Mix Test

Result

Mix Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following equations is equivalent to 5x + y = 6?

A
5x + 5y = 30

B
80x + 7y = 43

C
10x + 2y = 12

D
None of these

Solution

5x + y = 6 ……….. I
10x + 2y = 12………………..II
Equations will be equivalent if

On comparing the above all four equations, we get

Hence, 10x + 2y = 12 is equivalent to 5x + y = 6.
Question 2
1 / -0

If 6x – 2 > –x – 3 + 5(x + 1), then which of the following options best describes x?

A
x < 2

B
x 2

C
x > 1

D
x > 2

Solution

6x – 2 > –x – 3 + 5x + 5 gives 6x – 2 > 4x + 2 or 2x > 4 or x > 2.
Question 3
1 / -0

For what value of m will the roots of the equation 12x² + mx + 5 = 0 be in the ratio 3 : 2?

A

B

C

D

Solution

Let the roots of the equation be 3a and 2a.

Also, 3a + 2a =
⇒ 5a =
⇒ a = ... (1)

Product of roots is 6a² =
⇒ =
⇒ m² = 250

⇒ m = 5
Question 4
1 / -0

The area of a triangle formed by the lines x = 0, y = 0 and + = 1 is

A
ab sq.units

B
sq.units

C
2ab sq.units

D
sq.units

Solution

Area of a right-angled triangle
= ½ × (Perpendicular) × (Base)
Hence, area of the given triangle OAB = ½ ab sq.units
Question 5
1 / -0

A circle of radius 9 cm has an arc of length 12.1 cm. What is the angle subtended by the arc at the centre of the circle?

A
154°

B
231°

C
77°

D
38.5°

Solution

If is the angle subtended by an arc at the centre of the circle of radius r, then the length of that arc = .
Thus, angle subtended at the centre = = 12.1 cm
cm = 12.1 cm
= 77°
Question 6
1 / -0

Which of the following represents the solution set of – 11 4x – 3 13?

A
2 x 4

B
– 2 x 4

C
2 < x < 4

D
– 2 < x < 4

Solution

We have,
– 11 4x – 3 13
– 11 + 3 4x – 3 + 3 13 + 3 [Adding 3 throughout]
– 8 4x 16
x [Dividing by 4 throughout]
– 2 x 4
x [– 2, 4]
Hence, the interval [– 2, 4] is the solution set of the given inequality. Answer: (2)
Question 7
1 / -0

A straight line 6x + 2y = 3 is written in the form of y = mx + c. Which of the following is a correct set of values for m and c?

A
m = 3, c =

B
m = 3, c = -

C
m = - 3, c = -

D
m = - 3, c =

Solution

Given equation:
6x + 2y = 3 (Subtracting 6x from both sides)
6x - 6x + 2y = 3 - 6x
2y = - 6x + 3
(Dividing both sides by 2)

General straight line equation is y = mx + c.
Comparing above equation with general straight line equation, we get
m = - 3 and c =
Question 8
1 / -0

A cylindrical cistern of radius 42 cm is partly filled with water. If a rectangular block measuring 24 cm 21 cm 11 cm is fully immersed in the water, then by how much will the water level rise?

A
1 cm

B
1.5 cm

C
1.75 cm

D
2 cm

Solution

Volume of cylindrical column of increased height = Volume of rectangular block
42 42 h = 24 21 11
h = 1 cm
Therefore, water level rises by 1 cm.
Question 9
1 / -0

The current ages of Meena and Leena are in the ratio 4 : 3. The sum of their ages is 28 years. What will be the ratio of their ages after 8 years?

A
5 : 6

B
6 : 5

C
7 : 4

D
7 : 6

Solution

Ratio of ages of Meena and Leena = 4 : 3
Let the present age of Meena be 4x.
Present age of Leena = 3x
According to the question:
4x + 3x = 28
7x = 28
x = 4
Therefore, the present age of Meena = 4 × 4 = 16 years
Age of Leena = 3 × 4 = 12 years
After 8 years,
Age of Meena = 16 + 8 = 24 years
Age of Leena = 12 + 8 = 20 years
Therefore, required ratio = 24 : 20 or 6 : 5
Question 10
1 / -0

The diameter of a wheel is 63 cm. The distance covered by the wheel in 100 revolutions is

A
99 m

B
198 m

C
63 m

D
136 m

Solution

Circumference = = 198 cm
Distance travelled in one revolution = 198 cm
Hence, distance travelled by the wheel in 100 revolutions = 198 × 100 = 19,800 cm = 198 m
Question 11
1 / -0

The angles of a triangle are in the ratio 2 : 3 : 4. Find the measure of the smallest angle.

A
80°

B
60°

C
40°

D
20°

Solution

Given angles of a triangle are in ratio 2 : 3 : 4.
Sum of angles of a triangle is 180^o.
Let the angles of a triangle be 2x, 3x and 4x.
So, 2x + 3x + 4x = 180^o or 9x = 180^o x = 20^o
So, the smallest angle of a triangle is 2x or 2(20^o) = 40^o.
Question 12
1 / -0

Mr. Khanna pays 10% pa interest on an amount borrowed and lends this amount at 12% pa. If at the end of the year, he earns Rs. 2.4 crore as simple interest in the transaction, then what is the sum transacted?

A
Rs. 480 crore

B
Rs. 240 crore

C
Rs. 120 crore

D
Rs. 60 crore

Solution

Net rate = 2%
SI at 2% of money transacted == 2.4
x = 120 crore
Question 13
1 / -0

A boat can cover a distance upstream in 5 minutes and the same distance downstream in 3 minutes. If the speed of the river is 3 m/minute less than that of the boat, then find the speed of the river.

A
1 m/minute

B
2 m/minute

C
3 m/minute

D
4 m/minute

Solution

Let the speed of boat = x m/minute
Let the speed of river = y m/minute
Upstream speed of boat = (x – y) m/minute
Downstream speed of boat = (x + y) m/minute
According to question,
3(x + y) = 5(x – y)
3x + 3y = 5x – 5y
8y = 2x
x = 4y
Also,
y = x – 3
y = 4y – 3
3y = 3
y = 1 m/minute
Speed of river = 1 m/minute
Question 14
1 / -0

The sum of three consecutive terms of an AP is 21 and sum of their squares is 149. Find the product of the three numbers.

A
315

B
333

C
336

D
343

Solution

Let a - d, a, a + d be the 3 terms of the AP.
3a = 21
a = 7 -- (1)
(a - d)² + a² + (a + d)² = 149 -- (2)
from (1) and (2) , d = 1
= 6, 7, 8,
= 6 x 7 x 8 = 336
Question 15
1 / -0

In the diagram given below, FE and CD are two lines perpendicular to each other. What is the measure of a + b + e?

A
155°

B
150°

C
145°

D
140°

Solution

From the given information:
35° + e = 90°This gives e = 90°- 35°e = 55°d = 90°- 55° = 35°Also, d = a = 35° (vertically opposite angles)
And, e = b = 55° (vertically opposite angles)
So,
a + b + e = 35° + 55° + 55°= 145°