Free Printable 10th IIT Cumulative

1.

$\int_{ }^{ }\frac{x^3}{x+1}dx=$

a)

$\frac{x^3}{3}-\frac{x^2}{2}+x-\ln\left|x+1\right|+c$

b)

$\frac{x^3}{3}-2x+1-\ln\left|x\right|+c$

c)

$3x^2-\frac{x^2}{2}+x-\ln\left|x+1\right|+c$

d)

none of these

2.

$\int_{ }^{ }\frac{x^3}{2x+1}dx=$

a)

$\frac{1}{8}\left[\left(4x^3-x^2+x\right)-\ln\left|2x+1\right|\right]+c$

b)

$\frac{1}{8}\left[\left(\frac{4}{3}x^3-x^2+x\right)-\frac{\ln\left|2x+1\right|}{2}\right]+c$

c)

$\frac{1}{8}\left[\left(4x^3-x^2+x\right)\right]+c$

d)

None

3.

$\int_{ }^{ }\left(e^{x\ln a}-e^{a\ln x}+3e^{a\ln a}\right)dx=$

a)

$\frac{a^x}{\ln a}-\frac{x^{a+1}}{a+1}+3x+c$

b)

$\frac{a^x}{\ln a}+\frac{x^a}{a+1}+3+c$

c)

$\frac{a^x}{\ln a}+\frac{x^{a+1}}{a}+c$

d)

None

4.

$\int_{ }^{ }\frac{1}{\sqrt{1-4x^2}}dx=$

a)

$\frac{\sin^{-1}x}{2}+c$

b)

$\frac{\sin^{-1}2x}{2}+c$

c)

$\sin^{-1}2x+c$

d)

$\frac{\sin^{-1}2x}{3}+c$

5.

$\int_{ }^{ }\sin^2x.\cos^2xdx=$

a)

$\frac{1}{8}\left[x+\frac{\sin4x}{4}\right]+c$

b)

$\frac{1}{8}\left[x-\frac{\sin4x}{4}\right]+c$

c)

$\frac{1}{32}\left[x-\frac{\sin4x}{4}\right]+c$

d)

None of these

6.

$\int_{ }^{ }\left(\frac{\sin^6x+\cos^6x}{\tan^2x}\right)\sec^4xdx=$

a)

tanx+cotx+c

b)

cotx-tanx+c

c)

tanx-cotx+c

d)

None of these

7.

If $\int_{ }^{ }\frac{\sin x}{\sin\left(x-\alpha\right)}dx\ =$ $Ax+B\log\sin\left(x-\alpha\right)+C\$ $then\ \left(A,B\right)=$

a)

$\left(\cos\alpha,\sin\alpha\right)$

b)

$\left(\sin\alpha,\cos\alpha\right)$

c)

$\left(\sin\alpha,-\cos\alpha\right)$

d)

$\left(-\cos\alpha,-\sin\alpha\right)$

8.

The value of $\sqrt{2}\int_{ }^{ }\frac{\sin xdx}{\sin\left(x-\frac{\pi}{4}\right)}=$

a)

$x+\ln\left|\sin\left(x-\frac{\pi}{4}\right)\right|+c$

b)

$2\left[x+\ln\left|\sin\left(x-\frac{\pi}{4}\right)\right|\right]+c$

c)

$2\left[x-\ln\left|\sin\left(x-\frac{\pi}{4}\right)\right|\right]+c$

d)

None of these

9.

$\int_{ }^{ }\frac{dx}{\cos x-\sin x}=$

a)

$\frac{1}{\sqrt{2}}\ln\left|\tan\left(\frac{x}{2}+\frac{3\pi}{8}\right)\right|+c$

b)

$\sqrt{2}\ln\left|\tan\left(\frac{x}{2}+\frac{3\pi}{8}\right)\right|+c$

c)

$\sqrt{2}\ln\left|\tan\left(\frac{x}{2}-\frac{3\pi}{8}\right)\right|+c$

d)

None of these

10.

