Constructions – Important Questions Construct a triangle similar to a given triangle ABC with its sides equal to 3/4 of the corresponding sides of the triangle ABC (i.e., of scale factor 3/4). Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. Draw a […]
Constructions – Previous Years Questions Draw a circle of radius 5 cm. Construct a pair of tangents to it so that they are inclined at 60°. Measure the lengths of the two tangents. [CBSE 2017] [3 Marks] Construct a triangle with sides 5 cm, 6 cm and 7 cm. Now construct another triangle whose sides […]
Circles – Previous Years Questions In the given figure PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°. Find ∠PCA. [CBSE 2016] [1 Mark] Two concentric circles of radii a and b (a > b) are given. Find the length of […]
Some Applications of Trigonometry – Important Questions A person, standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank is 60°. When he retreated 20 m from the bank, he finds the angle to be 30°. Find the height of the tree and the breadth of […]
Some Applications of Trigonometry – Previous Years Questions A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder. [CBSE 2016] [1 Mark] If the shadow of a vertical pole at a particular […]
Triangles – Important Questions If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 […]
Quadratic Equations – Important Questions Find the roots of the equation 2×2– 5x + 3 = 0, by factorisation. Write the discriminant of the quadratic equation (x + 5)2 = 2(5x – 3). Using completing the square method, show that the equation x2 – 8x + 18 = 0 has no solution. Find the roots […]
Pair of Linear Equations in Two Variables – Important Questions Solve the following pair of equations:3x + 4y = 102x – 2y = 2 Draw the graph of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0, using this graph, find the values of x and y […]
Real Numbers – Important Questions HCF of 65 and 117 is expressible in the form 65n – 117, then find the value of n. On a morning walk, three persons step out together and their steps measure 30 cm, 36 cm and 40 cm respectively. What is the minimum distance each should walk so that […]
Arithmetic Progressions – Important Questions Show that the sequence defined by tn = 4n + 7 is an A.P. Find the number of terms for given AP: 7, 13, 19, 25, ……, 205. The 7th term of an AP is 32 and its 13th term is 62. Find AP. Find the sum of all two […]