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Find the value of sin 45° - cos 30°
If y = 3 cos 4x, dy/dx equals?
What is the value of r if the distance between the point (4,2) and (1,r) is 3 units?
What is the value of p if the gradient of the line joining (-1,p) and (p, 4) is \(\frac{2}{3}\)?
What is the locus of the mid-point of all the chords of length 6cm with circle of radius 5cm and with center O?
Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x = 0 and y = 0 (where k is a constant)?
Find the radius of a sphere whose surface area is 154 cm\(^2\)?
A chord drawn 5 cm away from the center of a circle of radius 13 cm. Calculate the length of the chord?
If the hypotenuse of a right-angled isosceles triangle is 2cm. What is the area of the triangle?
In the figure above , TS//XY and XY = TY, ∠STZ = 34°, ∠TXY = 47°, find the angle marked n?
A regular polygon has 150º as the size of each interior angle. How many sides does it have?
If P \(=\left[\begin{array}{cc}x+3 & x+2\\
x+1 & x-1\end{array}\right]\) evaluate x if |P| = -10
If Q is\( \left[ \begin{array}{cc}
9 & -2 \\
-7 & 4 \\
\end{array} \right]\) , then |Q| is?
A binary operation ⊗ defined on the set of integers is such that m⊗n = m + n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0?
If m * n = n - (m+2) for any real number m and n find the value of 3*(-5)?
Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3,.....\)
The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35, ... is?
Find the range of values of x for which 3x - 7 \(\leq\) 0 and x + 5 > 0?
Determine the value of x for which (x\(^2\) - 1) > 0?