JEE Shikhar Online Test

Remaining Time :

Name : Vedant Godhwani

Exam Name : XI_Tesla_Test_PCM_Mains_17.10.21

PHYSICS CHEMISTRY MATHEMATICS

Single Correct Type Question + 4 - 1

Q.1:

A ball is dropped from the top of a building. The ball takes 0.5 s to fall past the 3 m length of a window which is at some distance below from the top of the building. If the speed of the ball at the top and at the bottom of the window are \({{v}_{T}}\) and \({{v}_{B}}\) respectively, then \(\left( g=9.8\,m/{{\sec }^{2}} \right)\)

\({{v}_{T}}+{{v}_{B}}=12\,m{{s}^{-1}}\)
\({{v}_{T}}-{{v}_{B}}=4.9\,m{{s}^{-1}}\)
\({{v}_{B}}{{v}_{T}}=1\,m{{s}^{-1}}\)
\(\dfrac{{{v}_{B}}}{{{v}_{T}}}=1\,m{{s}^{-1}}\)

Single Correct Type Question + 4 - 1

Q.2:

When a particle is thrown from some height horizontally with speed u, the resultant velocity of the projectile at any time t is given by

\(gt\)
\(\dfrac{1}{2}g{{t}^{2}}\)
\(\sqrt{{{u}^{2}}+{{g}^{2}}{{t}^{2}}}\)
\(\sqrt{{{u}^{2}}-{{g}^{2}}{{t}^{2}}}\)

Single Correct Type Question + 4 - 1

Q.3:

A particle is projected with velocity \({{v}_{0}}\) along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e., \(a=\alpha {{x}^{2}}.\) The distance at which the particle stops is

\(\sqrt{\dfrac{3{{v}_{0}}}{2\alpha }}\)
\({{\left( \dfrac{3{{v}_{0}}}{2\alpha } \right)}^{\dfrac{1}{3}}}\)
\(\sqrt{\dfrac{3v_{0}^{2}}{2\alpha }}\)
\({{\left( \dfrac{3v_{0}^{2}}{2\alpha } \right)}^{\dfrac{1}{3}}}\)

Single Correct Type Question + 4 - 1

Q.4:

A stone is thrown vertically upward with an initial speed u from the top of a tower, reaches the ground with a speed 3u. The height of the tower is

\(\dfrac{3{{u}^{2}}}{g}\)
\(\dfrac{4{{u}^{2}}}{g}\)
\(\dfrac{6{{u}^{2}}}{g}\)
\(\dfrac{9{{u}^{2}}}{g}\)

Single Correct Type Question + 4 - 1

Q.5:

One second after projection, a stone moves at an angle of \(45{}^\circ \) with the horizontal. Two seconds after projection, it moves horizontally. Its angle of projection is \(\left( g=10\,m/{{s}^{2}} \right)\)

\(60{}^\circ \)
\({{\tan }^{-1}}\left( 4 \right)\)
\({{\tan }^{-1}}\left( 3 \right)\)
\({{\tan }^{-1}}\left( 2 \right)\)

Single Correct Type Question + 4 - 1

Q.6:

A particle starts from rest. Its acceleration is varying with time as shown in the figure. When the particle comes to rest, its distance from its starting point is

20 m
24 m
36 m
14 m

Single Correct Type Question + 4 - 1

Q.7:

The graph between the displacement \(x\) and time t for a particle moving in a straight line is shown is figure. During the interval OA, AB, BC and CD, the acceleration of the particle is

OA AB BC CD

+ 0 + +
- 0 + 0
+ 0 - +
- 0 - +

Single Correct Type Question + 4 - 1

Q.8:

A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4 h. The two stones cross each other after time

\(\sqrt{\dfrac{h}{8g}}\)
\(\sqrt{8gh}\)
\(\sqrt{2gh}\)
\(\sqrt{\dfrac{h}{2g}}\)

Single Correct Type Question + 4 - 1

Q.9:

A ball is dropped from top of a tower of 100 m height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of \(50\,m/s\left( g=10\,m/{{s}^{2}} \right).\) They will cross each other after

Single Correct Type Question + 4 - 1

Q.10:

The initial speed of a body moving with some constant acceleration is u. This speed is doubled while covering a distance S. When it covers an additional distance S, its speed would become

\(\sqrt{3}\,u\)
\(\sqrt{5}\,u\)
\(\sqrt{11}\,u\)
\(\sqrt{7}\,u\)

Single Correct Type Question + 4 - 1

Q.11:

A boy stops after travelling 3 km towards east and then goes 4 km towards north along a plane road. The resultant displacement of the boy is

7 km
4 km
5 km
15 km

Single Correct Type Question + 4 - 1

Q.12:

Fig. shows the position of a particle moving on X-axis as function of time. How many times particle comes to rest.

