Diagram (Questions 44 – 45): In each of the following questions, out of the four figures marked (1),(2), (3 and (4) three are similar in a certain manner. However, one figure is not like other three.Choose the figure which is different from the rest.

44.

44. 2Sol. Other objects have 3 lines.

45.

45. 3Sol. Other figures can be rotated into one another.

Directions (Question 46 – 47): Select from the alternatives, the box can be formed by folding thesheet shown in the given figure?



46.

46. 4Sol. By observation

47.

47. 1Sol. By observation

Directions (Questions 48 – 50): A code language has been used to write the words in capitalletters in English, in column ‘I’ as number letters in column ‘II’. Number letters in column II do notappear in the same order as letters in column I. Decode the language then choose the correct codefor the word given in each question from the given alternatives.I II ANT 307TEN 237SUN 345SET 752

48. Code for ‘A’ is:(1) 3 (2) 0(3) 7 (4) 5

48. 2Sol. N T A E S U

3 7 0 2 5 4

0 is the code of A.

49. Code for word ‘NUT’ is(1) 432 (2) 347




(3) 503 (4) 72449. 2Sol. 347 is code for ‘NUT’

50. Code for letter ‘U’ is:(1) 3 (2) 0(3) 5 (4) 4

50. 4

Sol. 4 is code for ‘U’

SCHOLASTIC APTITUDE TEST

91. A body falling from rest describes distances S1, S2 and S3 is the first, second and thirdseconds of its fall. Then the ratio of S1 : S2 : S3 is:(1) 1 : 1 : 1 (2) 1 : 3 : 5(3) 1 : 2 : 3 (4) 1 : 4 : 9

91. 2

Sol.1

g gS (2 1 1)

2 2 ,

2

g 3gS (2 2 1)

2 2 , S3 =

g 5g(2 3 1)

2 2

S1 : S2 : S3 = 1 : 3 : 5.

92. Two bodies with kinetic energies in the ratio 4 : 1 are moving with equal linear momentum.The ratio of their masses is:(1) 1 : 2 (2) 1 : 1(3) 4 : 1 (4) 1 : 4

92. 4

Sol.

2

1 1 2

2

2 1

2

P

K 2m m 4

K m 1P

2m

m1 : m2 = 1 : 4

93. Amount of light entering into the camera depends upon:(1) focal length of objective lens.(2) product of focal length & diameter of objective lens.(3) distance of objective from camera.(4) aperture setting of the camera.

93. 4Sol. Amount of light entering into the camera depends upon aperture setting of the camera.

94. A body starts from rest at time t = 0, the acceleration timesgraph is shown in figure. The maximum velocity attained bythe body will be:(1) 110 m/s (2) 55 m/s(3) 650 m/s (4) 550 m/s

10

11

a(m/s )

t(sec)

94. 2Sol. Area under a–t graph gives change in velocity.

V – O =1

11 102

= 55 m/s

95. A comb run through one’s dry hair attracts small bits of paper. This is due to:(1) comb is a good conductor (2) paper is a good conductor (3) the atoms in the paper gets polarised by the charged comb



(4) the comb possesses magnetic properties95. 3Sol. This is due to the atoms in the paper gets polarised by the charged comb.

96. A wire of resistance R is stretched to twice of its original length. Its new resistance will be:(1) 4R (2) R/4(3) 2R (4) R/2

96. 1

Sol. Rnew = n2

R = (2)2

R = 4R

97. On a cold morning, a metal surface will feel colder to touch than a wooden surface, because:(1) metal has high specific heat (2) metal has high thermal conductivity(3) metal has low specific heat (4) metal has low thermal conductivity

97. 2Sol. On a cold morning, a metal surface will feel colder to touch than a wooden surface, because

metal has high thermal conductivity.

98. The resultant focal length of the lenses as shown in the figure is:

(1) 2f (2)f

2

(3)f

4(4) f

98. 2

Sol.1 2

1 1 1 2

F f f f

f F

2

99. White colour of the cloud is due to:(1) reflection of seven colors of light (2) refraction of seven colors of light(3) scattering of seven colors of light (4) absorption of seven colors of light

99. 3Sol. White colour of the cloud is due to scattering of seven colors of light

100. The magnetic field lines inside a long current carrying solenoid are nearly:(1) Circular (2) Parabolic(3) Straight (4) Elliptical

100. 3Sol. The magnetic field lines inside a long current carrying solenoid are nearly straight.