$\int_{ }^{ }\frac{dx}{\cos x+\sqrt{3}\sin x}=$

a)

$\frac{1}{2}\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{12}\right)\right|+c$

b)

$\frac{1}{2}\ln\left|\tan\left(\frac{x}{2}-\frac{\pi}{12}\right)\right|+c$

c)

$\frac{1}{2}\left[\ln\left|\tan\left(x-\frac{\pi}{12}\right)\right|\right]+c$

d)

None

11.

$\int_{ }^{ }x^2\sin x^3dx=$

a)

$-\frac{\cos x^3}{3}+c$

b)

$\frac{\cos x^3}{3}+c$

c)

$\frac{\sin x^3}{3}+c$

d)

$-\ \frac{\sin x^3}{3}+c$

12.

$\int_{ }^{ }\sin3x.\sin6xdx=$

a)

$\frac{2}{3}\left(\sin^23x\right)+c$

b)

$\frac{2}{9}\left(\sin^23x\right)+c$

c)

$\frac{1}{9}\left(\sin^23x\right)+c$

d)

$\frac{2}{9}\left(\cos^23x\right)+c$

13.

$\int_{ }^{ }\frac{dx}{\sqrt{x\ \left(2-\sqrt{x}\right)}}=$

a)

$-2\ln\left|2-\sqrt{x}\right|+c$

b)

$2\ln\left|2+\sqrt{x}\right|+c$

c)

$-2\ln\left|2+\sqrt{x}\right|+c$

d)

None of these

14.

$\int_{ }^{ }\frac{x^2dx}{\left(a+bx\right)^2}\ =$

a)

$\frac{1}{b^3}\left[t-2a\ln\left|t\right|\frac{-a^2}{t}\right]$

b)

$\frac{1}{b^3}\left[t-2a\ln\left|t\right|\frac{-a^2}{t}\right]+c$

c)

$\frac{1}{b}$

d)

None of these

15.

$\int_{ }^{ }\frac{\sin x}{\sin x-\cos x}dx\ =$

a)

$\frac{1}{3}\left[x+\ln\left|\sin x-cox\right|\right]+c$

b)

$\frac{1}{3}\left[x+\ln\left|\sin x+cox\right|\right]+c$

c)

$\frac{1}{2}\left[x+\ln\left|\sin x-\cos x\right|\right]+c$

d)

None of these

16.

If $\int_{ }^{ }\sec^2x.\operatorname{cosec}^4xdx\ =$ $-\frac{1}{3}\cot^3x+k\tan x$ $-2\cot x+c\ \Longrightarrow k\ =$

a)

4

b)

3

c)

2

d)

1

17.

If $\int_x^y\ \frac{\sin^8x-\cos^8x}{1-2\sin^2x.\cos^2x}dx=$ $A\sin2x+B$ then A =

a)

$-\frac{1}{2}$

b)

$-1$

c)

$\frac{1}{2}$

d)

$1$

18.

$\int_{ }^{ }\left(\frac{\sqrt{a+x}}{a-x}+\frac{\sqrt{a-x}}{a+x}\right)dx=$

a)

$2\sin^{-1}\left(\frac{x}{a}\right)+c$

b)

$2a\sin^{-1}\left(\frac{x}{a}\right)+c$

c)

$2\cos^{-1}\left(\frac{x}{a}\right)+c$

d)

$2a\cos^{-1}\left(\frac{x}{a}\right)+c$

19.

$\int_{ }^{ }\left(1+x-\frac{1}{x}\right)e^{x+\frac{1}{x}}dx=$

a)

$\left(x+1\right)e^{x+\frac{1}{x}}+c$

b)

$-xe^{x+\frac{1}{x}}+c$

c)

$-xe^{x+\frac{1}{x}}$

d)

$xe^{x+\frac{1}{x}}+c$

20.

$\int_{ }^{ }\frac{dx}{\cos\left(x+4\right)\cos\left(x+2\right)}=$

a)

$\frac{1}{\sin^2}\log\left|\sec\left(x+4\right)^2\right|+c$

b)

$\frac{1}{2}\log\left|\frac{\sec\left(x+2\right)}{\sec\left(x+4\right)}\right|+c$

c)

$\frac{1}{\sin^2}\log\left|\frac{\cos\left(x+4\right)}{\cos\left(x+2\right)}\right|+c$

d)

None of these

21.