Single Correct Type Question + 4 - 1

Q.13:

The displacement time graphs of two particles A and B are straight lines making angles of respectively \(30{}^\circ \) and \(60{}^\circ \) with the time axis. If the velocity of A is \({{v}_{A}}\) and that of B is \({{v}_{B}},\) then the value of \(\dfrac{{{v}_{A}}}{{{v}_{B}}}\) is

\(\dfrac{1}{2}\)
\(\dfrac{1}{\sqrt{3}}\)
\(\sqrt{3}\)
\(\dfrac{1}{3}\)

Single Correct Type Question + 4 - 1

Q.14:

The velocity time graph of a particle moving along a straight line in a given time interval is as shown in figure. Then the particle (with increase in time starting from t = 0 sec.)

speeds up
speeds down
first speeds down and then speeds up
first speeds up and then speeds down

Single Correct Type Question + 4 - 1

Q.15:

The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point :

Single Correct Type Question + 4 - 1

Q.16:

Figure shows position-time graph of two cars A and B.

Car A is faster than car B
Car B is faster than car A
Both cars are moving with same velocity
Both cars have positive acceleration

Single Correct Type Question + 4 - 1

Q.17:

The initial velocity of a particle is u (at t = 0) and the acceleration f is given by (f = at). Which of the following relations is valid?

\(v=u+a{{t}^{2}}\)
\(v=u+\dfrac{a{{t}^{2}}}{2}\)
\(v=u+at\)
\(v=u\)

Single Correct Type Question + 4 - 1

Q.18:

A stone is released from a hot air balloon going up with an acceleration a. The acceleration of the stone after the release as seen from ground is

a upward
(g-a) upward
(g-a) downward
g downward

Single Correct Type Question + 4 - 1

Q.19:

A body starts from rest and is uniformly accelerated for 30 s. The distance travelled in the first 10 s is \({{x}_{1}},\) next 10 s is \({{x}_{2}}\) and the last 10 s is \({{x}_{3}}.\) Then \({{x}_{1}}:{{x}_{2}}:{{x}_{3}}\) is the same as

1 : 2 : 4
1 : 2 : 5
1 : 3 : 5
1 : 3 : 9

Single Correct Type Question + 4 - 1

Q.20:

If the displacement of a particle is zero, then what can we say about its distance covered

It must be zero
It cannot be zero
It is negative
It may or may not be zero

Numerical Correct Type Question + 4 - 0

Q.21:

A particle travels half the distance of a straight journey with a speed 5 m/s. The remaining part of the distance is covered with speed 6 m/s for half the remaining time, and with speed 4 m/s for the other half of the remaining time. The average speed of the particle is (in m/s)

Numerical Correct Type Question + 4 - 0

Q.22:

The diagram shows the displacement-time graph for the particle moving in a straight line. What is average speed (in m/s) for the interval 0-10 s?

Numerical Correct Type Question + 4 - 0

Q.23:

An object projected with same speed at two different angles covers the same horizontal range R. If the two times of flight be \({{t}_{1}}\) and \({{t}_{2}}.\)Then range is \(\dfrac{1}{\alpha }g{{t}_{1}}{{t}_{2}},\) find the value of \(\alpha \)

Numerical Correct Type Question + 4 - 0

Q.24:

The position of a particle is given by \(x={{\left( t-2 \right)}^{2}},\) where \(x\) is in metre and \(t\) is in second. Find the distance covered by the particle in first 4 seconds in m.

Numerical Correct Type Question + 4 - 0

Q.25:

A train traveling along a straight track with a speed of \(2\,m{{s}^{-1}},\)begins to accelerate with \(a=\dfrac{2}{v}\,m{{s}^{-2}},\) where \(v\) is in \(m{{s}^{-1}}.\)Find its velocity after 3 seconds in m/s.

Numerical Correct Type Question + 4 - 0

Q.26:

A person can throw a stone to a maximum distance of 100 m. The greatest height to which he can throw the stone is

Numerical Correct Type Question + 4 - 0

Q.27:

A thief is rutting away on a straight road in a jeep moving with a speed of \(9m\,{{s}^{-1}}.\) A police man chases him on a motor cycle moving at a speed of \(10m\,{{s}^{-1}}.\) If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the police man to catch the thief? (in s)

Numerical Correct Type Question + 4 - 0

Q.28:

A body is thrown horizontally from the top of a tower of height 5 m. It touches the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is \(\left( g=10m\,{{s}^{-2}} \right)\) (in m/s)

Numerical Correct Type Question + 4 - 0

Q.29:

A particle is moving in a straight line and passes through a point O with a velocity of \(6m\,{{s}^{-1}}.\) The particle moves with a constant retardation of \(2m\,{{s}^{-2}}\) for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O

Numerical Correct Type Question + 4 - 0

Q.30:

A particle, initially at rest, starts moving in a straight line with an acceleration \(a=10\,m/{{s}^{2}}.\) The distance covered by it in 3 s is

Single Correct Type Question + 4 - 1

Q.31:

Out of following which one has least value of melting point

LiCl
\(BeC{{l}_{2}}\)
\(MgC{{l}_{2}}\)
\(CaC{{l}_{2}}\)

Single Correct Type Question + 4 - 1

Q.32:

Polarisation power is defined for

cation
anion
for both
none of the above

Single Correct Type Question + 4 - 1

Q.33:

Which of the following compound have highest melting point.

ionic
covalent
coordination
metallic

Single Correct Type Question + 4 - 1

Q.34:

According to VBT theory covalent bond is formed by

overlapping of valence shell half filled orbital
overlapping of inner shell half filled orbital
overlapping of inner shell full filled orbital
overlapping of valence shell full filled orbital

