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10th Maths Revision Test-2

St. Britto Hr. Sec. School - Madurai

10th Maths Revision Test-2-Aug 2020

Time : 1:00 Hours

Part - A

Multiple Choice Question - Answer 10 Questions

if 5x=sec\(\theta \) and \(\frac { 5 }{ x } \) =tan\(\theta \), then x²-\(\frac { 1 }{ { x }^{ 2 } } \) is equal to

25
\(\frac { 1 }{ 25 } \)
5
1

The angle of elevation of a cloud from a point h metres above a lake is \(\beta \). The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is

\(\frac { h\left( 1+tan\beta \right) }{ 1-tan\beta } \)
\(\frac { h\left( 1-tan\beta \right) }{ 1+tan\beta } \)
h tan(45°-\(\beta \))
none of these

The variance of 5 values is 16. If each value is doubled. them the standard deviation of new values is_______

4
8
32
16

Find the ratio in which the line segment joining the points (-3,10) and (6,-8) is internally divided by (-1,6) :

7:2
3:4
2:7
5:3

The solution of (2x - 1)² = 9 is equal to

-1
2
-1, 2
None of these

The real roots of the quardractic equation x²-x-1 are

1,1
-1,1
\(\\ \\ \\ \\ \\ \cfrac { 1+\sqrt { 5 } }{ 2 } ,\cfrac { 1-\sqrt { 5 } }{ 2 } \)
None

The range of the data 8, 8, 8, 8, 8. . . 8 is

0
1
8
3

A Quadratic polynomial whose one zero is 5 and sum of the zeroes is 0 is given by

x²-25
x²-5
x²-5x
x²-5x+5

If an event occurs surely, then its probabllity is :

1
0
\(\cfrac { 1 }{ 2 } \)
\(\cfrac { 3 }{ 4 } \)

A solid is hemispherical at the bottom and conical above. If the curved surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is:

1:3
\(1:\sqrt { 3 } \)
1:1
\(\sqrt { 3 } :1\)

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

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

When three coins are tossed, the probability of getting the same face on all the three coins is

\(\cfrac { 1 }{ 8 } \)
\(\cfrac { 1 }{ 4 } \)
\(\cfrac { 3 }{ 8 } \)
\(\cfrac { 1 }{ 3 } \)

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%

Find the matrix X if 2X + \(\left( \begin{matrix} 1 & 3 \\ 5 & 7 \end{matrix} \right) =\left( \begin{matrix} 5 & 7 \\ 9 & 5 \end{matrix} \right) \)

\(\left( \begin{matrix} -2 & -2 \\ 2 & -1 \end{matrix} \right) \)
\(\left( \begin{matrix} 2 & 2 \\ 2 & -1 \end{matrix} \right) \)
\(\left( \begin{matrix} 1 & 2 \\ 2 & 2 \end{matrix} \right) \)
\(\left( \begin{matrix} 2 & 1 \\ 2 & 2 \end{matrix} \right) \)

A tower is 60 m height. Its shadow is x metres shorter when the sun’s altitude is 45° than when it has been 30°, then x is equal to

41.92 m
43.92 m
43 m
45.6 m

Part - B

Generic 2 - Answer All Question

The slant height of a frustum of a cone is 5 cm and the radii of its ends are 4 cm and 1 cm. Find its curved surface area.

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

Find the sum of
15²+16²+17²+..+28²

From a well shuffled pack of 52 cards, one card is drawn at random. Find the probability of getting (i) red card (ii) heart card (iii) red king (iv) face card (v) number card.

Find the value of a, b, c, d from the equation \(\left( \begin{matrix} a-b & 2a+c \\ 2a-b & 3c+d \end{matrix} \right) =\left( \begin{matrix} 1 & 5 \\ 0 & 2 \end{matrix} \right) \)
If α and β are the roots of x² + 7x + 10 = 0 find the values of
α⁴ + β⁴

prove that (cosec\(\theta \)-sin\(\theta \)) (sec\(\theta \)-cos\(\theta \)) (tan\(\theta \) +cot\(\theta \))=1

Let A = {x \(\in \) N| 1 < x < 4}, B={x \(\in \) W| 0 ≤ x < 2) and C={x \(\in \) N| x < 3} Then verify that
(i) A x (B U C) = (A x B) U (A x C)
(ii) A x (B ∩ C) = (A x B) ∩ (A x C)

Find the square root of the expression \(\frac { 4{ x }^{ 2 } }{ { y }^{ 2 } } +\frac { 20x }{ y } +13-\frac { 30y }{ x } +\frac { 9{ y }^{ 2 } }{ { x }^{ 2 } } \)

Find the equation of a line passing through the point (3, - 4) and having slope \(\frac { -5 }{ 7 } \)

Find x if gff(x) = fgg(x), given f(x) = 3x+1 and g(x)=x+.

Part - C

Generic 5 - Answer All Questions

Find the least positive integer n such that 1 + 6 +6² + ... + 6ⁿ > 5000

D and E are respectively the points on the sides AB and AC of a DABC such that AB=5.6 cm, AD=1.4 cm, AC=7.2 cm and AE = 1.8 cm, show that DE||BC

Find the GCD of the polynomials x³ + x² - x + 2 and 2x³ - 5x² + 5x - 3.

For the cylinders A and B (Fig. 7.27), (i) find out the cylinder whose volume is greater.
(ii) verify whether the cylinder with greater volume has greater total surface area.
(iii) find the ratios of the volumes of the cylinders A and B.

Two dice are rolled together. Find the probability of getting a doublet or sum of faces as 4.
In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 is the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?

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