$A$ body of mass $2 \, kg$ moving with a velocity of $3 \, m/s$ collides head-on with a body of mass $1 \, kg$ moving in the opposite direction with a velocity of $4 \, m/s$. After the collision,the two bodies stick together and move with a common velocity. What is the common velocity in $m/s$?
- A$1/4$
- B$1/3$
- C$2/3$
- D$3/4$
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$A$ tower,of $x$ metres high,has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant $y$ metres from the foot of the tower. Then,the length of the flagstaff (in metres) is:
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Match the columns.
Column $-I$ Column $-II$ $(a)$ Parturition $(p)$ Attachment of embryo to endometrium $(b)$ Gestation $(q)$ Release of egg from Graafian follicle $(c)$ Ovulation $(r)$ Delivery of Foetus from uterus $(d)$ Implantation $(s)$ Duration between pregnancy and birth $(t)$ Formation of zygote by fusion of egg and sperm
| Column $-I$ | Column $-II$ |
| $(a)$ Parturition | $(p)$ Attachment of embryo to endometrium |
| $(b)$ Gestation | $(q)$ Release of egg from Graafian follicle |
| $(c)$ Ovulation | $(r)$ Delivery of Foetus from uterus |
| $(d)$ Implantation | $(s)$ Duration between pregnancy and birth |
| $(t)$ Formation of zygote by fusion of egg and sperm |
$x=\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right), y=\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right) \Rightarrow \frac{d y}{d x}$ is equal to
The part of the castor seed from which oil is obtained is called the .....
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