Single Correct Type Question + 4 - 1

Q.35:

Which bond is most polar

\(OH\)
\(CH\)
\(FH\)
\(NH\)

Single Correct Type Question + 4 - 1

Q.36:

Which of the following have highest water solubility

\(LiF\)
\(LiCl\)
\(LiBr\)
\(LiI\)

Single Correct Type Question + 4 - 1

Q.37:

Which of the following have highest water solubility

\(LiCl\)
\(NaCl\)
\(KCl\)
\(CsCl\)

Single Correct Type Question + 4 - 1

Q.38:

Shape of \(S{{F}_{6}}\) is

tetrahedral shape
octahedral shape
pyramidal shape
triangular bi-pyramidal shape

Single Correct Type Question + 4 - 1

Q.39:

Shape of \(BC{{l}_{3}}\) is

tetrahedral shape
triangular planar shape
pyramidal shape
triangular bi-pyramidal shape

Single Correct Type Question + 4 - 1

Q.40:

According to VSEPR Theory, for a compound having formula \(A{{B}_{5}}\) (no lone pair), shape of molecule will be

tetrahedral shape
triangular planar shape
pyramidal shape
triangular bi-pyramidal shape

Single Correct Type Question + 4 - 1

Q.41:

Which of the following compound is exception for lewis theory

\(MgC{{l}_{2}}\)
\(NaCl\)
\({{H}_{2}}S{{O}_{4}}\)
\({{H}_{2}}O\)

Single Correct Type Question + 4 - 1

Q.42:

Which of the following compound is exception for lewis theory

\(NO\)
\(C{{O}_{2}}\)
\(C{{H}_{4}}\)
\(N{{H}_{3}}\)

Single Correct Type Question + 4 - 1

Q.43:

According to lewis atoms combines to get …………… electrons in valence shell.

Single Correct Type Question + 4 - 1

Q.44:

Lewis theory is based on

stability of noble gases
unstability of noble gases
stability of hydrogen
unstability of hydrogen

Single Correct Type Question + 4 - 1

Q.45:

How many \(\sigma \) and \(\pi \) bonds are there in the molecule of tetracyanoethylene -

Nine \(\sigma \) and nine \(\pi \)
five \(\sigma \) and nine
Nine \(\sigma \) and seven \(\pi \)
Five \(\sigma \) and eight \(\pi \)

Single Correct Type Question + 4 - 1

Q.46:

Among \(LiCl,BeC{{l}_{2}},BC{{l}_{3}}\) and \(CC{{l}_{4}}\) the covalent bond character follows the order -

\(LiCl\) < \(BeC{{l}_{2}}\) > \(BC{{l}_{3}}\) > \(CC{{l}_{4}}\)
\(LiCl\) > \(BeC{{l}_{2}}\) < \(BC{{l}_{3}}\) < \(CC{{l}_{4}}\)
\(LiCl\) < \(BeC{{l}_{2}}\) < \(BC{{l}_{3}}\) < \(CC{{l}_{4}}\)
\(LiCl\) > \(BeC{{l}_{2}}\) > \(BC{{l}_{3}}\) > \(CC{{l}_{4}}\)

Single Correct Type Question + 4 - 1

Q.47:

Which of the following has highest melting point -

NaCl
NaI
NaBr
NaF

Single Correct Type Question + 4 - 1

Q.48:

Out of following which one has maximum ionic character -

NaCl
KCl
\(CaC{{l}_{2}}\)
\(MgC{{l}_{2}}\)

Single Correct Type Question + 4 - 1

Q.49:

Polarisation may be called as the distortion of the shape of an anion by an adjacently placed cation. Which of the following statements is/are correct ?

Minimum polarization is brought about by a cation of low radius
A large cation is likely to bring about a large degree of polarisation
Maximum polarisation is brought about by a cation of high charge
A small anion is likely to undergo a large degree of polarisation

Single Correct Type Question + 4 - 1

Q.50:

According to VSEPR Theory maximum repulsion is in between

bond pair – bond pair
lone pair – bond pair
lone pair – lone pair
All have same repulsion

Numerical Correct Type Question + 4 - 0

Q.51:

Number of \(\sigma -\) bond in methane

Numerical Correct Type Question + 4 - 0

Q.52:

How many \(\pi -\)bond are present in \(HCN\)

Numerical Correct Type Question + 4 - 0

Q.53:

How many \(\sigma -\)bond are present in benzene

Numerical Correct Type Question + 4 - 0

Q.54:

How many of the following are hypo-valent compound
\(C{{H}_{4}},PC{{l}_{5}},S{{F}_{6}},N{{H}_{3}},BeC{{l}_{2}},AlC{{l}_{3}},B{{F}_{3}},S{{O}_{3}},S{{O}_{2}}\)

Numerical Correct Type Question + 4 - 0

Q.55:

How many of the following are hyper valent compound
\(NO,PC{{l}_{5}},S{{F}_{6}},N{{H}_{3}},BeC{{l}_{2}},AlC{{l}_{3}},B{{F}_{3}},S{{O}_{3}},S{{O}_{2}}\)

Numerical Correct Type Question + 4 - 0

Q.56:

How many of the following are exception for lewis theory
\(NO,PC{{l}_{5}},S{{F}_{6}},N{{H}_{3}},BeC{{l}_{2}},AlC{{l}_{3}},B{{F}_{3}},S{{O}_{3}},S{{O}_{2}}\)

Numerical Correct Type Question + 4 - 0

Q.57:

How many of the following are not exception for lewis theory
\(C{{H}_{4}},NO,N{{O}_{2}},PC{{l}_{5}},S{{F}_{6}},N{{H}_{3}},BeC{{l}_{2}},AlC{{l}_{3}},B{{F}_{3}}\)

Numerical Correct Type Question + 4 - 0

Q.58:

How many \(\pi -\)bonds are present in \({{P}_{4}}{{O}_{10}}\)

Numerical Correct Type Question + 4 - 0

Q.59:

How many \(\sigma -\)bonds are present in \({{P}_{4}}{{O}_{6}}\)

Numerical Correct Type Question + 4 - 0

Q.60:

How many \(\sigma -\)bonds are present in \(PC{{l}_{5}}\)

Single Correct Type Question + 4 - 1

Q.61:

\(\dfrac{\cos 20{}^\text{o}+\ 8\sin 70{}^\text{o}\ \sin 50{}^\text{o}\ \sin 10{}^\text{o}}{{{\sin }^{2}}80{}^\text{o}}\)is equal to -

1
2
\(\dfrac{3}{4}\)
None of these

Single Correct Type Question + 4 - 1

Q.62:

\(\dfrac{\sin 7x+6\sin 5x+17\sin 3x+12\sin x}{\sin 6x+5\sin 4x+12\sin 2x}\)is equal to

\(\cos x\)
\(2\cos x\)
\(\sin x\)
\(2\sin x\)

Single Correct Type Question + 4 - 1

Q.63:

The circular wire of diameter 10 cm is cut and placed along the circumference of a circle of diameter 1 metre. The angle subtended by the wire at the centre of the circle is equal to-

\(\dfrac{\pi }{4}\)radian
\(\dfrac{\pi }{3}\)radian
\(\dfrac{\pi }{5}\)radian
\(\dfrac{\pi }{10}\)radian

Single Correct Type Question + 4 - 1

Q.64:

\(\left( 1+\cos \dfrac{\pi }{8} \right)\)\(\left( 1+\cos \dfrac{3\pi }{8} \right)\)\(\left( 1+\cos \dfrac{5\pi }{8} \right)\)\(\left( 1+\cos \dfrac{7\pi }{8} \right)\) is equal to-

\(\dfrac{1}{2}\)
cos\(\dfrac{\pi }{8}\)
\(\dfrac{1}{8}\)
\(\dfrac{1+\sqrt{2}}{2\sqrt{2}}\)

Single Correct Type Question + 4 - 1

Q.65:

The value of \(\tan 6{}^\circ \tan 42{}^\circ \tan 66{}^\circ \tan 78{}^\circ \) is-

Single Correct Type Question + 4 - 1

Q.66:

\(\dfrac{sin\theta +\sin 2\theta }{1+cos\theta +\cos 2\theta }=\)

\(\dfrac{1}{2}\tan \theta \)
\(\dfrac{1}{2}cot\theta \)
\(tan\theta \)
\(cot\theta \)

Single Correct Type Question + 4 - 1

Q.67:

If tan A = 1/3 and tan B = 1/7 then the value of 2A + B is -

\(30{}^\circ \)
\(60{}^\circ \)
\(45{}^\circ \)
\(145{}^\circ \)

Single Correct Type Question + 4 - 1

Q.68:

\(tan\dfrac{2\pi }{5}-tan\dfrac{\pi }{15}-\sqrt{3}tan\dfrac{2\pi }{5}\tan \dfrac{\pi }{15}\) is equal to -

\(-\sqrt{3}\)
\(\dfrac{1}{\sqrt{3}}\)
1
\(\sqrt{3}\)

Single Correct Type Question + 4 - 1

Q.69:

\(tan225{}^\circ \cot 405{}^\circ +tan765{}^\circ \cot 675{}^\circ =\)

0
1
\(\sqrt{2}\)
None

Single Correct Type Question + 4 - 1

Q.70:

\({{\sin }^{2}}5{}^\circ +{{\sin }^{2}}10{}^\circ +{{\sin }^{2}}15{}^\circ +.......+{{\sin }^{2}}85{}^\circ +{{\sin }^{2}}90{}^\circ =\)

7
8
9\(\dfrac{1}{2}\)
10

Single Correct Type Question + 4 - 1

Q.71:

If \(\sin x+{{\sin }^{2}}x=1,\) then \(co{{s}^{8}}x+2{{\cos }^{6}}x+{{\cos }^{4}}x=..........\)

0
– 1
2
1

Single Correct Type Question + 4 - 1

Q.72:

The value of \(\cos 1{}^\circ \cos 2{}^\circ \cos 3{}^\circ .........\cos 179{}^\circ \)is-

\(\dfrac{1}{\sqrt{2}}\)
0
1
None of these

Single Correct Type Question + 4 - 1

Q.73:

