CTET (Central Teacher Eligibility Test) Practice Test: Mathematics - 2

By observing & comparing the given figures, rectangle B is the longest rectangle.

= ( -30) + (-12)

= -30 - 12

= -42 

Just add the Symbol of ⊥ between the vectors

In the pictograph, 1 image equals 1 Absentee. 

On Thursday there are no such images. 

Therefore, Thursday has full attendance.

Given:
₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins
The coins are in the ratio of 6 : 9 : 10
Calculation:
Let the number of coins of ₹ 2, ₹ 5 and ₹ 10 be 6x, 9x, and 10x respectively
⇒ (2 × 6x) + (5 × 9x) + (10 × 10x) = 785
⇒ 157x = 785
∴ x = 5
Number of coins of ₹ 5 = 9x = 9 × 5 = 45
∴ 45 coins of ₹ 5 are in the bag

Let the incomes be 4x, 5x, 6x and the spending be 6y, 7y, 8y and savings are (4x–6y), (5x–7y) & (6x–8y)
Sheldon saves 1/4^th of his income.

Therefore:

⇒ 4x – 6y = 4x / 4
⇒ 4x – 6y = x
⇒ 3x = 6y
⇒ x / y = 2
∴ y = x / 2

Ratio of Sheldon’s Leonard’s & Howard’s savings:

= 4x – 6y : 5x – 7y : 6x – 8y
= x : 5x – 7y : 6x – 8y
= x : 5x – 7x / 2 : 6x – 8x / 2
= x : 3x / 2 : 2x
= 2 : 3 : 4 

Step 1: Question statement and Inferences

We are given an equation to calculate the distance travelled (d) by a free falling body within a time (t).

...(I)

It is given that on earth, a ball dropped from a height of 16 feet takes 1 second to reach the ground.

Therefore from (I), we have

16=

⇒g=32

Thus, we have found the value of acceleration due to gravity for earth.

Let the acceleration due to gravity of the other planet be G_P

It is given that G_P=7g

⇒G_P=7*32……. (II)

Step 2 & 3: Finding required values and calculating the final answer

Once again, using (I) we can write the equation for the free-fall of the ball on the other planet:

2800=

However, from (II), we know that

G_P=7*32

Using this in the above equation, we get,

•  
• t²= 25
• t² – 25 = 0
• (t -5)(t + 5) = 0
• t = 5 or t = -5

However, t denotes time. Therefore, it cannot have a negative value.

Rejecting the negative value, we get t = 5

Thus, on the other planet, it will take a ball 5 seconds to reach the ground from a height of 2800 feet under conditions of free fall.

Answer: Option (C)

 0 is in right side of -1 in the number line therefore, - 1 < 0 is the correct answer.

First, the largest 7 digit number is --?
Its 9,999,999
Now, add 1 to it
9,999,999 + 1 = 10,000,000
Or in Indian numbering system - 1,00,00,000

Here ∠Q = 90° [Angle between tangent and radius through the point of contact]
Now, in triangle OPQ:
Using Pythagores theorem,
OP² = OQ² + PQ²
⇒ OP² = (6)² + (8)² = 36 + 64 = 100
⇒ OP = √100 = 10
⇒ OP = 10 cm
∴ PR = OP + OR = OP + OQ  [OR = OQ = Radii]
⇒ PR = 10 + 6 = 16 cm

Total surface area of a cylinder = πr²+2πrh+πr²=2πr(r+h)

Step 1: Question statement and Inferences

We are given two quadratic equations in x. We will solve both of them and look for a common value of x

Step 2 & 3: Finding required values and calculating the final answer

Approach:

1. We observe that both the given quadratic equations are already in factored form.
2. By putting each factor of an equation equal to zero, we can find the roots of an equation. So, we will be able to find the two roots of each equation.
3. The common root of both equations will be our answer

Implementing the approach:

Finding the roots of the first equation:

(x - 3)(2x - 5)

Either

x - 3 = 0

• x = 3  . . . Root 1A

Or

2x - 5 = 0

• x = 5/2 . . . Root1B

Finding the roots of the second equation:

Either

• x = 5/2 . . . Root 2A

Or

x - 4 = 0

• x = 4 . . . Root 2B

We observe that x=5/2

 is a common root of both equations.

• The value of x that satisfies both equations is x=5/2

Answer: Option (C)

The sum of -19 and -21 is calculated as follows:
(−19)+(−21)=−40
So, the correct answer is (a) -40.

SP = 1.50 Rs. Profit = 25%.
CP = 1.50 × (100/125) = 1.20 Rs.

When adding integers with different signs, the sign of the sum depends upon the sign of the number with the greater absolute value. This can be understood by regrouping and then using addition of opposites.

Step 1: Question statement and Inferences

Given equation is x³−7x²+12x=0

and p, q, r are the roots of this equation.

We need to find the value of the expression  

. For this we need to find the values of p, q and r by solving the given equation.

Step 2 & 3: Finding required values and calculating the final answer

x³−7x²+12x=0

⇒x(x²−7x+12)=0 ....(I)

Note that x²−7x+12

is a standard form quadratic equation. It can be factorized as follows:

x²−4x−3x+12=(x−3)(x−4)

Therefore (I) can be rewritten as:

x(x-3)(x-4) = 0

By putting each factor equal to zero, we can find the roots of (I):

x = 0(Root 1)

x – 3 = 0

⇒ x = 3 (Root 2)

x – 4 = 0

⇒ x = 4 (Root 3)

Therefore possible values for p, q, r: {0, 3, 4}

Since it is given that p < q < r, we have:

p = 0, q = 3 and r =4

Therefore

=

When a number is raised to the power zero, we get 1.

So,=1

⇒=1

Answer: Option (C)

Lateral surface area -> Total Surface area of cuboid - surface area of Top and Bottom Surfaces.
=> 2LB + 2BH + 2HL - LB - LB
=> 2BH + 2HL
=> 2H(L + B)
hence option A is correct 

In the given pictograph one image represents 10 people. 

Therefore, the number of people who prefer white colour are 2 x 10 = 20.

Let's examine each statement to verify its correctness:

1. Statement: −7+(−6)=−13

   • Solution: Adding two negative numbers, −7+(−6)=−13-7 + (-6) = -13−7+(−6)=−13.
   • Result: This statement is true.

2. Statement: −5+1=4

   • Solution: Adding −5 and 1 gives −4, not 4.
   • Result: This statement is false.

3. Statement: 2+(−1)=1

   • Solution: Adding 2 and −1 gives 1.
   • Result: This statement is true.

4. Statement: 8+(−9)=−1

   • Solution: Adding 888 and −9 gives −1.
   • Result: This statement is true.

Therefore, the false statement is:

2: −5+1=4. The correct result should be −5+1=−4.

Here SD = RD = 5 units [Tangents from an external point]
And PB = QB = 4 cm [Tangents from an external point]
∴ QC = 10 - QB = 10 - 4 = 6 units
Also QC = RC = 6 units [Tangents from an extemal point]
∴ CD = RD + RC = 5 + 6 = 11 units
Also AP = AS = 2 units [Tangents from an external point]
∴ AD = AS + DS = 2 + 5 = 7 units Therefore. Perimeter of quadrilateral ABCD = 6 + 10 + 11 + 7 = 34 units 

Keeping 6 fixed at its own place. If we want to create a smallest number. Then we can do it by using the small numbers from the remaining numbers.
After 6, 0 will come, then 3, 4,5,7,9.
Therefore, option 'c' is the correct answer.

 There is no predecessor for natural number 1. As natural number starts from 1