$2n_{c2}+2n_{c4}+....+2n_{c2n}=$

a)

$2^{2n}$

b)

$2^{2n}-1$

c)

$2^{2n-1}$

d)

$2^{2n-1}-1$

22.

If n is odd, $n_{c1}+n_{c3}+n_{c5}+..........$ $....+nc_{2\left[\frac{n}{2}\right]-1}=$ where [ ] denotes g.i.f

a)

$2^n-1$

b)

$2^{n-1}-1$

c)

$2^n$

d)

$2^n-1$

23.

$C_0+2.C_1+3.C_2+.....$ $...+\left(n+1\right).C_n=$

a)

$\left(n+2\right)2^n$

b)

$n.2^n$

c)

$n.2^{n-1}$

d)

$\left(n+2\right).2^{n-1}$

24.

If $n\ge2$ then $3.c_1-4.c_2+5.c_3....$ $...+\left(-1\right)^{n-1}\left(n+2\right).c_n=$

a)

$-1$

b)

$2$

c)

$-2$

d)

$1$

25.

$\frac{c_1}{c_0}+2.\ \frac{c_r}{c_1}+3.\ \frac{c_3}{c_2}+....$ $...+n\ \frac{c_n}{c_{n-1}}=$

a)

$\frac{\left(n+1\right)\left(n+2\right)}{2}$

b)

$\frac{n\left(n+1\right)}{2}$

c)

$\frac{n\left(n-1\right)}{2}$

d)

$\frac{n\left(n+2\right)}{2}$

26.

If $n_{p_1}=42\times n_{p_5}$ then n =

a)

24

b)

12

c)

36

d)

7

27.

If $18_{p_{\left(r-1\right)}}:\ 17_{p_{\left(r-1\right)}}=9:7$ then r =

a)

5

b)

15

c)

20

d)

25

28.

The number of ways in which ‘n’ people can be seated around a circular table is _______

a)

n!

b)

$\frac{1}{2}$ (n-1)!

c)

(n-1)!

d)

n(n-1)!

29.

No.of 4 letter words that begin with E from EQUATION ____

a)

210

b)

120

c)

360

d)

480

30.

$n_{P_r}=$

a)

$r!\ n_{C_r}$

b)

$n_{C_r}-n_{C_{r-1}}$

c)

$n_{P_{r-1}}$

d)

None of these

31.

A spring of spring constant 8Ncm-1 has an extension of 5cm. The minimum work done in joules in increasing the extension from 5 cm to 15cm is

a)

4

b)

6

c)

8

d)

10

32.

For a parallel combination of two springs of force constants $k_1$ and $k_2$ the equivalent force constant of the combination is

a)

$k_1+k_2$

b)

$\frac{k_1k_2}{k_1+k_2}$

c)

$\frac{k_1+k_2}{k_1k_2}$

d)

$k_1-k_2$

33.

Work done in stretching the spring through a distance x is given by [k is a spring constant]

a)

$kx$

b)

$kx^2$

c)

$\frac{1}{2}kx^2$

d)

$\frac{1}{4}kx^2$

34.

Work done by spring force round the trip is

a)

zero

b)

positive

c)

negative

d)

infinite

35.

Work is said to be done by a force

a)

if the body has a displacement

b)

if the magnitude of the force is not equal to zero

c)

if the force or component of the force is along the direction of

the displacement

d)

None of the above

36.

A body is pushed through 4.0m across a floor offering 100N resistance, then the work done by the force is

a)

40J

b)

4000J

c)

zero

d)

400J

37.

When a force vector $\overrightarrow{\ F\ \ }=\left(_i^{\wedge}+2_j^{\wedge}+_k^{\wedge}\right)N$ acts on a body and produces a displacement of $\overrightarrow{\ S\ \ }=\left(4_i^{\wedge}+_j^{\wedge}+7_k^{\wedge}\right)N$ , then the work done is

a)

13 J

b)

5J

c)

9 J

d)

1 J

38.

