1. If = √3+√2/√3−√2 and = √3−√2/√3+√2
then find the value of ^2 + ^2.
2. Find the value of
4(216)
−2
3
+
1
(256)
−3
4
+
2
(243)
−1
5
3. Using factor theorem, factorize : x3 – 6x2 + 3x + 10
4. Using the long division method, determine the remainder when the polynomial 4x5 +
2x4 - x3 + 4x2 - 7 is divided by (x - 1).
5. ABCD is a rectangle. The co-ordinates of two vertices A and C are (2,3) and (7,7)
respectively. Find the coordinates of remaining vertices.
6. A point (x + 2, x + 4) lies in the first quadrant, the mirror image for which for x-axis is (5,
–7). What is the value of x?
7. If the cost of 5 tables exceeds the cost of eight chairs by ₹ 150. Write a linear
equation in two variables to represent this statement. Also find the cost of 1 table if
the cost of one chair is ₹ 240.
8. Draw the graph of y = −5 and y = 5 on the same graph. Are the lines parallel?
9. In the triangle ABC, BE is perpendicular to AC, ∠ EBC = 40° and ∠DAC = 30°. Find
the values of x, y and z