9. Which is the wrong step that shows 5− 3 is irrational?
(I) Contradiction: Assume that 5− 3 is rational. (II) F i n d c o p r i m e a & b ( b ≠ 0) such that
5− 3=a ∴ − =5 3
b
a b
,
Rearranging above equation 3= − =5 a 5 −
b
b a b
(III) Since a & b are integers, we get 5−a
b is irrational
and so 3 is irrational.
(IV) But this contradicts the fact that 3 is irrational. Hence 5− 3 is irrational.
A. Both I and II B. Only III
C. Only II D. Both II and III
10. Find the missing number in the number pattern below.
A. 11 B. 14 C. 20 D. 12
11. Housing Board built 100 flats. A painter is engaged to serially number each flat individually from 1 to 100. How many times will he be required to write ONE? A. 21 B. 6 C. 20 D. 18 12. If 123 × 754 = 715243, then 935 × 487 = ? A. 973984 B. 793857 C. 498379 D. 498375
13. The shaded portion depicts a group of people ___. A. Who belong to all
classes, i.e. athletes, politician, cricketers, film stars
B. Who are cricketers and politicians but also are athletes and film stars as well
C. Politicians-turned cricketers who also do athletics as exercise and are friendly with film stars D. None of these
14. Study the following information to answer the given question.
(i) Six books are kept one above the other.
(ii) History book is just above Commerce, Mathematics book is between Civics and Physics.
(iii) English is between History and Civics. Which book is between Mathematics and English?
A. History B. Commerce
C. Physics D. Civics
15. Study the following letter-number arrangement and answer the question given below :
B 8 4 C R M 9 P D K W FA 2 E J 7 X U Q H LT Y 6 G S L If the first half of the above arrangement is written in reverse order followed by the second half-written in reverse order, which letter/number will be eighteenth from left?
A. Y B. K
C. 7 D. 6
Science
16. The cable of an electric fan becomes so worn that the live wire makes electrical contact with the metal case. The case is earthed. The plug to the fan contains a 5 A fuse. There is a current of 4 A when the fan works normally. What will happen in this case? A. The current will run to earth and the fuse will
not be affected.
B. The metal case will become very hot.
C. T he met al ca se w ill become live a nd dangerous.
D. The fuse will melt and switch off the circuit. 17. Read the given statements and mark the correct
option.
Statement 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement 2 : Principle of conservation of momentum holds true for all kinds of collision.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1.
C. Statement 1 is true but statement 2 is false. D. Both statements 1 and 2 are false.
18. A body is suspended from a spring balance kept in a satellite. The reading of the balance is W1 when the satellite goes in an orbit of radius R and is W2 when it goes in an orbit of radius 2R. Then A. W1 = W2
B. W1 < W2 C. W1 > W2 D. W1 ≠ W2
19. Three closed similar coils P, Q and R are placed such that their planes are parallel. In the coil P and R, current of same magnitude flows as shown in the figure. Coils Q and R are static while coil P is moved with a uniform speed towards Q, then
A. Clockwise current will be induced in coil Q, as seen by eye
B. Anti-clockwise current will be induced in coil Q, as seen by eye
C. No current will flow in coil P
D. Current induced in coil Q will be equal to
P and R, but in opposite direction, hence net current
in Q will be zero.
20. Light is incident normally on face AB of a prism as shown in the figure. A liquid of refractive index
n is placed on face AC of the prism. The prism is
made of glass of refractive index 3/2. The limits of
n for which total internal reflection takes place on
face AC is A. n>3 3 2 B. n> 3 C. n< 3 3 4 D. n <3 38 .
