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10th Maths Revision Test-1

St. Britto Hr. Sec. School - Madurai

10th Maths Revision Test-1-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

if f(x)+f(1-x)=2 then \(f\left( \cfrac { 1 }{ 2 } \right) \) is

5
-1
-9
1

Find the slope of the line 2y=x+8 :

\(\cfrac { 1 }{ 2 } \)
1
8
2

Two concentric circles if radill a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is

\(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)
\(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)
\(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)
\(2\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)

Given a₁=-1, \(a=\cfrac { { a }_{ n } }{ n+2 } \),then a₄ is :

\(-\cfrac { 1 }{ 20 } \)
\(-\cfrac { 1 }{ 4 } \)
\(-\cfrac { 1 }{ 840 } \)
\(-\cfrac { 1 }{ 120 } \)

Transpose of a column matrix is

unit matrix
diagonal matrix
column matrix
row matrix

The range of the relation R ={(x,x²) |x is a prime number less than 13} is

{2,3,5,7}
{2,3,5,7,11}
{4,9,25,49,121}
{1,4,9,25,49,121}

If \(A=\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix} \right] _{ 3\times 2 }\) \(B=\left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix} \right] _{ 2\times 3 }\) then which of the following products can be made from these matrices
(i) A²
(ii) B²
(iii) AB
(iv) BA

(i) only
(ii) and (iii) only
(iii) and (iv) only
all the above

The radius of a wire is decreased to one-third of the original. If volume the sam4e, then the length will be increased _______of the original.

3 times
6 times
9 times
27 times

Which of the following are linear equation in three variables

2x=z
2sinx+ycosy+ztanz=2
x+2y²+z=3
x-y-z=7

If the angle between two radil of a circle is ^o, the angle between the tangents at the end of the radii is

50^o
90^o
40^o
70^o

If f(x)=x+1 then f(f(f(y+2)) is :

y+5
y+7
y+7
y+9

In an A.P if the p^th term is q and the q^th term is p, then its n^th term is

p+q-n
p+q+n
p-q+n
p-q-n

The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

\(\frac { q }{ p+q+r } \)
\(\frac { p }{ p+q+r } \)
\(\frac { p+q }{ p+q+r } \)
\(\frac { p+r }{ p+q+r } \)

The standard deviation is the ____ of variance

cube
square
square root
cube root

In the arithemetic series Sn=k+2k+3k+...+100, k is positive integer and k is a factor 100 then S_n is:

\(1000\cfrac { 10 }{ k } \)
\(5000\cfrac { 50 }{ k } \)
\(\cfrac { 1000 }{ k } +10\)
\(\cfrac { 5000 }{ k } +50\)

If the standard deviation of x, y, z is p then the standard deviation of 3x+5, 3y+5, 3z +5 is

3p+5
3p
p + 5
9p + 15

If S₁ denotes the total surface area at a sphere of radius u0aea and S₂ denotes the total surface area of a cylinder of base radius u0aeaand height 2r, then

S₁=S₂
S₁>S₂
S₁<S₂
S₁=2S₂

A girl Calculates the probability of her winning in a match is 0.08 what is the probability of her losing the game

91%
8%
92%
80%

The ratio of the volumes of two spheres is 8:27. If r and R are the radii of sphere respectively, Then (R-r):r is

1:2
1:3
2:3
4:9

If m and n are the two positive integers then m² and n² are

Co-prime
Not co-prime
Even
odd

Part - B

Generic 2 - Answer All Question

Prove that \(\sqrt { 3 } \) is irrational

Find the equation of the straight line passing through (5, 7) and is
Parallel to X axis

A mother devides Rs.207 into three parts such that the amount are in A.P. and gives it to her three children. The product of the two least amounts that the children had Rs 4623. Find the amount received by each child.

In a Geometric progression, the 4^th term is \(\frac { 8 }{ 9 } \) and the 7th term is \(\frac { 64 }{ 243 } \). Find the Geometric Progression.
Solve 8x \(\equiv \) 1 (mod 11)

The given diagram shows a plan for constructing a new parking lot at a campus. It is estimated that such construction would cost Rs. 1300 per square feet. What will be the total cost for making the parking lot?

A circular garden is bounded by East Avenue and Cross Road. Cross Road intersects North Street at D and East Avenue at E. AD is tangential to the circular garden at A(3, 10). Using the figure.

Where does the Cross Road intersect the
(i) East Avenue ?
(ii) North Street ?

Find the area of the triangle whose vertices are (-3,5) , (5,6) and (5,-2)

Reduce the rational expressions to its lowest form
\(\frac { { x }^{ 2 }-16 }{ { x }^{ 2 }+8x+16 } \)

Consider the following information regarding the number of men and women workers in three factories I, II and III.

Factory Men Women

I 23 18

II 47 36

III 15 16

Represent the above information in the form of a matrix. What does the entry in the second row and first column represent?

Which of the following sequences form a Geometric Progression?
7,14,21,28,.... ,

Construct a triangle similar to a given triangle PQR with its sides equal to 35 of the corresponding sides of the triangle PQR (scale factor \(\cfrac { 3 }{ 5 } <1\)) Solution Given a triangle PQR we are required to construct another triangle whose sides are \(\cfrac { 3 }{ 5 } \) of the corresponding sides of the triangle PQR.

If the base area of a hemispherical solid is 1386 sq. metres, then find its total surface area?

Solve \(2{ x }^{ 2 }-2\sqrt { 6 } x+3\) = 0

If X = {–5,1,3,4} and Y = {a,b,c}, then which of the following relations are functions from X to Y ?
(i) R₁= {(–5,a), (1,a), (3,b)}
(ii) R₂= {(–5,b), (1,b), (3,a),(4,c)}
(iii) R₃ = {(–5,a), (1,a), (3,b),(4,c),(1,b)}

Show that \(\triangle\)PST~\(\triangle\)PQR

Part - C

Generic 5 - Answer All Question

Without using Pythagoras theorem, show that the vertices (1, - 4) , (2, - 3) and (4, - 7) form a right angled triangle.

Find the square root of the following expressions
16x² + 9y² - 24xy + 24x - 18y + 9

Find the equation of a straight line perpendicular to the line \(y=\frac { 4 }{ 3 } x-7\) and passing through the point (7, –1).

Determine the nature of roots for the following quadratic equations
x² - x - 20 = 0

Write down the quadratic equation in general form for which sum and product of the roots are given below.
\(-\frac { 3 }{ 5 } ,-\frac { 1 }{ 2 } \)

If A = \(\left[ \begin{matrix} 7 & 8 & 6 \\ 1 & 3 & 9 \\ -4 & 3 & -1 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 4 & 11 & -3 \\ -1 & 2 & 4 \\ 7 & 5 & 0 \end{matrix} \right] \) then Find 2A + B.
Solve x² + 2x - 2 by formula method

From the top of a 12 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Determine the height of the tower.

Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
(i) R₁={(3,7), (4,7), (7,10), (8,1)}
(ii) R₂= {(3,1), (4,12)}
(iii) R₃= {(3,7), (4,10), (7,7), (7,8), (8,11), (8,7), (8,10)}

If sin (A - B) = \(\frac12\), cos (A + B) = \(\frac12\), 0^o < A + ≤ 90°, A > B, find A and B.

Find
\(\frac { { x }^{ 2 }-16 }{ x+1 } \div \frac { x-4 }{ x+4 } \)

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