A bob of mass m is suspended from the ceiling of a train moving with an acceleration ‘a’ as shown in the figure. Find the angle θ in equilibrium position.

a)

$\tan^{-1}\left(\frac{a}{g}\right)$

b)

$\tan^{-1}\left(\frac{2a}{g}\right)$

c)

$\tan^{-1}\left(\frac{a}{2g}\right)$

d)

$\tan^{-1}\left(\frac{a}{3g}\right)$

39.

All surfaces are smooth in the following figure. Find F such that block remains stationary with respect to wedge.

a)

$\left(M+m\right)g\sin\theta$

b)

$2\left(M-m\right)g\tan\theta$

c)

$\left(M+m\right)g\tan\theta$

d)

$\left(M+m\right)g\cot\theta$

40.

A cage in which a bird is sitting is hung from a spring balance. After some time the bird starts flying in the cage. The reading of weight in the spring balance will

a)

remains unchanged

b)

increase

c)

decrease

d)

depends upon whether the bird flies up or down

41.

The number of normal forces acting on a body depends on

a)

number of points or surfaces of contact

b)

mass of body

c)

color of the body

d)

both (1) and (2)

42.

A book lying on a smooth horizontal table. Then the free body diagram of the book.

a)

b)

c)

d)

43.

A screw jack of pitch 5 mm is used to lift the tyre of a vehicle of load 200 kg with the help of a handle of length 0.5 m. Neglecting the friction force between screw and nut of the jack, the least force required to raise the load is _________ $\times10^{-1}N$

a)

79

b)

75

c)

32

d)

47

44.

The work done by gravity on a mass 2 kg falling from a height 3 m is _______ Joule. $\left(g=10\ \frac{m}{s^2}\right)$

a)

60 J

b)

40 J

c)

100 J

d)

30 J

45.

A particle is displaced to position $\left(3_i^{\wedge}+4_j^{\wedge}\right)$ from $\left(3_j^{\wedge}-2_k^{\wedge}\right)$ under the force $\left(_i^{\wedge}-_j^{\wedge}+_k^{\wedge}\right)N.$ The work done by the force is _______joule.

a)

2 J

b)

3 J

c)

5 J

d)

4 J

46.

The work done depends upon

a) mass of the body

b) Displacement of the body

c) Initial velocity of the body

d) Angle between the force vector and displacement vector

a)

a,b,d

b)

a,c,d

c)

b,c,d

d)

a,b,c

47.

20 J of work is done by applying a force 5N on the object, the displacement of the object is

a) 40

b) 0.4m

c) 4m

d) 400cm

a)

a,c

b)

b,c

c)

c,d

d)

a,d

48.

Find the mass M of the hanging block in figure which will prevent the

smaller block from slipping over the triangular block. All the surfaces

are frictionless and the strings and the pulleys are light.

a)

a,b

b)

b,c

c)

c,d

d)

a,d

49.

a)

a,b,c

b)

b,c,d

c)

a,c,d

d)

a,b,c,d

50.

Spring force is a

a) Variable force

b) Constant force

c) conservative force

d) non-conservative force

a)

a,b

b)

a,c

c)

b,c

d)

a,b,c,d

51.

Find the work done, at the end of displacement 1m.

a)

1 J

b)

5 J

c)

9 J

d)

4 J

52.

Find the work done, at the end of displacement 3 m.

a)

20 J

b)

30 J

c)

10 J

d)

5 J

53.

Find the work done in displacing the body from x=1m to x=5m

a)

30 J

b)

25 J

c)

20 J

d)

15 J

54.

The free body diagram of ' $m_1$ '

a)

b)

c)

d)

55.

The free body diagram of ' $m_2$ ' is

a)

b)

c)

d)

56.

The acceleration of the system is

a)

$a=\frac{m_2g}{m_1+m_2}$

b)

$a=\left(\frac{m_2-m_1}{\left(m_1+m_2\right)}\right)g$

c)

$a=\left(\frac{m_1g}{\left(m_1+m_2\right)}\right)$

d)

$a=\left(\frac{2m_1m_2}{\left(m_1+m_2\right)}\right)g$

57.

Statement-I: The work done by a friction on a body sliding down on inclined plane is positive.