21. Match the Column I with Column II.
Column I Column II
(a) Geothermal energy (i) Obtained from the splitting of atom (b) Nuclear energy (ii) Obtained from the
interior of earth (c) Biomass energy (iii) Obtained from the decay
of organic matter. A. (a)-(i), (b)-(iii), (c)-(ii)
B. (a)-(ii), (b)-(i), (c)-(iii) C. (a)-(iii), (b)-(ii), (c)-(i) D. (a)-(i), (b)-(ii), (c)-(iii)
22. An electric current runs counterclockwise in a rectangular loop around the outside edge of the page which lies flat on your table. A uniform magnetic field is then turned on, directed parallel to the page from the top to bottom. The magnetic force on the page will cause
A. The left edge to lift up B. The right edge to lift up C. The top edge to lift up D. The bottom edge to lift up.
23. A sound is played on a flute. A sound of same pitch is played on a trumpet, then the frequency and speed of two sound waves respectively at the same place are
A. Different, different B. Same, same
C. Different, same D. Same, different
24. Study the given circuit. At which point is the value of current smallest? A. P and Q
B. Q only
C. P and R
D. S only
25. The diagram shows the paths of two rays of light from an object. The object is 10 cm in front of a lens as shown in the diagram.
Which of the following statements is true about the given diagram?
A. The lens is converging and focal length of lens is greater than 10 cm.
B. The lens is converging and focal length of lens is less than 10 cm.
C. The lens is diverging and focal length of lens is greater than 10 cm.
D. The lens is diverging and focal length of lens is less than 10 cm.
26. Vivek was given few models of atoms representing their structures. He was asked to choose one pair of isotopes and one pair of isobars.
17 18pn 1822pn (i) (ii) 17 20pn 2020pn (iii) (iv)
Which of the following options contains the correct pairs?
Isotopes Isobars
A. (i) and (ii) (iii) and (iv) B. (i) and (iv) (ii) and (iii) C. (i) and (iii) (ii) and (iv)
27. Four metals P, Q, R and S are tested with water, steam and dilute hydrochloric acid. The table given below shows the results of the experiment.
Metals Reaction with water Reaction with steam Reaction with dil. HCl P × Q × × R S × × ×
Between which two metals should hydrogen be placed in the series?
A. P and Q B. Q and S
C. P and R D. R and S
28. An experimental set up is shown in the figure. Identify the metal X and gas Y respectively in the figure.
MetalX Glass wool soaked with water Burner Y gas Water Gas jar
A. Zinc, H2 gas B. Copper, CO2 gas
C. Aluminium, CO2 gas D. Platinum, H2 gas 29. The mass of few entities are mentioned in the column II.
Match the two columns and mark the correct option from the codes given below.
Column I Column II
a. 10 moles of Na2SO3 (i) 124.5 g
b. 1.5 moles of Na (ii) 34.5 g
c. 1.5 × 1023 molecules of NH
3 (iii) 1260 g d. 0.5 mole of CuSO4·5H2O (iv) 4.23 g A. a-(iii), b-(ii), c-(iv), d-(i)
B. a-(i), b-(ii), c-(iii), d-(iv) C. a-(ii), b-(iv), c-(i), d-(iii) D a-(iv), b-(i), c-(ii), d-(iii)
30. The states of matter depending upon the interparticle distances are shown in the following diagram.
a b, c d,
The conditions a, b, c, d are
a b c d
A. Increase Decrease Increase Decrease heat pressure heat pressure B. Increase Increase Decrease Decrease
heat pressure heat pressure C. Decrease Increase Increase Decrease
heat pressure heat pressure D. Decrease Increase Decrease Increase heat pressure heat pressure
31. Match the reactions given in column I with the type of reactions given in column II and mark the correct option from the codes given below.
Column I Column II
a. CaO + H2O → (i) Decomposition Ca(OH)2 reaction b. 2FeSO4 Heat (ii) Redox reaction Fe2O3 + SO2 + SO3
c. Al + 3AgNO3 → (iii) Combination reaction Al(NO3)3 + 3Ag
d. 2H2S + SO2 → (iv) Displacement reaction 2H2O + 3S
A. a-(i), b-(iii), c-(ii), d-(iv) B. a-(iii), b-(i), c-(iv), d-(ii) C. a-(ii), b-(iv), c-(i), d-(iii) D. a-(iv), b-(ii), c-(iii), d-(i)
32. A metal rod M was dipped in a coloured solution Y. After some time it was observed that the metal rod starts dissolving in the solution and the solution starts fading in colour. However, a coloured precipitate Z was seen at the bottom of the beaker. M, Y and Z could be M Y Z A. M = Zn, Y = FeSO4, Z = Fe B. M = Cu, Y = Al2(SO4)3, Z = Al C. M = Ag, Y = CuSO4, Z = Cu D. M = Fe, Y = ZnSO4, Z = Zn
