Question 1 |
Consider a spherical globe rotating about an axis passing through its poles. There are three points P, \mathrm{Q}, and \mathrm{R} situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, \mathrm{Q}, and \mathrm{R} move with speeds v_{P}, v_{Q}, and v_{R}, respectively.
Which one of the following options is CORRECT?
Which one of the following options is CORRECT?
v_{P} \lt v_{R} \lt v_{Q} | |
v_{P} \lt v_{Q} \lt v_{R} | |
v_{P}\gt v_{R} \gt v_{Q} | |
v_{P}=v_{R} \neq v_{Q} |
Question 1 Explanation:
Velocity, V=\omega r.
Here, \omega= constant.
Hence, more is the distance from the axis of rotation more will be the velocity.
\therefore \quad \mathrm{V}_{\mathrm{P}} \gt \mathrm{V}_{\mathrm{R}} \gt \mathrm{V}_{\mathrm{Q}}
Question 2 |
If x satisfies the equation 4^{8^{x}}=256, then x is equal to
\frac{1}{2} | |
\log _{16} 8 | |
\frac{2}{3} | |
\log _{4} 8 |
Question 2 Explanation:
4^{8^{x}}=256
\rightarrow Taking log to the base 4 . on both side.
8^{x}=\log _{4} 256=4
Taking lot to the base 8 on both sides, we get
\begin{aligned} x & =\log _{8} 4 \\ & =\log _{2^{3}} 2^{2} \\ x & =\frac{2}{3} \end{aligned}
\rightarrow Taking log to the base 4 . on both side.
8^{x}=\log _{4} 256=4
Taking lot to the base 8 on both sides, we get
\begin{aligned} x & =\log _{8} 4 \\ & =\log _{2^{3}} 2^{2} \\ x & =\frac{2}{3} \end{aligned}
Question 3 |
Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people. How many seating arrangements are possible such that every husband sits next to his wife?
16 | |
4 | |
120 | |
720 |
Question 3 Explanation:
Let us form the pairs of Husband-wife. Now these pairs can be arranged around circular table in
\begin{aligned} & =(3-1) ! \text { ways } \\ & =2 \text { ways } \end{aligned}
Their possible internal arrangement \mathrm{s}
\begin{aligned} & =2 ! \times 2 ! \times 2 ! \\ & =8 \end{aligned}
Hence, total seating arrangement.
=2 \times 8=16
\begin{aligned} & =(3-1) ! \text { ways } \\ & =2 \text { ways } \end{aligned}
Their possible internal arrangement \mathrm{s}
\begin{aligned} & =2 ! \times 2 ! \times 2 ! \\ & =8 \end{aligned}
Hence, total seating arrangement.
=2 \times 8=16
Question 4 |
Consider a circle with its centre at the origin (O), as shown. Two operations are
allowed on the circle.
Operation 1: Scale independently along the x and y axes.
Operation 2: Rotation in any direction about the origin.
Which figure among the options can be achieved through a combination of these two operations on the given circle?
Operation 1: Scale independently along the x and y axes.
Operation 2: Rotation in any direction about the origin.
Which figure among the options can be achieved through a combination of these two operations on the given circle?
A | |
B | |
C | |
D |
Question 5 |
There are 4 red, 5 green, and 6 blue balls inside a box. If ?? number of balls are
picked simultaneously, what is the smallest value of ?? that guarantees there will be
at least two balls of the same colour?
One cannot see the colour of the balls until they are picked.
One cannot see the colour of the balls until they are picked.
4 | |
15 | |
5 | |
2 |
There are 5 questions to complete.
And solution??
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