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Find the equation of a line passing through the points (2012, 2014) and (2013, 2015).
Find the equation of the line perpendicular to \(4x5y2016=0 \) and passing through (1, 1).
In a rhombus KLMN, the diagonal KM is equal to the side of the rhombus. Find the measure of \( \angle\)LMN.
In the given figure, ‘O’ is the centre of the circle. AB and CD are diameters perpendicular to each other. Find the ratio of the perimeters of the semicircle ADB and triangle ADB.
In the given figure, ABC is a triangle. BD and CD are internal and external bisector of \(\angle \)B and \(\angle \)C, respectively. If \(\angle \)BAC = \(50^o \), then \(\angle \) BDC =
If the common solution of the equations \(3x+2y=5 \) and \(9x2y=3 \) is (p, q). then find the product of p and q.
In an examination consisting of 100 questions, three mark are given for every question attempted correctly and one mark is deducted for every question attempted wrongly. A student attempts all the questions and gets 100 marks. How many questions did he mark wrong?
If \(7x+8y=10 \) and \(9xky=20 \) have a unique solution, then which of the following cannot be the value of k?
If \(x=\log_510 \), then \(x+\dfrac{1}{x}+2= \)
The diagonal of a rectangle ABCD is the side of a rhombus AEFC. What is the ratio of the areas of the rectangle and the rhombus?
The lateral surface area of a regular tetrahedron is \(450\sqrt3 \) sq. cm. What is the volume of the regular tetrahedron (in cu cm)?
\((\sqrt{324+2\sqrt{323}})(\sqrt{3242\sqrt{323}})= \)
\(\dfrac{9^{3^{6^{0^{8^{7}}}}}7^{3^{5^{0^{4^{9}}}}}}{(63)^{3^{0^{7}}}+(81)^{5^{0^{7}}}+(49)^{6^{0^8}}}= \)
What is the value of \(x \), if \(\sqrt[3]{5^{2x+1}}=\sqrt[6]{25^{4x+5}} \)?
If the LCM of two polynomials \(f(x) \) and \(g(x) \) is \((x1)\ (x2)^2\ (x3)^3 \), then \(f(x)\cdot g(x) \) can be
The remainder obtainded when \(x^4+3x^22x10 \) is divided by \( x+2\) is
The square root of \(x^4+6x^2+4x+9+\dfrac{12}{x}+\dfrac{4}{x^2} \) is
Find the median of a grouped data. If the lower boundary of the median class is 20, the cumulative frequency of the median class is 24, frequency of the median class is 8, the total frequency of the data is 40 and the length of each class interval is 5.
A company EMIT produces playing articles for children. The production of the articles in the year 2012 is as follows:
Grade I – 70%
Grade II 20%
Grade III – x%
Grade IV – 4%
Total – 100%
If an article is selected from the production of the year 2012 randomly, then what is the probability that it is a Grade III article?
If the cost price of an article is increased by 60%, then by what percentage should it be decreased to bring it back to its original price?
The value of \(\cot^2\alpha\left(1\dfrac{1}{\cos\alpha}\right)\left(1+\dfrac{1}{\cos\alpha}\right) \) is
In the given figure, ABCD is a quadrilateral inscribed in a circle and BD is a diagonal passing through the centre of the circle ‘O’. Find \(\angle BOC+\angle AOD \).
In the given figure, a circle is inscribed in a square and the square is circumscribed by another circle. If the diagonal of the square is 14 cm, then find the difference between the areas of the region A and B (in sq. cm).
Simplify: \(\log_{(343)^4}(2401)^3 \).
40% of the employees of an office are women. If 70% of the employees are postgraduates, then what is the least percentage of the women who are postgraduates?
The centroid of \(\triangle \) ABC whose vertices are A(2, 3), B(4, 2) and C(3, 2) is
Find the mode when median is 8 and mean is 10
If \(4x+3y=25 \) and \(5x+2y=26 \), the value of x and y are
A shopkeeper bought a cycle for Rs. 1200 and sold it for Rs. 1800. Find his profit or loss percentage
A Buffoon’s cap is in the form of a cone of radius 7 cm and height 24 cm. Find the area of the paper required to make the cap