101. An AC generator is connected to an electric appliance. In 10 revolutions of the armature thecurrent in the appliance changes direction:(1) 5 times (2) 10 times(3) 20 times (4) 40 times

101. 3Sol. In one revolution current changes its direction twice Hence in 10 revolution current will

change its direction 20 times.

102. Ice is floating on water in a beaker when Ice completely melts then level of water in beaker:(1) Increases (2) Decreases(3) Remains the same (4) First increases then decreases

102. 3

Sol. Before melting: W = B mg = V1g 1

mV

After melting:2m V

2

mV




V1 = V2 hence level will not change.

103. Which one of the following is not a base?(1) B(OH)3 (2) KOH(3) Ca(OH)2 (4) NH4OH

103. 1Sol. B(OH)3 is a Lewis Acid

104. Which of the following orders of atomic radii is correct represented?(1) B < Al < Ga (2) B < Ga < Al(3) Al < B < Ga (4) B > Ga > Al

104. 2Sol. Due to presence of d- electron in penultimate shell of Ga. The order of atomic radii becomes

B < Ga < Al.

105. A sample of MgCO3 contains 3.01 1023 Mg2+ ion and 3.01 1023 2

3CO ions. The mass of

the sample is:(1) 42 mg (2) 84 g(3) 0.042 kg (4) 42 mol

105. 3

Sol. Gram Mol. mass of MgCO3 = 84 g contains 6.022 10

23

Mg

+

& 6.022 10

23

carbonate ion sothe mass of half mole of MgCO3 is 0.042 kg.

106. What are the electronic configuration of Na+ and Cl – ions?(1) Na+ = 2, 8, 1 and Cl – 2, 8, 7 (2) Na+ = 2, 8, and Cl – 2, 8, 8(3) Na+ = 2, 8, 2 and Cl – 2, 8, 6 (4) Na+ = 2, 8, and Cl – 2, 8, 7

106. 2Sol. Na+ = 2, 8, and Cl – 2, 8, 8

107. Which of the following has shortest carbon- carbon bond length?(1) C2H2 (2) C2H4

(3) C2H6 (4) C6H6

107. 1

Sol. C C < C = C < C – C, bond length order.

108. Which of the following may be isomer of aldehyde having general formula CnH2nO?(1) Alcohol (2) Ether (3) Ester (4) Ketone

108. 4Sol. Aldehyde & Ketone are functional group isomer having same general formula CnH2nO.

109. Which of the following solution has the lowest pH value?(1) 0.1 Molar NaCl solution (2) 0.01 Molar NaHCO3 solution(3) 0.001 Molar Na2CO3 solution (4) 0.01 Molar NaOH solution

109. 1Sol. pH of NaCl solution = 7

The solution of NaHCO3, Na2CO3 & NaOH is basic in nature, so its pH is greater than 7

110. Which of the following has the greatest concentration of H+ ions?(1) 1 mol L –1 HCl solution (2) 1 mol L –1 H3PO2 solution(3) 1 mol L –1 H2SO4 solution (4) 1 mol L –1 H2CO3 solution

110. 3

Sol. 2

2 4 4H SO 2H SO

111. Solder is an alloy of (1) Cu + Zn (2) Pb + Sn




(3) Pb + sb (4) Cu + Sn111. 2Sol. Alloy of solder contain Pb & Sn

112. Which is the symbol of the element tungsten?(1) Ta (2) Tc(3) W (4) V

112. 3Sol. Symbol of tungsten is W.

113. What mass of hydrogen and oxygen will be produced on complete electrolysis of 18 g of water?(1) 2 g hydrogen and 32 g oxygen (2) 2 g hydrogen and 16 g oxygen(3) 4 g hydrogen and 32 g oxygen (4) 4 g hydrogen and 14 g oxygen

113. 2

Sol.2 2 2

1H O H O

2

18g 2g 16g

114. A cell will plasmolyse, if it is placed in(1) Hypertonic solution(2) Hypotonic solution(3) Isotonic solution(4) Concentration of water molecules does not matter

114. 1Sol. Cell will plasmolyse because exosmosis takes place.

