Mix Test

Result

Mix Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following equations is not equivalent to x – y = 6?

A
– 7x + 7y = – 42

B
8x – 8y = 48

C
4x – 4y = 24

D
3x – 3y = 16

Solution

3x – 3y = 16
3 (x – y) = 16
x – y = is not equivalent to x – y = 6.
Question 2
1 / -0

Solve: < 1

A
x > 5 or x < -1

B
x < 5

C
x ≤ 5

D
x > 5 or x < 0

Solution

< 1

Case 1: x > 0
Then, 5 < x
i.e. x > 5

Case 2: x < 0
Then, x < 5 and x < 0
i.e. x < 0

Therefore, either x > 5 or x < 0
Question 3
1 / -0

In the quadratic equation ax² + bx + c = 0, what will be the discriminant if a, b and c are all negative integers?

A
b²+ 4ac

B
b² – 4ac

C
– b² – 4ac

D
– b² + 4ac

Solution

Discriminant will be b²– 4ac.
Question 4
1 / -0

Two points (a, 0) and (0, b) are joined by a straight line. Another point on this line is

A
(3a, –2b)

B
(a², ab)

C
(–3a, 2b)

D
(a, b)

Solution

The equation of the line passing through (a, 0) and (0, b) is:
(y – 0) =
y = –
On putting the options, we get to know that option (1) is correct.
Question 5
1 / -0

The radius of a circle is 6 cm and the angle of a sector of the circle is 60°. What is the area of the sector?

A
12 cm²

B
6 cm²

C
24 cm²

D
2 cm²

Solution

If and r respectively are the angle of the sector of the circle and the radius of the circle, then the area of the sector of angle
Thus, area of the sector of angle 60° = = 6 cm²
Question 6
1 / -0

Which of the following satisfies x > y?

A
x = 2y

B
2x = y

C
x + 2 = y

D
x – 2 = y

Solution

The equation x – 2 = y means that y is 2 less than x. So, x must be greater than y.
Question 7
1 / -0

Find the reflection of point (4, -13) in the line 5x + y + 6 = 0.

A
(-1, -14)

B
(3, 4)

C
(1, 2)

D
(-4, 13)

Solution

Let Q (a, b) be the reflection of P (4, -13) in the line 5x + y + 6 = 0. The mid-point R lies on 5x + y + 6 = 0.
∴ 5+ + 6 = 0
⇒ 5a + b + 19 = 0 â¦ (i)
Also, PQ is perpendicular to 5x + y + 6 = 0.
Therefore, = -1
⇒ a - 5b - 69 = 0 â¦ (ii)
Solving (i) and (ii), we get a = -1, b = -14.
Question 8
1 / -0

A town recorded 2 cm rainfall. Find the volume of water that falls on a land of 5 hectare area.

A
100 m³

B
1000 m³

C
10,000 m³

D
10 m³

Solution

Height of rain that fell = 2 cm
Volume of water that falls on 5 hectares of ground = 5 × 10,000 × = 1000 m³
Question 9
1 / -0

A spider goes up 5'9'' from the bottom and then falls 1'6'', and then again climbs 2'5''. What height does it climb from the bottom?

A
6'6''

B
6'8''

C
7'9''

D
8'3''

Solution

Correct option is (2).
Question 10
1 / -0

A square of side 2 metres has its corners cut away to form an octagon with all sides equal. The length of each side of the octagon (in metres) is

A

B

C

D

Solution

Let the side of the octagon be X units.
Each interior angle of a regular octagon is 135°.
Then, the exterior angle = 45°

SF = ER =
The side of the square =
Solving this, we get
X =
Length of each side of octagon = metres
Question 11
1 / -0

In the given figure, || m and n is a transversal. If 1 = 65°, then find the measure of 5.

A
25°

B
125°

C
65°

D
115°

Solution

Given: 1 = 65^o and || m

By linear pair axiom,
Sum of adjacent angles on the same line is 180^o and interior alternate angles are equal if two lines are parallel.
1 + 7 = 180^o …… (1) (By linear pair axiom)
Also, 7 = 5
1 + 5 = 180^o
65^o + 5 = 180^o or 5 = 115^o
Question 12
1 / -0

If p, q, r and s are four numbers such that q is 20% more than p, r is 25% less than q, s is 40% more than r, and s is k% higher than p, then what is the value of k?

A
22%

B
24%

C
26%

D
28%

Solution

Let p = 100
q = 100 + 20% of 100 = 120
r = 120 - 25% of 120 = 120 - 30 = 90
s = 90 + 40% of 90 = 90 + 36 = 126
s - p = 126 - 100 = 26
So, s is 26 higher than p.
Required percentage = (26/100) × 100% = 26%
Question 13
1 / -0

The sum of the digits of a two-digit number is 9. If the number is reversed, the number obtained is 9 less than the original number. Find the number.

A
54

B
45

C
36

D
63

Solution

Let the digit at unit's place be x.
Let the digit at ten's place be y.
Original number = 10 y + x
Reversed number = 10 x + y
According to the question,
10 y + x = 10x + y + 9
10y + x – 10 x – y = 9
9y – 9x = 9
Dividing by 9, y – x = 1 …………….. (1)
Also, x + y = 9 …………….. (2)
Adding equation (1) & (2), we get
2y = 10
y = 5
Put value of y in equation (2), we get
x = 4
Original number = 54
Question 14
1 / -0

The sum of the 9^th, 14^th and 18^th terms of an AP is equal to the sum of the 20^th and 24^th terms. What is the ratio of the 4^th term to the 2^nd term?

A
3 : 2

B
7 : 5

C
5 : 3

D
9 : 7

Solution

T₉ + T₁₄+ T₁₈ = T₂₀ + T₂₄
a + 8d + a + 13d + a + 17d = a + 19d + a + 23d (where, a is first term and d is common difference)
3a + 38d = 2a + 42d
a = 4d
= =
Question 15
1 / -0

What are the values of x, y and z in the given figure?

A
x = 45^o, y = 55^o, z = 55^o

B
x = 55^o, y = 135^o, z = 55^o

C
x = 55^o, y = 145^o, z = 125^o

D
x = 55^o, y = 125^o, z = 125^o

Solution

In the given figure,
x and 55^o are vertically opposite angles.
So, x = 55^o
we know that y & 55^o form a linear pair.
So, y + 55^o = 180^o
y = 125^o
y and z are also vertically opposite angles.
So, y = z
z = 125^o
Therefore, x = 55^o y = 125^o z = 125^o