If a, b, c are the sides of a right triangle where c is the hypotenuse, then the radius r of the circle which touches the sides of a triangle, will be ________.
If the radius of a sphere is increased by 3 cm, its surface area is increased by \[792\,\,c{{m}^{2}}\]. The radius of the sphere, before change is _________.\[\left( use\,\pi =\frac{22}{7} \right)\]
A right angled triangle PQR is right angled at P, S and T are points on PQ and PR, respectively, which divide these sides in the ratio 2 : 1, then which one of the following is correct?
A rectangular water reservoir is 10.8 metres long and 3.75 metres wide at base. Water flows into it at the rate of 36 m per second through the pipe having the cross section 7.5 cm \[\times \] 4.5 cm. Then the height to which the water will rise in the reservoir in 15 minutes is _______.
If \[\alpha \] and \[\beta \] are the roots of the given equation \[2\,\sqrt{3}{{x}^{2}}+4x-3\,\sqrt{3},\] then the value of \[\frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}}\].
A cylindrical metallic pipe is 14 cm long. The difference between the outer and inner curved surface area is \[44\,c{{m}^{2}}\]. If the sum of outer and inner radius is 1.5 cm, then find the ratio of outer and inner radius of the pipe, respectively. \[\left( use\,\pi =\frac{22}{7} \right)\]
In a triangle PQR (as shown below), \[\angle PQR=90{}^\circ \]and QS is its bisector. If \[SM\bot QR,\] then \[SM\times (PQ+QR)\] is equal to ________.
Area swept by a clock in a time interval is\[\frac{84\pi }{5}\,\,c{{m}^{2}}\]. If it is given that the length of the minute hand of the clock is 12 cm, then which one of the following can be the correct time interval?
There are 567 sealed envelopes in a box, 14 of them contain a cash prize of Rs. 1000 each, 126 of them contain a cash prize of Rs. 500 each and 60 of them contain a cash prize of Rs. 200 each and rest do not contain any cash prize. If they are well shuffled and an envelope is picked up randomly, find the probability that it contains a cash prize of Rs. 500.
If A cone of maximum size is carved out from a cube of edge 14 cm, then the surface area of the remaining solid left out after the cone carved out will be _______. \[\left( use\,\pi =\frac{22}{7} \right)\]
The angle of elevation of the top of a tree from a point A on the ground is \[60{}^\circ \]. On walking 20 m away from its base, to a point B, the angle of elevation changes to \[30{}^\circ \]. Find the height of the tree.
In the shown figure, if OQ is the perpendicular bisector of the line segment ST, \[UP\bot OQ\] and UT intersects OQ at the point R, then \[\frac{1}{OP}+\frac{1}{OQ}=\]________.
A die has its six faces marked 0, 2, 2, 2, 6, 6. Two such dice are thrown together and the total score is recorded. Find the probability of getting a total of 8.
Two buses start from the opposite points of a main road, 150 km apart. The first bus runs for 25 km and takes a right turn and then runs for 15 km. It then turns left and runs for another 25 km and takes the direction back to reach the main road. In the meantime, due to a minor breakdown, the other bus has run only 35 km along the main road. What would be the distance between the two buses at this point?
If '+' means 'minus', '\[\times \]' means 'divided by', '\[\div \]' means 'plus' and '\[-\]' means 'multiplied by', then which of the following will be the value of the expression \[252\times 9-5+32\div 92\] ?
Directions: Study the following information carefully to answer the questions given below:
P, Q, R, S, T, U, V and W are sitting around a circular table facing the centre. R is third to the left of U who is to the immediate right of Q. S is third to the left of V but is not a neighbour of R or U. P is second to the right of W.
Directions: Study the following information carefully to answer the questions given below:
P, Q, R, S, T, U, V and W are sitting around a circular table facing the centre. R is third to the left of U who is to the immediate right of Q. S is third to the left of V but is not a neighbour of R or U. P is second to the right of W.
Directions: Study the following information carefully to answer the questions given below:
P, Q, R, S, T, U, V and W are sitting around a circular table facing the centre. R is third to the left of U who is to the immediate right of Q. S is third to the left of V but is not a neighbour of R or U. P is second to the right of W.
Which of the following groups of persons has the first person sitting between the next two?
At t minutes past 4 pm, the time needed by the minute hand of clock to show 5 pm was found to be 18 minutes less than \[\frac{{{(t-6)}^{2}}}{6}\]minutes. Find t.
A bucket is in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm, respectively. Based on this information, choose the correct option.\[[use\,\pi =3.14]\]
A)
The capacity of the bucket is 25.980 litres.
doneclear
B)
Surface area of the bucket is \[3292.60\,\,c{{m}^{2}}\](approx).
doneclear
C)
The cost of milk which can completely fill the container at the rate of Rs. 50 per litre is Rs. 549.50.
bisector of the line segment ST, \[UP\bot OQ\] and UT intersects OQ at the point R, then \[\frac{1}{OP}+\frac{1}{OQ}=\]________. 
