If (2,3) is a solution of linear equation 2x + 3y = k then, the value of k is _______.

If \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } \neq \frac { { b }_{ 1 } }{ { b }_{ 2 } } \) where a₁x + b₁y + c₁ = 0 and a₂x + b₂ y + c₂ = 0 then the given pair of linear equation has _______ solution(s)

The coordinates of the point C dividing the line segment joining the points P(2, 4) and Q(5, 7) internally in the ratio 2:1 is______.

If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3, 4), (1, 1) and (2, −3) respectively, then the vertices A and B of the triangle are ______.

The value of tan72° tan18° is ________.

The value of \(\frac { sin{ 29 }^{ 0 }31' }{ cos{ 60 }^{ 0 }29' } \) is

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

The volume of a cuboid is 660 cm³ and the area of the base is 33 cm². Its height is _______.

A number between 0 and 1 that is used to measure uncertainty is called _______.

Probability lies between _______.

Solve the following linear equations
(i) \(\frac { 2(x+1) }{ 3 } =\frac { 3(x-2) }{ 5 } \)
(ii) \(\frac { 2 }{ x+1 } =4-\frac { x }{ x+1 } ,(x\neq -)\)

Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.

The points A(−3, 6), B(0, 7) and C(1, 9) are the mid-points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallellogram.

Find the coordinates of the point which divides the line segment joining A(−5,11) and B(4,−7) in the ratio 7:2.

A boy standing at a point O finds his kite flying at a point P with distance OP = 25 m. It is at a height of 5m from the ground. When the thread is extended by 10 m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios) 

Find the area of a right triangle whose hypotenuse is 10cm and one of the acute angle is 24⁰24'

A land is in the shape of rhombus. The perimeter of the land is 160 m and one of the diagonal is 48 m. Find the area of the land.

The adjacent sides of a parallelogram measures 34 m, 20 m and the measure of the diagonal is 42 m. Find the area of parallelogram.

Two dice are rolled, find the probability that the sum is
(i) equal to 1
(ii) equal to 4
(iii) less than 13

In a football match, a goalkeeper of a team can stop the goal, 32 times out of 40 attempts tried by a team. Find the probability that the opponent team can convert the attempt into a goal.

Check whether (5, −1) is a solution of the simultaneous equations x – 2y = 7 and 2x + 3y = 7.

Solve 2x + 3y = 14 and 3x − 4y = 4 by the method of elimination.

If the centroid of a triangle is at (−2, 1) and two of its vertices are (1, −6) and (−5, 2), then find the third vertex of the triangle.

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

(i) If cosec A = sec 34⁰, then find A
(ii) If tan B = cot 47⁰, then find B.

Find the value of sin 64⁰34'.

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

The length, breadth and height of a hall are 25 m, 15 m and 5 m respectively. Find the cost of renovating its floor and four walls at the rate of Rs. 80 per m².

Two identical cubes of side 7 cm are joined end to end. Find the Total and Lateral surface area of the new resulting cuboid.

Team I and Team II play 10 cricket matches each of 20 overs. Their total scores in each match are tabulated in the table as follows:

What is the relative frequency of Team I winning?

In a recent year, of the 1184 centum scorers in various subjects in tenth standard public exams, 233 were in mathematics. 125 in social science and 106 in science. If one of the student is selected at random, find the probability of that selected student,
(i) is a centum scorer in Mathematics
(ii) is not a centum scorer in Science

Solve for x and y: 8x − 3y = 5xy, 6x − 5y = −2xy by the method of elimination.

In what ratio does the point P(–2, 4) divide the line segment joining the points A(–3, 6) and B(1, –2) internally?