If \(A=\tan 6{}^\circ \tan 42{}^\circ \) and \(B=\cot 66{}^\circ \cot 78{}^\circ \), then -

A = 2B
\(A=\dfrac{1}{3}B\)
A = B
3A = 2B

Single Correct Type Question + 4 - 1

Q.74:

If \(f\left( \theta \right)=5\cos \theta +3\cos \left( \theta +\dfrac{\pi }{3} \right)+3,\) then range of \(f\left( \theta \right)\) is-

[–5, 11]
[–3, 9]
[–2, 10]
[–4, 10]

Single Correct Type Question + 4 - 1

Q.75:

The value of the expression \(\left( \sqrt{3}\sin 75{}^\circ -\cos 75{}^\circ \right)\) is -

\(2\sin 15{}^\circ \)
\(1+\sqrt{3}\)
\(2\sin 105{}^\circ \)
\(\sqrt{2}\)

Single Correct Type Question + 4 - 1

Q.76:

If secA + tanA = 3 then cosA is :

\(\dfrac{5}{3}\)
\(\pm \dfrac{3}{5}\)
\(\dfrac{3}{5}\)
none

Single Correct Type Question + 4 - 1

Q.77:

The numerical value of tan\(\dfrac{\pi }{3}\)+ 2tan\(\dfrac{2\pi }{3}\)+ 4tan \(\dfrac{4\pi }{3}\)+8 tan \(\dfrac{8\pi }{3}\)is equal to-

– 5\(\sqrt{3}\)
\(\dfrac{-5}{\sqrt{3}}\)
5\(\sqrt{3}\)
\(\dfrac{5}{\sqrt{3}}\)

Single Correct Type Question + 4 - 1

Q.78:

\(\dfrac{3cos\theta +cos3\theta }{3sin\theta -sin3\theta }\) is equal to-

\(1+{{\cot }^{2}}\theta \)
\({{\cot }^{4}}\theta \)
\({{\cot }^{3}}\theta \)
\(2\cot \theta \)

Single Correct Type Question + 4 - 1

Q.79:

If \(\cos A=\dfrac{3}{4}\) then the value of \(\sin \dfrac{A}{2}\)\(\sin \dfrac{5A}{2}\)is-

\(\dfrac{1}{32}\)
\(\dfrac{11}{8}\)
\(\dfrac{11}{32}\)
\(\dfrac{11}{16}\)

Single Correct Type Question + 4 - 1

Q.80:

If \(a\cos \theta -b\sin \theta =c,\) then \(a\sin \theta +b\cos \theta =\)

\(\pm \,\sqrt{{{a}^{2}}-{{b}^{2}}+{{c}^{2}}}\)
\(\pm \,\sqrt{-{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}\)
\(\pm \sqrt{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}\)
None

Numerical Correct Type Question + 4 - 0

Q.81:

If \(2\sin \theta +3\cos \theta =3.\) Then \(3\sin \theta -2\cos \theta =k,\left( k>0 \right),\) then find out value of k.

Numerical Correct Type Question + 4 - 0

Q.82:

If \({{\cos }^{2}}{{\theta }_{1}}+{{\cos }^{2}}{{\theta }_{2}}+{{\cos }^{2}}{{\theta }_{3}}=0\left( 0<\theta <\pi \right),\) then find out value of \(\sin {{\theta }_{1}}+\sin {{\theta }_{2}}+\sin {{\theta }_{3}}=.............\)

Numerical Correct Type Question + 4 - 0

Q.83:

If \(\sin x={{\cos }^{2}}x,\) then \({{\cos }^{2}}x\left( 1+{{\cos }^{2}}x \right)\) equals to….

Numerical Correct Type Question + 4 - 0

Q.84:

If the length of an arc of a circle of radius 5 cm subtending \(15{}^\circ \) angle of centre of circle is given by \(\dfrac{k\pi }{12}\)cm. Then value of k is equal to ………

Numerical Correct Type Question + 4 - 0

Q.85:

Value of \(4\cos 36{}^\circ -4\cos 72{}^\circ +4\sin 18{}^\circ \cos 36{}^\circ \) is

Numerical Correct Type Question + 4 - 0

Q.86:

If \(15{{\sin }^{4}}\alpha +10{{\cos }^{4}}\alpha =6\)then value of \(8{{\operatorname{cosec}}^{6}}\alpha +27se{{c}^{6}}\alpha -241\) is

Numerical Correct Type Question + 4 - 0

Q.87:

Value of \(\tan 9{}^\circ -\tan 27{}^\circ -\tan 63{}^\circ +\tan 81{}^\circ \) is equals to –

Numerical Correct Type Question + 4 - 0

Q.88:

The maximum value of the expression \(\dfrac{1}{{{\sin }^{2}}\theta +3\sin \theta \cos \theta +5{{\cos }^{2}}\theta }\) is

Numerical Correct Type Question + 4 - 0

Q.89:

Value of \(3{{\left( \sin x-\cos x \right)}^{4}}+6{{\left( \sin x+\cos x \right)}^{2}}+4\left( {{\sin }^{6}}x+{{\cos }^{6}}x \right)\)

Numerical Correct Type Question + 4 - 0

Q.90:

