Evaluate \[\frac{1+\sqrt{2}}{\sqrt[{}]{5}+\sqrt[{}]{3}}+\frac{1-\sqrt[{}]{2}}{\sqrt[{}]{5}-\sqrt[{}]{3}}\] it is being given that \[\sqrt{5}=2.236\] and \[\sqrt{6}=2.449\]
The perimeter of a rectangular field is 80 m. If the length of the field is decreased by 2 m and its breadth is increased by 2m, the area of the field is increased by \[16\,{{m}^{2}}\]. Find the length and breadth of the rectangular field.
In the figure AD is the external bisector of\[\angle \,EAC,\] intersects BC produced to D. If AB = 12 cm, AC = 8 cm and BC = 4 cm, find the value of CD.
The ratio between the number of sides of two regular polygon 1 : 2 and the ratio between their interior angle is 3 : 4. The number of sides of these polygons are respectively:
In the given figure, \[\angle \,BAC\] and \[\angle \,BDC\] are the angles of same segment \[\angle \,DBC=30{}^\circ \] and\[\angle \,BCD=110{}^\circ \]. Find\[\angle \,BAC\].
In the given figure, CD is a direct common tangent to two circles intersecting each other at A and B, then find the value of\[\angle \,CDA\,\,+\,\,\angle \,CBD.\]
A ladder 6.5 m long is standing against a wall and the difference between the base of the ladder and wall is 5.2 m. If the top of the ladder now slips by 1.4 m, then by how much will the foot of the ladder slip?
In the given diagram, circle represents professionals, square represents dancers, triangle represents musicians and rectangle represents Europeans. Different region in the diagram are numbered from 1 to 11. Who among the following is neither a dancer nor a musician but is professional and not a European?
Directions: Study the following information carefully and answer these questions.
(i) Six children B, D, C, M, J and K are split into two groups of three each and are made to stand in two rows in such a way that a child in one row is exactly facing a child in the other row.
(ii) M is not at the ends of any row and is to the right of J, who is facing C. K is to the left of D, who is facing M.
Directions: Study the following information carefully and answer these questions.
(i) Six children B, D, C, M, J and K are split into two groups of three each and are made to stand in two rows in such a way that a child in one row is exactly facing a child in the other row.
(ii) M is not at the ends of any row and is to the right of J, who is facing C. K is to the left of D, who is facing M.
Which of the following groups of children is in the same row?
Directions: One/two statements are given followed by two conclusions I and II. You have to consider the statements to be true even if they seem to be at variance from commonly known fact. You have to decide which of the given conclusions if any follow from the given statements.
Directions: One/two statements are given followed by two conclusions I and II. You have to consider the statements to be true even if they seem to be at variance from commonly known fact. You have to decide which of the given conclusions if any follow from the given statements.
From a circular sheet of paper of radius 25 cm, a sector area 4% is removed. If the remaining part is used to make a conical surface, then find the ratio of the radius and height of the cone.
The area of isosceles trapezium is \[176\,c{{m}^{2}}\] and the height is \[\frac{2}{11}th\] of the sum of its parallel sides. If the ratio of the length of the parallel sides is 4 : 7, then the length of a diagonal (in cm) is
The median of the following observations having frequency distribution of 50, is 35. If the median class is \[30-40,\] then the value of a and b is _______.
The internal dimensions of a tank are 12 dm, 8 dm and 5 dm. How many cubes each of edge 7 cm can be placed in the tank with faces parallel to the sides of the tank. Find also, how much space is left unoccupied?
The value of \[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\]\[\frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}\]is_____.
If \[\frac{p}{a}+\frac{q}{b}+\frac{r}{c}=1\] and \[\frac{a}{p}+\frac{b}{q}+\frac{c}{r}=0\], where p, q, r, a, b, c are non-zero, then the value of \[\frac{{{p}^{2}}}{{{a}^{2}}}+\frac{{{q}^{2}}}{{{b}^{2}}}+\frac{{{r}^{2}}}{{{c}^{2}}}\]