Two brands of chocolates are available in packs of 24 and 15 respectively. John needs to buy an equal numbers of chocolates of both kinds, what is the least numbers of boxes of each kind he would need to buy?
There are 60, 108, 84 students of different standards. The minimum number of groups in which they can be divided so that each group has equal number of students is:
If \[\alpha \] and \[\beta \] are the zeroes of the polynomial \[f(x)=a{{x}^{2}}+bx+c\], then what is the value of \[\frac{1}{\alpha }+\frac{1}{\beta }-2\alpha \beta \] ?
Find a quadratic polynomial whose zeros are \[2\alpha +1\] and \[2\beta +1\] if \[\alpha \] and \[\beta \] are the zeros of the polynomial \[f(t)=2{{t}^{2}}-7t+6.\]
A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km upstream and 48 km downstream in 9 hrs. Find the speed of boat in still water.
One-fourth of a herd of camels were seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the number of camels.
The hypotenuse of a right-angled triangle is\[3\,\sqrt{5}\,cm\]. If smallest side is tripled and larger side is doubled, the new hypotenuse will be 15 cm. Find the length of larger side.
Some students planned a picnic. The budget for food was Rs. 500, but 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?
A body falls 16 metre in the first second of its motion, 48 metre in the next second, 80 metre in the third and so on. How long will it take to fall 4096 metres?
A aquarium is in the shape of a cuboid whose length, width and height are 12 cm, 10 cm and 8 cm respectively. Find the area of the glass required to make the aquarium.
A cylindrical metallic pipe is 14 cm long. The difference between the outside and inside curved surface area is \[44\text{ }c{{m}^{2}}.\] If the sum of outer and inner radius is 1.5 cm. Find the outer and inner radius of the pipe.
A sphere of diametre 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the, 5 water level in the cylindrical vessel rises by \[3\,\,\frac{5}{9}\,\,cm\]. Find the diametre of the cylindrical vessel.
A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.
The shadow of a tower standing on a level ground is found to be 40 m longer when Sun's altitude is \[30{}^\circ \] than when it was \[60{}^\circ \]. What is the height of the tower?
Find the coordinates of the point equidistant from three given points \[A\,\left( 5,3 \right),\] \[B\left( 5,-\,5 \right)\] and \[C\left( 1,-\,5 \right)\].
Mary has 9 balls in her bag of which 4 are green, 3are blue and 2 are yellow. The ball are similar in shape and size. A ball is drawn at a random from the bag and is found to be blue. Find the probability of this event.