Statement-II: Work done is greater than zero if angle between force and displacement is acute.

a)

Both Statement I and II are true

b)

Both Statement I and II are false

c)

Statement I is true, Statement II is false

d)

Statement I is false, Statement II is true

58.

Statement-I: Both a stretched spring and a compressed spring have potential energy

Statement-II: Work is to be done against restoring force in each case of stretching and compressing of the spring.

a)

Both Statement I and II are true

b)

Both Statement I and II are false

c)

Statement I is true, Statement II is false

d)

Statement I is false, Statement II is true

59.

a)

$a\rightarrow q;\ b\rightarrow p;\ c\rightarrow r;\ d\rightarrow s$

b)

$a\rightarrow p;\ b\rightarrow q;\ c\rightarrow r;\ d\rightarrow s$

c)

$a\rightarrow q;\ b\rightarrow s;\ c\rightarrow r;\ d\rightarrow p$

d)

$a\rightarrow r;\ b\rightarrow p;\ c\rightarrow s;\ d\rightarrow q$

60.

a)

$a\rightarrow q;\ b\rightarrow p;\ c\rightarrow r;\ d\rightarrow s$

b)

$a\rightarrow p;\ b\rightarrow q;\ c\rightarrow r,s;\ d\rightarrow t$

c)

$a\rightarrow q;\ b\rightarrow s;\ c\rightarrow r;\ d\rightarrow p$

d)

$a\rightarrow r;\ b\rightarrow p;\ c\rightarrow t;\ d\rightarrow q$

61.

Elements of IB and III B are called :

a)

Normal elements

b)

Transition elements

c)

Alkaline earth metals

d)

Alkali metals

62.

The electronic configuration of Rb :

a)

$2s^1$

b)

$3s^1$

c)

$\left(Ar\right)4s^1$

d)

$\left(Kr\right)5s^1$

63.

Which of the following group contains coinage metals :

a)

IB

b)

II B

c)

III B

d)

IV B

64.

Which pair of elements is from the same period of the periodic table?

a)

Cl, Br

b)

Na, Ca

c)

K, Br

d)

Cl, Li

65.

The atom having the valence shell electronic configuration $4s^24p^2$ would be in

a)

Group 2 or IIA and period 3

b)

Group 12 or IIB and period 4

c)

Group 14 or IVA and period 4

d)

Group 14 or IVA and period 3

66.

Hybrid orbital having maximum P- character is

a)

$sp^3d$

b)

$sp^3$

c)

sp

d)

$sp^3d^2$

67.

The hybridisation of Nitrogen in Nitrate ion is

a)

sp

b)

$sp^2$

c)

$sp^3$

d)

$sp^3d$

68.

Which of the following is the correct set with reference to molecular

formula hybridisation of central atom and shape of the molecule?

a)

$CO_2,\ sp^2\ bent$

b)

$H_2O,\ sp^2bent$

c)

$BeCl_2,\ sp\ linear$

d)

All

69.

Number of hybrid orbitals present in a molecules of propane are

[CH3–CH2–CH3]

a)

8

b)

10

c)

12

d)

14

70.

The hybridisation of Bromine in $BrF_5$ molecule is

a)

$sp^3$

b)

$sp^3d$

c)

$sp^3d^2$

d)

$sp^3d^3$

71.

The bonds present in NaCN are

a)

Ionic bond

b)

covalent bond

c)

Co-ordinate covalent bond

d)

Ionic and covalent bonds

72.

In which of the following dative bond is not present

a)

$H_2O^+$

b)

$NH_4^+$

c)

$Al_2Cl_6$

d)

$N_2H_4$

73.

The compound which contains both ionic and covalent bonds is

a)

$CH_4$

b)

$H_2O$

c)

KCN

d)

KCl

74.

The types of bonds present in $CuSO_4,\ 5H_2O\$ are

a)

Electrovalent and covalent

b)

Electrovalent and co-ordinate covalent

c)

Electrovalent, covalent, co-ordinate covalent and hydrogen bond

d)

Covalent and co-ordinate covalent

75.

The maximum number of molecules that one water molecule can hold through hydrogen bonding is

a)

2

b)

4

c)

6

d)

8

76.