115. In Xerophytes, the rate of water loss get reduced due to covering of epidermis by(1) Cuttin (2) Suberin(3) Lignin (4) Gum

115. 1Sol. Cuttin is present on the surface of xerophytes.

116. Given below are the pairs of disease and causal pathogen. Which one of these is not amatching pair?

(1) Kala azar Leishmania (2) Sleeping sickness Trypanosoma

(3) Malaria Salmonella (4) Acne Staphylococci116. 3Sol. Causal organism of malaria is plasmodium vivax.

Typhoid caused by salmonella typhi.

117. During lack of oxygen in tissues of our body, the pyruvate is converted into lactic acid in(1) Mitochondria (2) Nucleus(3) Cytoplasm (4) Ribosome

117. 3

Sol. During vigorous physical exercise anaerobic respiration takes place in cytoplasm of mammalian muscles.

118. The accumulation of non-biodegradable substances in a food chain in increasing amount ateach higher tropic level is known as(1) Accumulation (2) Eutrophication(3) Pollution (4) Bio magnification

118. 4Sol. Bio-magnification is basically accumulation of non-biodegradeable substances on the body

of living organisms.




119. Kidneys do not perform the function of :(1) Regulation of blood pressure (2) Filtration of blood(3) Regulation of ions concentration (4) Secretion of antibodies

119. 4Sol. Kidney helps in excretion as well as osmoregulation of the body.

120. Double fertilization is a unique feature of (1) Bryophytes (2) Angiosperm

(3) Algae (4) Gymnosperm120. 2Sol. In Angiosperm plant seed and seed coat formation takes place after double fertilization.

121. Phototrophic and geotropic response of a plant is under control of following harmone :(1) Auxin (2) Gibberlin(3) Cytokinin (4) Ethylene

121. 1Sol. Concentration of auxin is responsible for phototrophic and geotrophic response of a plant.

122. The following blood vessel does not contain deoxygenated blood :(1) Pulmonary artery (2) Vena Cava(3) Hepatic Vein (4) Pulmonary Vein

122. 4Sol. Pulmonary vein carry oxygenated blood from lungs to heart.

123. If, in a plant, red colour of the flower is dominant over white. A cross was made between aplant containing red flower and other with white flower. The cross yielded 50% whiteflowered plant and 50% red flowered plant. The genotype of the parent with red flowers is(1) Homozygous (2) Heterozygous(3) Cannot be determined (4) Can be homozygous or heterozygous

123. 2Sol. The genotype of the parent Rr (Red flower is heterozygous).

124. Spinal cord originates from :(1) Cerebrum (2) Cerebellum

(3) Medulla (4) Pons124. 3Sol. Spinal cord originated from the medulla ablongata of hind brain.

125. Photosynthesis is an important mode of autotrophic nutrition. The event which does notoccur in photosynthesis is(1) Conversion of light energy to chemical energy(2) Reduction of carbon dioxide to carbohydrate(3) Oxidation of carbon to carbondioxide(4) Absorption of light energy by chlorophyll

125. 3

Sol. Oxidation of carbon to carbon di oxide does not takes place in calvin benson cycle

(photosynthesis).

126. If x a x b x c

3 0b c c a a b

.

a > 0, b > 0, c > 0, then the value of x is :

(1) (a2 + b2 + c2) (2) (a + b + c)

(3) (a + b + c) (4) a b c 126. 3

Sol.x a x b x c

1 1 1 0b c c a a b




1 1 1

x a b c 0b c c a a b

as a > 0, b > 0, c > 0

so, x = (a + b + c)

127. Sum of the roots of the equation x x 34 3 2 128 0 , is

(1) 0 (2) 7

(3) 5 (4) 8127. 2

Sol. Put x2 tThen 2t 24t 128 0 t 16,8 x = 4, 3

128. If sinx + cos x = 2, then 10 10sin x cosec x is equal to :

(1) 3 (2) 0(3) 1 (4) 2

128. 4Sol. Sin x + Cosec x = 2

x can be 90° Sin

10

x + Cosec

10

x = 2

129. The hypotenuse of a right triangle is 10 cm and radius of the inscribed circle is 1 cm. Theperimeter of the triangle is :(1) 15 cm (2) 22 cm(3) 24 cm (4) 18 cm