33. P is produced by the action of chlorine on dry slaked lime.
Q is a non-corrosive base and used for faster
cooking.
On heating R at 373 K, it becomes calcium sulphate hemihydrate.
Identify P, Q and R respectively. A. CaOCl2, NaHCO3, gypsum B. CaO, Na2CO3, CaOCl2 C. Ca(OH)2, NaHCO3, CaSO4 D. CaOCl2, Na2CO3, NH4Cl
34. An element X belongs to group 2 and period 3 of the periodic table. The chemical formulae of its nitrate, sulphate and phosphate respectively will be
A. X(NO3)2, XSO4, X3(PO4)2
B. X NO3, XSO4, X PO4
C. X3(NO3)2, X2(SO4)2, X2(PO4)3 D. X(NO3)3, X2(SO4)3, X2(PO4)3
35. A drop of a sample of food colouring (X) and four dyes (P, Q, R and S) are put onto a chromatography paper. The four dyes are banned because they are not safe to consume.
X P Q R S
Study the given chromatogram carefully and choose the correct statement among the following.
A. X contains P and Q dyes.
B. Dyes P and S are mixtures of two different dyes. C. X contains R dye.
D. Dyes P and R are pure.
36. Refer to the given flow chart for kingdom Plantae.
Z
Y X Plant body is differentiated into
true roots, stem and leaves Plants possess seeds
Yes
No
No Yes
Select the correct statement regarding X, Y and Z. A. X can be thallophytes such as algae and fungi. B. Y can be bryophytes or pteridophytes.
C. Y can be cryptogams such as pteridophytes. D. Z can be angiosperms only.
37. Which of the following statements is incorrect? A. Walls of the arteries are elastic, enabling them
to stretch and contract with changes in blood pressure.
B. Blood pressure in the veins is normally too low for blood to return to the heart without the action of skeletal muscles.
C. Because of their small size, the blood in capillaries move more quickly than in other parts of circulatory system.
D. Veins are typically larger in diameter than the arteries.
38. Identify the given type of animal tissue and select the incorrect statement regarding this.
A. In the intestinal mucosa, these cells possess microvilli to increase the absorptive surface area and the tissue is called as brush- bordered columnar epithelium.
B. In Fallopian tubes of females, these cells possess cilia for the movement of ovum/zygote and
the tissue is referred to as ciliated columnar epithelium.
C. In mucous membrane of stomach, these cells develop mucus secreting cells called goblet cells and the tissue is referred to as glandular columnar epithelium.
D. In the nephrons of kidneys, these cells possess cilia which keep the urine moving and the tissue is called as ciliated columnar epithelium.
39. Read the given statements and select the correct option.
Statement 1 : The trees that are present on road sides, usually do not show the growth of lichens.
Statement 2 : Lichens are very sensitive to the levels of contaminants like SO2 present in air.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1. C. Statement 1 is true and statement 2 is false. D. Both statements 1 and 2 are false.
40. Study the given pedigree chart. The disease is caused by a recessive allele t and T is the dominant allele for normal condition.
1 1 1 2 2 2 3 Normal female Key I II III Normal male Diseased female Diseased male
Work out the genotypes of individuals from the given pedigree chart and select the correct option.
I-2 II-1 III-2
A. Tt tt Tt
B. TT tt Tt
C. Tt tt TT
D. tt Tt Tt
41. Given figure shows a part of the food web in terrestrial ecosystem.
Which of the following correctly represents pyramid of energy based on the given food web?
A. B.
C.