Mathematics (St...

The ratio of LCM and HCF of the least composite and the least prime numbers is

The value of k for which the lines \(5x+7y=3 \) and 1\(5x + 21y = k\) coincide is

A girl walks 200m towards East and then 150m towards North. The distance of the girl from the starting point is

The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the altitude of the rhombus is

Two fair coins are tossed. What is the probability of getting at the most one head?

\(\Delta ABC\sim\Delta PQR\). If AM and PN are altitudes of \(\Delta ABC\) and \(\Delta PQR\) respectively and \(AB^2 : PQ^2 = 4 : 9\), then \(AM:PN\) =

If \(2sin^2\beta - cos^2\beta = 2, \) then \(\beta\) is

Prime factors of the denominator of a rational number with the decimal expansion 44.123 are

The lines \(x = a\) and \(y = b,\) are

The distance of point A(-5, 6) from the origin is

If \(a^2=\frac{23}{25}\), then a is

If LCM(x, 18) = 36 and HCF(x, 18) = 2, then x is

In \(\Delta ABC\) right angled at B, if \(tan\;A=\sqrt3,\) then \(cos\; A cos \;C- sin \;A sin\; C =\)

If the angles of \(\Delta ABC\) are in ratio 1:1:2, respectively (the largest angle being angle C), then the value of \(\frac{sec\;A}{cosec\;B}-\frac{tan\;A}{cot\;B}\) is

The number of revolutions made by a circular wheel of radius 0.7m in rolling a distance of 176m is

\(\Delta ABC\) is such that AB = 3 cm, BC = 2cm, CA = 2.5 cm. If \(\Delta ABC\sim\Delta DEF\) and EF = 4cm, then perimeter of \(\Delta DEF\) is

If \(4\;tan\beta=3,\) then \(\frac{4\;sin\beta-3\;cos\;\beta}{4\;sin\;\beta+3\;cos\;\beta}=\)

One equation of a pair of dependent linear equations is \(–5x + 7y = 2\). The second equation can be

A letter of English alphabets is chosen at random. What is the probability that it is a letter of the word ‘MATHEMATICS’?

If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs of such numbers are

If \(tan\; \alpha + cot\;\alpha = 2,\) then \(tan^{20}\alpha+cot^{20}\alpha\)

If \(217x + 131y = 913, \) \(131x + 217y = 827,\) then \(x + y\) is

The LCM of two prime numbers p and q (p > q) is 221. Find the value of 3p – q.