129. 2

Sol. In radius =a b c

2

a + b = 12, perimeter = a + b + c = 22 cm

a

b

c

130. A shopkeeper blends two varieties of tea costing Rs.18 and Rs.13 per 100 gms in the ratio7 : 3. He sells the blended variety at the rate of Rs.18.15 per 100 gm. His percentage gain inthe transaction is :(1) 8% (2) 12%(3) 15% (4) 10%

130. 4Sol. C.P.=16.5 S.P. = 18.15

Percentage gain = 10%

131. If Cosec 39° = x, the value of 2 22 2 21 1Sin 39 tan 51

cosec 51 Sin 51 Sec 39 is :

(1) 2x 1 (2) 21 x(3) x2 – 1 (4) 1 – x2

131. 3

Sol. 2 2

2 2 2

1 1Sin 39 tan 51

Cosec 51 Sin 51 Sec 39

= sin251° + cos251° + tan251° 1= tan251° = x2 – 1




132. If tan cot

2, 0 90 ,tan cot

then the value of is :

(1) 60° (2) 30°(3) 90° (4) 45°

132. 1Sol. Apply componendo – dividendo

2tan3 tan 3

2cot

133. In a hostel, there was sufficient food for 200 students for 31 days. After 27 days 120

students left the hostel. For how many extra days will the rest of food last for remainingstudents :(1) 8 days (2) 6 days(3) 12 days (4) 10 days

133. 2Sol. Left food is sufficient for 800 students

Now, required number of days =800

4 680

, extra days = 6

134. If

1

x ,1 2 then the value of x

2

+ 2x + 3 is :

(1) 3 (2) 0(3) 4 (4) 1

134. 3

Sol. x 2 1 2 2x 1 2 x 2x 3 4

135. If and are the zeroes of the polynomial f(x) = x2 – 5x + k such that - = 1, the value of K is :(1) 8 (2) 6

(3)13

2(4) 4

135. 2Sol.

2 24

1 = 25 – 4k k = 6

136. The value of 1 2 n

1 1 ....... 1n 1 n 1 n 1

is :

(1) n (2)n

2(3) n + 1 (4) 2n

136. 2

Sol.n n 1 n 2 1

.......

n 1 n 1 n 1 n 1

1 2 3 .......n

n 1

n n 1n2

n 1 2

137. In ABC, segment AD BC, if BD = x units, then x is :




A

B CDx

a

b

c

(1)2 2 2c a b

x2a

(2)

2 2 2a b cx

2c

(3)2 2 2b c a

x2b

(4)

2 2 2b c ax

2abc

137. 1

Sol. AD2 = c2 – x2

ADCb2 = (a – x)2 + AD2

= (a2 + x2 – 2ax) + c2 – x2

b2 = a2 + c2 – 2ax

2ax = a2 + c2 – b2

2 2 2a c b

x2a

A

B CDx

a

bc

a-x

138. The average marks scored by Ajay in certain number of tests is 84. He secured 100 marks inhis last test. His average score of all these tests is 86, then the total number of tests heappeared is :(1) 8 (2) 7(3) 9 (4) 10

138. 1Sol. Initially total score = t

Initially number of test = n

t

84n

&

t 10086

n 1

t + 100 = 86 (n + 1)

t + 100 = 86n + 8684n + 100 = 86n + 86

14 = 2n

n = 7 n + 1 = 8

139. The first and last terms of an A.P. of n terms is 1 and 31 respectively. The ratio of 8th termand (n – 2)th term is 5 : 9, the value of n is :(1) 14 (2) 15(3) 16 (4) 13

139. 3Sol. a = 1

an = 31

a + (n – 1)d = 31

1 + (n – 1)d = 31




(n – 1)d = 30 ….(1)

According to question

a 7d 5

a n 3 d 9

9 (1 + 7d) = 5 [1 + (n – 3)d]

9 + 63d = 5 + 5(n – 3)d

9 + 63d = 5 + 5[(n – 1)d – 2d] 9 + 63d = 5 + 5 (30 – 2d)