If \(A={{\cos }^{2}}\theta +{{\sin }^{4}}\theta ,\) then for all value of \(\theta \), Maximum value of A

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All Questions

Q.1) A ball is dropped from the top of a building. The ball takes 0.5 s to fall past the 3 m length of a window which is at some distance below from the top of the building. If the speed of the ball at the top and at the bottom of the window are \({{v}_{T}}\) and \({{v}_{B}}\) respectively, then \(\left( g=9.8\,m/{{\sec }^{2}} \right)\)

Question Type: single

Q.2) A body starts from rest and is uniformly accelerated for 30 s. The distance travelled in the first 10 s is \({{x}_{1}},\) next 10 s is \({{x}_{2}}\) and the last 10 s is \({{x}_{3}}.\) Then \({{x}_{1}}:{{x}_{2}}:{{x}_{3}}\) is the same as

Question Type: single

Q.3) When a particle is thrown from some height horizontally with speed u, the resultant velocity of the projectile at any time t is given by

Question Type: single

Q.4) A particle is projected with velocity \({{v}_{0}}\) along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e., \(a=\alpha {{x}^{2}}.\) The distance at which the particle stops is

Question Type: single

Q.5) A stone is thrown vertically upward with an initial speed u from the top of a tower, reaches the ground with a speed 3u. The height of the tower is

Question Type: single

Q.6) One second after projection, a stone moves at an angle of \(45{}^\circ \) with the horizontal. Two seconds after projection, it moves horizontally. Its angle of projection is \(\left( g=10\,m/{{s}^{2}} \right)\)

Question Type: single

Q.7) A particle starts from rest. Its acceleration is varying with time as shown in the figure. When the particle comes to rest, its distance from its starting point is

Question Type: single

Q.8) The graph between the displacement \(x\) and time t for a particle moving in a straight line is shown is figure. During the interval OA, AB, BC and CD, the acceleration of the particle is

OA AB BC CD

Question Type: single

Q.9) A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4 h. The two stones cross each other after time

Question Type: single

Q.10) A ball is dropped from top of a tower of 100 m height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of \(50\,m/s\left( g=10\,m/{{s}^{2}} \right).\) They will cross each other after

Question Type: single

Q.11) The initial speed of a body moving with some constant acceleration is u. This speed is doubled while covering a distance S. When it covers an additional distance S, its speed would become

Question Type: single

Q.12) If the displacement of a particle is zero, then what can we say about its distance covered

Question Type: single

Q.13) A boy stops after travelling 3 km towards east and then goes 4 km towards north along a plane road. The resultant displacement of the boy is

Question Type: single

Q.14) Fig. shows the position of a particle moving on X-axis as function of time. How many times particle comes to rest.

Question Type: single

Q.15) The displacement time graphs of two particles A and B are straight lines making angles of respectively \(30{}^\circ \) and \(60{}^\circ \) with the time axis. If the velocity of A is \({{v}_{A}}\) and that of B is \({{v}_{B}},\) then the value of \(\dfrac{{{v}_{A}}}{{{v}_{B}}}\) is

Question Type: single

Q.16) The velocity time graph of a particle moving along a straight line in a given time interval is as shown in figure. Then the particle (with increase in time starting from t = 0 sec.)

Question Type: single

Q.17) The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point :

Question Type: single

Q.18) Figure shows position-time graph of two cars A and B.

Question Type: single

Q.19) The initial velocity of a particle is u (at t = 0) and the acceleration f is given by (f = at). Which of the following relations is valid?

Question Type: single

Q.20) A stone is released from a hot air balloon going up with an acceleration a. The acceleration of the stone after the release as seen from ground is

Question Type: single

Q.21) A particle, initially at rest, starts moving in a straight line with an acceleration \(a=10\,m/{{s}^{2}}.\) The distance covered by it in 3 s is

Question Type: integer

Q.22) A particle travels half the distance of a straight journey with a speed 5 m/s. The remaining part of the distance is covered with speed 6 m/s for half the remaining time, and with speed 4 m/s for the other half of the remaining time. The average speed of the particle is (in m/s)

Question Type: integer

Q.23) The diagram shows the displacement-time graph for the particle moving in a straight line. What is average speed (in m/s) for the interval 0-10 s?

Question Type: integer

Q.24) An object projected with same speed at two different angles covers the same horizontal range R. If the two times of flight be \({{t}_{1}}\) and \({{t}_{2}}.\)Then range is \(\dfrac{1}{\alpha }g{{t}_{1}}{{t}_{2}},\) find the value of \(\alpha \)

Question Type: integer

Q.25) The position of a particle is given by \(x={{\left( t-2 \right)}^{2}},\) where \(x\) is in metre and \(t\) is in second. Find the distance covered by the particle in first 4 seconds in m.

Question Type: integer

Q.26) A train traveling along a straight track with a speed of \(2\,m{{s}^{-1}},\)begins to accelerate with \(a=\dfrac{2}{v}\,m{{s}^{-2}},\) where \(v\) is in \(m{{s}^{-1}}.\)Find its velocity after 3 seconds in m/s.

