The linear equation in one variable is __________

The value of k for which the pair of linear equations 4x + 6y −1 = 0 and 2x + ky − 7 = 0 represents parallel lines is  _______.  

If \(P(\frac{a}{3},\frac{b}{2})\)is the mid-point of the line segment joining A(−4, 3) and B(−2, 4) then (a, b) is ______.

The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, −7) is ______.

The value of \(\frac { 2tan\ 30° }{ 1-{ tan }^{ 2 }30° } \) is equal to ________.

The value of 2tan30° tan60° is

The lateral surface area of a cube of side 12 cm is _______.

The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is _______.

Probability lies between _______.

If A is any event in S and its complement is A' then, P(A′) is equal to _______.

The monthly income of A and B are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs. 5,000 per month, find the monthly income of each.

Five years ago, a man was seven times as old as his son, while five year hence, the man will be four times as old as his son. Find their present age.

Using section formula, show that the points A(7, −5), B(9, −3) and C(13, 1) are collinear.

Find the centroid of the triangle whose vertices are
(i) (2, −4), (−3, −7) and (7, 2)
(ii) (−5, −5), (1, −4) and (−4, −2)

Evaluate: 
(i) sin 30⁰ +cos 30⁰
(ii) tan 60⁰ cot 60⁰
(iii) \(\frac { tan45° }{ tan30°+tan60° } \)
(iv) sin² 45⁰ +cos² 45⁰

Find the value of 8 sin 2x cos 4x sin 6x , when x =15⁰

The sides of the triangular ground are 22 m, 120 m and 122 m. Find the area and cost of levelling the ground at the rate of Rs. 20 per m².

Find the area of a quadrilateral ABCD whose sides are AB = 13cm, BC = 12cm, CD = 9cm, AD = 14cm and diagonal BD = 15cm.

What is the probability of throwing an even number with a single standard dice of six faces?

The probability of guessing the correct answer to a certain question is \(\frac { x }{ 3 } \). If the probability of not guessing the correct answer is \(\frac { x }{ 5 } \), then find the value of x.

Solve by cross-multiplication method
(i) 8x − 3y = 12 ; 5x = 2y + 7
(ii) 6x + 7y −11 = 0 ; 5x + 2y = 13
(iii) \(\frac { 2 }{ x } +\frac { 3 }{ y } =5;\frac { 3 }{ x } -\frac { 1 }{ y } +9=0\)

Find the value of k, for the following system of equation has infinitely many solutions. 2x − 3y = 7;(k + 2)x − (2k +1)y = 3(2k −1)

Find the centroid of the triangle whose veritices are A(6, −1), B(8, 3) and C(10, −5).

Express
(i) sin 74° in terms of cosine
(ii) tan 12° in terms of cotangent
(iii) cosec 39° in terms of secant

Find the value of sin 64⁰34'.

Find the value of
(i) sin 38⁰36' + tan 12⁰12'
(ii) tan 60⁰25' - cos 49⁰20'

The lengths of sides of a triangular field are 28 m, 15 m and 41 m. Calculate the area of the field. Find the cost of levelling the field at the rate of Rs. 20 per m²

A cube has the Total Surface Area of 486 cm². Find its lateral surface area.

The total surface area of a cube is 864 cm². Find its volume

In an office, where 42 staff members work, 7 staff members use cars, 20 staff members use two-wheelers and the remaining 15 staff members use cycles. Find the relative frequencies.

The probability that it will rain tomorrow is \(\\ \frac { 91 }{ 100 } \). What is the probability that it will not rain tomorrow?

Use graphical method to solve the following system of equations y = 2x + 1; −4x + 2y = 2

Find the points of trisection of the line segment joining (−2, −1) and (4, 8)