9 + 63d = 5 + 150 – 10d

73d = 155 – 9 = 146

d = 2by equation (1)(n – 1)d = 30(n – 1)2 = 30n – 1 = 15

n = 16

140. A number is selected at random from first 50 natural numbers. The probability that selectednumber is a multiple of 3 or 4 is :

(1)12

25(2)

14

25

(3)14

50(4)

8

25140. 1

Sol. Multiple of 3 =50

16 number 3

Multiple of 4 =50

12 number 4

Multiple of 12 =50

412

16 + 12 – 4 = 24

P =24 12

50 25

141. The value(s) of a for which area of triangle, whose vertices are A(a, 2a), B(2, 6) and C(3, 1)is 10 square units, are:(1) 0, 3 (2) 5, 8

(3)8

3,3

(4)8

0,3

141. 4

Sol..

a 2a

2 620

3 1a 2a

6a 2 6a 4a 18 a 20

12a 2 + 4a 18 a = 20

15a = 0 a = 0, aand 15a = 40

40a

15

80,

3

(a, 2a)

(2, 6) (3, 1)




142. The ratio in which the line 3x + y – 9 = 0 divides the line segment joining points (1, 3) and(2, 7) is :(1) 3 : 4 (2) 2 : 3(3) 4 : 3 (4) 3 : 2

142. 1

Sol. Substituting in 3x + y 9 = 0

2k 1 7k 33 9

k 1 k 1

6k 3 7k 3 9k 9 13k + 6 = 9k + 94k = 3

3k

4

Ratio 3 : 4

(1, 3)

(2, 7)

2k 1 7k 3,

k 1 k 1

k : 1

143. The radii of two circles are 9 cm and 12 cm. The circumference of a circle whose area isequal to sum of the areas of the two circles is :

(1) 12 cm (2) 15 cm

(3) 30 cm (4) 225 cm143. 3

Sol. 1 2 3 A A A

3

2 2 2

1 2r r r

81 144 2

3 3225 r r 15cm

Circumference of circle2 15 30

144. The diameter of a right circular cylinder is decreased by 10%. The volume of cylinder remains the same then the percentage increase in height is :(1) 20% (2) 45%(3) 5% (4) 20.5%

144. 2Sol.

1h r radius

1h original height

2

1r h volume

2

2

2 1

9r h r h

10

(Since volume remains same)

2 2

2 1

81r h r h

100

2 1

100h h

81

% =1 1

1

100h h

1981 100 100 23.45h 81

145. In an examination A got 25% marks more then B, B got 10% less than C and C got 25%more than D. If D got 320 marks out of 500, the marks obtained by A were :(1) 450 (2) 405(3) 360 (4) 400

145. 1

146. Kheda Movement (1917) was started for :(1) Famers (2) Labourers




(3) Mill Owners (4) Soldiers146. 1

147. Bharat Mata. Painting was drawn by(1) Rabindranath Tagore (2) Nand Lal Basu(3) Amrita Shergil (4) Abanindra Nath Tagore

147. 4

148. Gutenberg was associated with :(1) Powerloom (2) Rail Engine(3) Computer (4) Printing Press

148. 4

149. ‘Depressed Class Association’ was formed by :(1) Jyoti Ba Phule (2) Mahatma Gandhi(3) B.R. Ambedkar (4) Shahuji Maharaj

149. 3

150. Who were the ‘Kulak’ in soviet society?(1) Small Farmers (2) Big Farmers(3) Shop Keepers (4) Lawyers

150. 2

151. Reichstag was :(1) French Parliament (2) Russian Parliament(3) German Parliament (4) Japan Parliament

151. 3

152. Who was Viceroy of India during Civil disobedience Movement?(1) Lord Curzon (2) Lord Minto(3) Lord Canning (4) Lord Irwin

152. 4

153. Saffrage Movement was started for :

(1) The Right to Vote for Women (2) Right to Education(3) Food for Poors (4) Peasant’s Right

153. 1

154. Jacobin Club was the most powerful political organization in :(1) Germany (2) Russia(3) France (4) Britain

154. 3

155. What was ‘Dawes Plan’?(1) Nazi Plan to suppress the Jews(2) America plan to control the Bolsevik(3) Stalin plan of collectivisation(4) American plan to take out Germany from the financial crisis (great depression)

