BRAINICS INSTITUTION
(TUITION CENTRE)
UNIT TEST – 3 (Algebra, Graphs, Practical
geometry) MATHEMATICS
CLASS: X standard Marks 100
Time : 2.30 hours
PART-I [Marks 14]
Answer all the 14 questions 14x1=14
1. A system of three linear equations in three variables is inconsistent if their planes
a) Intersect only at a point b) intersect in a line
c) Coincides with each other d) do not intersect
2. If (x -6) is the HCF of and hen the value of k is
a) 3 b) 5 c) 6 d) 8
3. y2 + 1/y2 is not equal to
a) y4+1 b) (y + 1/y)2 c) (y – 1/y)2+2 d) (y + 1/y)2-
2 y2
4. The square root of 361x4y2
(a)19x2y (b) 19x4y2 (c) 19xy2 (d) 19xy
5. Which of the following should be added to make x4+64 perfect square
(a)4x2 (b)16x2 c)8x2 d) -8x2
6. The solution of (2x-1)2 = is equal to
(a) -1 (b)2 c)-1 ,2 d)none of these
7. If a polynomial is a perfect square then, its factors will be repeated number
of times(odd/even)
(a)1 (b) 2 (c) 3 (d) 4
8. The values of a and b if 4x —24x +76x +ax+bis a perfect square are
4 3 2
a) 100, 120 (b) 10, 12 (c) -120, 100 (d) 12, 10
9. Graph of a linear polynomial is a
(a) straight line (b) circle (c) parabola (d) hyperbola
10. If A is a 2 x 3 matrix and B is a 3 x 4 matrix, how many columns does AB have
(a) 3 (b) 4 (c) 2 (d) 5
BRAINICS INSTITUTION
(TUITION CENTRE)
11. If number of columns and rows are not equal in a matrix then it is said to be a
(a) diagonal matrix (b) rectangular matrix
(c) square matrix (d) identity matrix
12. For the given matrix A = 1 5 7 9 the order of matrix AT
5 7 2 1
2 4 8 2
a) 3 x 2 b) 2 x 3 c) 3 x 4 d) 4 x 3
13. Transpose of a column matrix is
(a) unit matrix (b) diagonal matrix
(c) column matrix (d) row matrix
14. A square matrix in which elements in the leading diagonal are all “1” and rest are all
zero is called
a) unit matrix b) diagonal matrix c) zero matrix d) scalar matrix
PARTS-II [MARKS: 20]
Answer all the questions :- 10x2=20
15. Solve 2x-3 y = 6, x+ y = 1
16. Find the LCM of p2-3p+2, p2-4
17. Reduce the rational expressions to its lowest form 9x2 + 81x
x3+8x2-9x
18. Find the excluded values of the following expressions t
t2-5t+6
19. Simplify x3 + y3
x-y y-x
20. Write down the quadratic equation in general form for which sum and product of
the roots are given below 5/3, 4
21. Solve the quadratic equations by factorization method 4x2-7x-2=0
22. Solve the quadratic equations by completing the square method x2-3x-2=0
23. Determine the nature of roots for the quadratic equations 9x2-24x+16=0
BRAINICS INSTITUTION
(TUITION CENTRE)
24.Find the zeroes of the quadratic expression x2+8x+12
PARTS-III [MARKS: 50]
Answer all the questions :- 10x5=50
25.Solve the system of linear equations in three variables
3x-2y+z =2, 2x+3y-z=5, x + y + z=6
26. Discuss the nature of solutions of the following system of equations
. 3x-y+z = 1, 2x-y+2z=1, -x-y +z = 2
27. Find the GCD of the polynomials x3+x2-x+2 and 2x3-5x +5x-3
28. Simplify 1 + 1 - 1
x2-5x+6 x2-3x+2 x2-8x+15
29. If A = 2x+1 and B = 2x-1 find 1 - 2B
2x-1 2x+1 A-B A2-B2
30. If A = x and B = 1 find (A+B)2+(A-B)2 = 2(x2+1)
X+1 x+1 A÷B x(x+1)2
31.Find the square root of (6x2+x-1) (3x2+2x-1) (2x2+3x+1)
32 Find the square root of the following polynomials by division method
x2 - 10x +27 - 10y +y2
y2 y x x2
33 Find the values of m and n if the polynomials are perfect squares x4-8x3+mx2+nx+16
BRAINICS INSTITUTION
(TUITION CENTRE)
34 If α, β are the roots of the equation 3x2+7x-2=0 find the values of
i) α + β ii) α2 + β2
β α β α
PARTS-IV [MARKS: 16]
Answer both questions 2x8=16
35 a) Draw a circle of radius 4 cm. At a point L on it draw a tangent to the
circle using the alternate segment
(or)
b)Draw a triangle ABC of base BC = 8 cm, A= 60o and the bisector of ÐA meets BC
at D such that BD = 6 cm.
36 a) Draw the graph of y=2x2 and hence use it to solve 2x2-x-6=0
(or)
b)Draw the graph of y=x -4 and hence use it to solve x2-x-12=0
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