Question Type: integer

Q.27) A person can throw a stone to a maximum distance of 100 m. The greatest height to which he can throw the stone is

Question Type: integer

Q.28) A thief is rutting away on a straight road in a jeep moving with a speed of \(9m\,{{s}^{-1}}.\) A police man chases him on a motor cycle moving at a speed of \(10m\,{{s}^{-1}}.\) If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the police man to catch the thief? (in s)

Question Type: integer

Q.29) A body is thrown horizontally from the top of a tower of height 5 m. It touches the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is \(\left( g=10m\,{{s}^{-2}} \right)\) (in m/s)

Question Type: integer

Q.30) A particle is moving in a straight line and passes through a point O with a velocity of \(6m\,{{s}^{-1}}.\) The particle moves with a constant retardation of \(2m\,{{s}^{-2}}\) for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O

Question Type: integer

Q.31) Polarisation power is defined for

Question Type: single

Q.32) Which of the following compound have highest melting point.

Question Type: single

Q.33) According to VBT theory covalent bond is formed by

Question Type: single

Q.34) Which bond is most polar

Question Type: single

Q.35) Which of the following have highest water solubility

Question Type: single

Q.36) Which of the following have highest water solubility

Question Type: single

Q.37) Shape of \(S{{F}_{6}}\) is

Question Type: single

Q.38) Shape of \(BC{{l}_{3}}\) is

Question Type: single

Q.39) According to VSEPR Theory, for a compound having formula \(A{{B}_{5}}\) (no lone pair), shape of molecule will be

Question Type: single

Q.40) According to VSEPR Theory maximum repulsion is in between

Question Type: single

Q.41) Which of the following compound is exception for lewis theory

Question Type: single

Q.42) Which of the following compound is exception for lewis theory

Question Type: single

Q.43) Polarisation may be called as the distortion of the shape of an anion by an adjacently placed cation. Which of the following statements is/are correct ?

Question Type: single

Q.44) Out of following which one has least value of melting point

Question Type: single

Q.45) Out of following which one has maximum ionic character -

Question Type: single

Q.46) Which of the following has highest melting point -

Question Type: single

Q.47) Among \(LiCl,BeC{{l}_{2}},BC{{l}_{3}}\) and \(CC{{l}_{4}}\) the covalent bond character follows the order -

Question Type: single

Q.48) How many \(\sigma \) and \(\pi \) bonds are there in the molecule of tetracyanoethylene -

Question Type: single

Q.49) Lewis theory is based on

Question Type: single

Q.50) According to lewis atoms combines to get …………… electrons in valence shell.

Question Type: single

Q.51) Number of \(\sigma -\) bond in methane

Question Type: integer

Q.52) How many \(\pi -\)bond are present in \(HCN\)

Question Type: integer

Q.53) How many \(\sigma -\)bond are present in benzene

Question Type: integer

Q.54) How many of the following are hypo-valent compound
\(C{{H}_{4}},PC{{l}_{5}},S{{F}_{6}},N{{H}_{3}},BeC{{l}_{2}},AlC{{l}_{3}},B{{F}_{3}},S{{O}_{3}},S{{O}_{2}}\)

Question Type: integer

Q.55) How many of the following are hyper valent compound
\(NO,PC{{l}_{5}},S{{F}_{6}},N{{H}_{3}},BeC{{l}_{2}},AlC{{l}_{3}},B{{F}_{3}},S{{O}_{3}},S{{O}_{2}}\)

Question Type: integer

Q.56) How many of the following are exception for lewis theory
\(NO,PC{{l}_{5}},S{{F}_{6}},N{{H}_{3}},BeC{{l}_{2}},AlC{{l}_{3}},B{{F}_{3}},S{{O}_{3}},S{{O}_{2}}\)

Question Type: integer

Q.57) How many of the following are not exception for lewis theory
\(C{{H}_{4}},NO,N{{O}_{2}},PC{{l}_{5}},S{{F}_{6}},N{{H}_{3}},BeC{{l}_{2}},AlC{{l}_{3}},B{{F}_{3}}\)

Question Type: integer

Q.58) How many \(\pi -\)bonds are present in \({{P}_{4}}{{O}_{10}}\)

Question Type: integer

Q.59) How many \(\sigma -\)bonds are present in \({{P}_{4}}{{O}_{6}}\)

Question Type: integer

Q.60) How many \(\sigma -\)bonds are present in \(PC{{l}_{5}}\)

Question Type: integer

Q.61) \({{\sin }^{2}}5{}^\circ +{{\sin }^{2}}10{}^\circ +{{\sin }^{2}}15{}^\circ +.......+{{\sin }^{2}}85{}^\circ +{{\sin }^{2}}90{}^\circ =\)

Question Type: single

Q.62) If \(\cos A=\dfrac{3}{4}\) then the value of \(\sin \dfrac{A}{2}\)\(\sin \dfrac{5A}{2}\)is-

Question Type: single

Q.63) \(\dfrac{\cos 20{}^\text{o}+\ 8\sin 70{}^\text{o}\ \sin 50{}^\text{o}\ \sin 10{}^\text{o}}{{{\sin }^{2}}80{}^\text{o}}\)is equal to -