Statement 1: An atom with lone pair of electron may act as donor

Statement 2 : $BF_3,\ BCl_3$ acts as donor species

a)

Both statement I and II are correct

b)

Both statement I and II are incorrect

c)

Statement I is correct and statement II is incorrect

d)

Statement I is incorrect and statement II is correct

77.

Statement I : The ratio of lone pair of electron to bond pair of electron

in valence shell of a molecule of $IF_7$ is 3:1

Statement II : In $IF_7$ I shows $sp^3d^3$ hybridisation to attain pentagonal

bi-pyramid geometry

a)

Both statement I and II are correct.

b)

Both statement I and II are incorrect

c)

Statement I is correct and statement II is incorrect.

d)

Statement I is incorrect and statement II is correct.

78.

Which of the following are planar molecule?

a) $BF_3$

b) $C_2H_4$

c) $XeF_4$

d) $NH_3$

a)

a,b,c

b)

b,c,d

c)

a,c,d

d)

a,b,d

79.

The state of hybridisation of carbon atoms in $H_2C\ =\ CH-C=CH$ is

a) $sp^3$

b) $sp^2$

c) sp

d) $sp^3d$

a)

a,b

b)

b,c

c)

c,d

d)

a,d

80.

Group 18 (or zero group) elements are also called as:

a) Inert gases b) Rare gases c) Noble gases d) Inactive gases

a)

a,b only

b)

c,d only

c)

a,b,c only

d)

a,b,c,d

81.

Among the following elements having same general electronic configuration is $nS^2$

a) Ca b) Sr c) Be d) Li

a)

a,b only

b)

cd only

c)

abc only

d)

abcd

82.

$NH_4CN$ contains

a) Ionic bond b) Covalent bond

c) Dative bond d) Vander Walls bond

a)

abc

b)

bcd

c)

acd

d)

abcd

83.

The bond formed between two atoms by the sharing of an electron

pair which is contributed by only one of the two atoms is known as

the co-ordinate covalent bond

When a cation gets hydrated, normally the bond formed between

cation and water molecule is

a)

Dative bond

b)

Ionic bond

c)

Covalent bond

d)

Hydrogen bond

84.

The bond formed between two atoms by the sharing of an electron

pair which is contributed by only one of the two atoms is known as

the co-ordinate covalent bond

Molecule having maximum number of dative bonds is

a)

$H_2O_2$

b)

$NH_4^+$

c)

$Al_2Cl_6$

d)

$B_3N_3H_6$

85.

The bond formed between two atoms by the sharing of an electron

pair which is contributed by only one of the two atoms is known as

the co-ordinate covalent bond

$NH_3$ and $BF_3$ form an adduct readily because they form

a)

A co-ordinate covalent bond

b)

A covalent bond

c)

An ionic bond

d)

A hydrogen bond

86.

Which of the Xenon fluorides is iso structural with $ICl_4^-$

a)

$XeF_4$

b)

$XeF_6$

c)

$XeF_2$

d)

$XeF_{\ \ \ 8}^{2-}$

87.

The shape of $XeO_3$ is

a)

Tetrahedral

b)

Pyramidal

c)

Trigonal planar

d)

square planar

88.

Hybridisation of Xe in $XeF_2$ is

a)

$sp^3$

b)

$sp^3d$

c)

$sp^3d^2$

d)

$sp^3d^3$

89.

a)

$a\rightarrow s;\ b\rightarrow r;\ c\rightarrow q;\ d\rightarrow q$

b)

$a\rightarrow r;\ b\rightarrow p;\ c\rightarrow s;\ d\rightarrow q$

c)

$a\rightarrow r;\ b\rightarrow s;\ c\rightarrow q;\ d\rightarrow q$

d)

$a\rightarrow q,s;\ b\rightarrow r,s;\ c\rightarrow p,q;\ d\rightarrow r,s$

90.

a)

a-4;b-1;c-3;d-2

b)

a-2;b-1;c-3;d-4

c)

a-2;b-3;c-3;d-4

d)

a-3;b-2;c-1;d-4

10th IIT Cumulative - 5

Total questions: 90

Worksheet time: 3hrs 0mins

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