Which of the following is a solution of the equation 2x − y = 6.

Which condition does not satisfy the linear equation ax + by + c = 0.

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______.

The centroid of the triangle with vertices (−1, −6), (−2, 12) and (9, 3) is

if sin \(\alpha\) = \(\frac { 1 }{ 2 } \) and \(\alpha\) is a cute, then (3 cos\(\alpha\) - 4cos³ \(\alpha\)) is equal to

The value of 2tan30° tan60° is

If the lateral surface area of a cube is 600 cm², then the total surface area is _______.

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

A particular result of an experiment is called _______.

A letter is chosen at random from the word “STATISTICS”. The probability of getting a vowel is

Draw the graph for the following linear equations
(i) y = 4
(ii) x = -2
(iii) 2x - 4 =0
(iv) 6 + 2y = 0
(v) 9 – 3x = 0

Draw the graph of the equations x= 3, x = 5 and 2x – y – 4 = 0. Also find the area of the quadrilateral formed by these lines and the x-axis.

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 the points A(4,−3) and B(9,7) in the ratio 3:2.

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) 

Verify 3 cos A = 4 cos³ A - 3 cosA , when A = 30⁰

Using Heron’s formula, find the area of a triangle whose sides are
(i) 10 cm, 24 cm, 26 cm
(ii) 1.8 m, 8 m, 8.2 m

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

You are walking along a street. If you just choose a stranger crossing you, what is the probability that his next birthday will fall on a sunday?

What is the probability of drawing a King or a Queen or a Jack from a deck of cards?

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

Check the value of k for which the given system of equations kx + 2y = 3; 2x − 3y = 1 has a unique solution.

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.

If sec \(\theta\) = \(\frac { 13 }{ 5 } \), then show that \(\frac { 2sin\theta -3cos\theta }{ 4sin\theta -9cos\theta } \) = 3

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

Find the value of cos19⁰59'

Find the TSA and LSA of a cuboid whose length, breadth and height are 7.5 m, 3 m and 5 m respectively.

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.

The length, breadth and height of a cuboid are in the ratio 7: 5: 2. Its volume is 35840 cm³. Find its dimensions.

When a dice is rolled, find the probability to get the number greater than 4?

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 perimeter of a rectangle is 36 metres and the length is 2 metres more than three times the width. Find the dimension of rectangle by using the method of graph.

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