Question Type: single

Q.64) \(\dfrac{3cos\theta +cos3\theta }{3sin\theta -sin3\theta }\) is equal to-

Question Type: single

Q.65) The numerical value of tan\(\dfrac{\pi }{3}\)+ 2tan\(\dfrac{2\pi }{3}\)+ 4tan \(\dfrac{4\pi }{3}\)+8 tan \(\dfrac{8\pi }{3}\)is equal to-

Question Type: single

Q.66) If secA + tanA = 3 then cosA is :

Question Type: single

Q.67) The value of the expression \(\left( \sqrt{3}\sin 75{}^\circ -\cos 75{}^\circ \right)\) is -

Question Type: single

Q.68) If \(f\left( \theta \right)=5\cos \theta +3\cos \left( \theta +\dfrac{\pi }{3} \right)+3,\) then range of \(f\left( \theta \right)\) is-

Question Type: single

Q.69) If \(A=\tan 6{}^\circ \tan 42{}^\circ \) and \(B=\cot 66{}^\circ \cot 78{}^\circ \), then -

Question Type: single

Q.70) The value of \(\cos 1{}^\circ \cos 2{}^\circ \cos 3{}^\circ .........\cos 179{}^\circ \)is-

Question Type: single

Q.71) If \(\sin x+{{\sin }^{2}}x=1,\) then \(co{{s}^{8}}x+2{{\cos }^{6}}x+{{\cos }^{4}}x=..........\)

Question Type: single

Q.72) If \(a\cos \theta -b\sin \theta =c,\) then \(a\sin \theta +b\cos \theta =\)

Question Type: single

Q.73) \(tan225{}^\circ \cot 405{}^\circ +tan765{}^\circ \cot 675{}^\circ =\)

Question Type: single

Q.74) \(tan\dfrac{2\pi }{5}-tan\dfrac{\pi }{15}-\sqrt{3}tan\dfrac{2\pi }{5}\tan \dfrac{\pi }{15}\) is equal to -

Question Type: single

Q.75) If tan A = 1/3 and tan B = 1/7 then the value of 2A + B is -

Question Type: single

Q.76) \(\dfrac{sin\theta +\sin 2\theta }{1+cos\theta +\cos 2\theta }=\)

Question Type: single

Q.77) The value of \(\tan 6{}^\circ \tan 42{}^\circ \tan 66{}^\circ \tan 78{}^\circ \) is-

Question Type: single

Q.78) \(\left( 1+\cos \dfrac{\pi }{8} \right)\)\(\left( 1+\cos \dfrac{3\pi }{8} \right)\)\(\left( 1+\cos \dfrac{5\pi }{8} \right)\)\(\left( 1+\cos \dfrac{7\pi }{8} \right)\) is equal to-

Question Type: single

Q.79) The circular wire of diameter 10 cm is cut and placed along the circumference of a circle of diameter 1 metre. The angle subtended by the wire at the centre of the circle is equal to-

Question Type: single

Q.80) \(\dfrac{\sin 7x+6\sin 5x+17\sin 3x+12\sin x}{\sin 6x+5\sin 4x+12\sin 2x}\)is equal to

Question Type: single

Q.81) If \(A={{\cos }^{2}}\theta +{{\sin }^{4}}\theta ,\) then for all value of \(\theta \), Maximum value of A

Question Type: integer

Q.82) Value of \(3{{\left( \sin x-\cos x \right)}^{4}}+6{{\left( \sin x+\cos x \right)}^{2}}+4\left( {{\sin }^{6}}x+{{\cos }^{6}}x \right)\)

Question Type: integer

Q.83) If \(2\sin \theta +3\cos \theta =3.\) Then \(3\sin \theta -2\cos \theta =k,\left( k>0 \right),\) then find out value of k.

Question Type: integer

Q.84) If \({{\cos }^{2}}{{\theta }_{1}}+{{\cos }^{2}}{{\theta }_{2}}+{{\cos }^{2}}{{\theta }_{3}}=0\left( 0<\theta <\pi \right),\) then find out value of \(\sin {{\theta }_{1}}+\sin {{\theta }_{2}}+\sin {{\theta }_{3}}=.............\)

Question Type: integer

Q.85) If \(\sin x={{\cos }^{2}}x,\) then \({{\cos }^{2}}x\left( 1+{{\cos }^{2}}x \right)\) equals to….

Question Type: integer

Q.86) If the length of an arc of a circle of radius 5 cm subtending \(15{}^\circ \) angle of centre of circle is given by \(\dfrac{k\pi }{12}\)cm. Then value of k is equal to ………

Question Type: integer

Q.87) Value of \(4\cos 36{}^\circ -4\cos 72{}^\circ +4\sin 18{}^\circ \cos 36{}^\circ \) is

Question Type: integer

Q.88) If \(15{{\sin }^{4}}\alpha +10{{\cos }^{4}}\alpha =6\)then value of \(8{{\operatorname{cosec}}^{6}}\alpha +27se{{c}^{6}}\alpha -241\) is

Question Type: integer

Q.89) Value of \(\tan 9{}^\circ -\tan 27{}^\circ -\tan 63{}^\circ +\tan 81{}^\circ \) is equals to –

Question Type: integer

Q.90) The maximum value of the expression \(\dfrac{1}{{{\sin }^{2}}\theta +3\sin \theta \cos \theta +5{{\cos }^{2}}\theta }\) is

Question Type: integer