155. 4

156. Which continent of today is not a part of Gondwana land :(1) North America (2) South America(3) Africa (4) Australia

156. 1

157. Which of the following rivers of India flows through a rift valley ?(1) Tapi River (2) Ganga River




(3) Mahanadi River (4) Yamuna River 157. 1

158. Rainfall in the Northern and North-Western parts of India in the month of October-November is caused mainly due to ?(1) Western disturbances (2) Jet streams(3) Advancing Monsoon (4) Upper Air circulation

158. 1

159. The Slash and burn agriculture is known as Milpa in which of the following countries?(1) Indonesia (2) Mexico(3) Vietnam (4) Sudan

159. 2

160. Which of the following is a non-renewable as well as non-recyclable resource?(1) Iron (2) Coal(3) Water (4) Forests

160. 2

161. Which of the following is not a nuclear power station :(1) Kaiga (2) Narora

(3) Korba (4) Kakrapara161. 3

162. Which of the following is the working age group of the population?(1) 15 – 59 years (2) 20 – 60 years(3) 20 – 65 Years (4) 18 – 60 years

162. 1

163. According to Census of India 2001 a literate person is the one who :(1) Can read and write his/her name(2) Can read and write any language(3) Is 7 years old and can read and write any language with understanding(4) Knows 3 R’s (reading, writing, arithmetic)

163. 3

164. National Waterway No.1 of India connects which two cities of India :(1) Sadia – Dubri (2) Allahabad – Haldia(3) Kottapuram – Kollam (4) Delhi – Kanpur

164. 2

165. Which state of India has made root top rain water harvesting compulsory to all houses :(1) Andhra Pradesh (2) Tamil Nadu(3) Kerala (4) Karnataka

165. 2

166. In contemporary world, which quality makes democracy superior to any other form of Government :(1) Efficiency (2) Responsiveness(3) Transparency (4) Legitimacy governance

166. 4

167. Gender division refers to :(1) Unequal child sex ratio (2) Absence of voting rights(3) Biological differences (4) Unequal roles assigned to men and women

167. 4




168. When was the “Kiittiko-Hachchiko” movement started?(1) 1984 (2) 1986(3) 1987 (4) 1983

168. 3

169. Who is the Political Head of Municipal Corporation :(1) Collector (2) Pradhan(3) Mayor (4) Sarpanch

169. 3

170. Which one of the following parties grew out of a movement :(1) Communist Party of India (2) Bahujan Samaj Party(3) Assam Gana Parishad (4) Assam United Democratic Front

170. 3

171. Who was the Chairman of the Drafting Committee of Indian Constitution :(1) Moti Lal Nehru (2) B.R. Ambedkar (3) Jawahar Lal Nehru (4) Rajender Prasad

171. 2

172. Amnesty International is an international organisation which works for :

(1) World Peace (2) Human Rights(3) Justice (4) Restoration of Democracy

172. 2

173. Name the Law which empowers the people to carry on democratic reforms :(1) Company Act (2) M.R.T.P.(3) Right to information (4) Right to Voice

173. 3

174. Which of the following is the main feature of Pressure groups?(1) Direct control on Political power (2) Try to influence the policies of Government(3) Lax Organisation (4) Direct participation in Political power

174. 2

175. In case of conflict between the centre and the State Government over a subject in theconcurrent list :(1) The state has the upper hand(2) The centre has the upper hand(3) Both are equally applicable(4) Supreme Court decides whether the state Law should prevail or Central Law

175. 2

176. Who is known as the father of Green Revolution in India?(A) Verghese Kurien (B) Babu Jagjivan Ram(C) M.S. Swaminathan (D) M.S. Subhramanyam

176. 3

177. An example of indirect taxes is(A) Income Tax (B) Corporate Tax(C) Estate Tax (D) Entertainment Tax

177. 4

178. Which academy supports food security programme?(A) Academy of Development Science(B) Academy of Crop Science(C) Academy of Food Security



(D) Academy of Grain Science178. 1

179. Which summit of BRICS held in 2014?(A) 5th (B) 6th

(C) 4th (D) 7th

179. 2

180. COPRA is related to(A) Trader (B) Environment(C) Agriculture (C) Consumer

180. 4

solutions- ntse 2014 stage - i

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