In a seminar the number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required if in each room same number of participants are to be seated and all of them being from the same subject.
A man travels 370 km partly by train and partly by car. If he covers 250 km by train and rest by car, it takes him 4 hours. But if he travels 130 km by train and rest by car, he takes 18 minutes longer. Find the speed of the train.
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/h and the time of flight increased by 30 minutes. Find the actual duration of flight.
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?
In a garden - bed there are 23 rose plants in the first row, 21 in the second row, 19 in the third row and so on. There are 5 plants in the last row. How many rows are there?
Ramesh buys a shop for Rs. 120000. He pays half of the amount in cash and agrees to pay the balance in 12 annual installments of Rs. 5000 each. If the rate of interest is 12% and he pays with the installment the interest due on the unpaid amount, find the total cost of the shop.
A solid iron pillar has some part in the form of a right circular cylinder and the remaining in the form of a right circular cone. The radius of the base of each part is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar, if the density of iron is 7 g per \[c{{m}^{3}}\] .
In \[\Delta \,ABC\]and \[\Delta \,DEF,\] it is being given that AB = 5 cm, BC = 4 cm, CA = 4.2 cm and DE = 10 cm, EF = 8 cm, FD = 8.4 cm. If \[AL\bot BC\] and \[DM\bot EF,\] then AL : DM is equal to:
If the angle subtended by two tangents at an outer point is \[60{}^\circ \]and length of the chord formed by joining the point of contact of tangents is 12 cm, then the length of the tangent is given by:
In the figure given below, DPQR is inscribed in a circle with centre O. If \[\angle POQ=130{}^\circ \] and\[\angle QOR=120{}^\circ ,\] then which one of the following is the measurement of\[\angle PQR\] ?
In the given figure, C and D are the points on the semicircle described on AB as diameter. Given that \[\angle BAD=60{}^\circ \] and \[\angle DBC=40{}^\circ \]. Which one of the following options represent the measure of\[\angle ABD?\]
At a point on level ground, the angle of elevation of a tower is found to be such that its tangent is\[\frac{5}{12}\]. On walking 192 meters towards the tower, the tangent of the angle of elevation is\[\frac{3}{4}\]. The height of the tower is:
Find the coordinates of the vertex A of \[\Delta \,ABC,\] If \[D\left( 3,-\,2 \right),\] \[E\left( -\,3,\,\,1 \right)\] and \[F\left( 4,-3 \right)\] are the midpoints of BC, AC and AB respectively.
At the foot of a mountain, the elevation of its summit is \[45{}^\circ \]. After ascending 1 km towards the mountain upon an incline of \[30{}^\circ ,\] the elevation changes to \[60{}^\circ \]. Find the height of the mountain.
If \[P\left( -\,3,2 \right),\] \[Q\left( -\,5,-\,5 \right),\] \[R\left( 2,-\,3 \right)\] and \[S\left( 4,4 \right)\]are the vertices of a quadrilateral, then the quadrilateral will be a:
Consider the following frequency distributor of the height of 60 students of a class. The sun of lower limit of the modal class and upper limit of the median class is:
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
A man earns Rs. 20 on the first day and spends Rs. 15 on the next day. He again earns Rs. 20 on the third day and spends Rs. 15 on the fourth day. If he continues to save like this, how soon will he have Rs. 60 in hand?
If a round balloon of radius 'a' meters subtends an angle\[\theta \]at the eye of an observer while the angle of elevation of its centre is \[\phi \], then the height of the centre of the balloon is
The tangent at a point C of a circle and a diameter AB when extended intersect at P. 0 is the centre of the circle. If \[\angle PCA=110{}^\circ ,\] then find the value of\[\angle CBA\].
ABCD is a square of side a cm. AB, BC, CD and AD all are the chords of circles with equal radii each. If the chords subtends an angle of \[120{}^\circ \] at their respective centres, find the total area of the given figure where arcs are part of the circles: