CTET (Central Teacher Eligibility Test) Practice Test: Mathematics - 4

a – 24 = 2a/3
we get a = 72
so one-eighth of the number = 72/8 = 9

Here, OP = 00 = 5 cm [Radii]
And OR = PR -  OP = 8 - 5 = 3 cm Also, OA = 5 cm [Radius]
Now, in triangle AOQ, OA² = OR² + AR² ⇒ 52 = 32 + AR²
⇒AR² = 25-9= 160 AR= 4cm
Since, perpendicular from centre of a circle to a chord bisects the chord.
∴ AB = AR+ BR = 4+ 4 = 8cm 

It can be observed from the bar graph that on Wednesday, 20 shirts were sold. 

• When the length of stick = 20 m, then length of shadow = 10 m i.e. in this case length = 2 * shadow
• With the same angle of inclination of the sun, the length of the tower that casts a shadow of 50 m is: 2 * 50m = 100m
  ⇒ Height of tower = 100 m

Numbers which have more than two factors are called composite numbers.

(25/100)*a = 2*(65/100)*b
b:a = 5:26

In the pictograph, 1 image equals 10 people. 

The colour red has 11 such images representing it. 

Therefore, the number of people preferring green colour are 11 x 10 = 110

Volume is nothing but multiplication of Length breadth and height:
V = L * B * H
SI unit of Length is m (Meter)
so as the breadth and height.
SI unit of Volume =  m * m * m
=> m³ .
Hence option c is correct.

Chalk box and soap have breadth,length and height . Cylinder has 2 radii and height. A ring (here) is made up of two concentric circles which is a 2d figure. Hence ring is 2 dimensional

It can be observed from the graph that 3 units, or 15 shirts, were sold on Monday.

• The triangle BOC is an isosceles triangle with sides OB and OC both being equal as they are the radii of the circle. Hence, the angle OBC = angle OCB = 30°.
• Hence, the third angle of the triangle BOC i.e. Angle BOC would be equal to 120°.
  ⇒ BOC = AOD = 120° 
• Also, in the isosceles triangle DOA: 
  Angle ODA = Angle DAO = x = 30°

The angle between perpendicular lines is 90°.

A diameter divides the circle into 2 equal parts. So, it can be considered as a line of symmetry.

Given:

A : B = 3 : 4

B : C = 5 : 6

C : D = 8 : 9

Sum to divided among them = Rs. 12,384

Concept used:

Ratio Proportion

Calculation:

A : B = 3 : 4 = 15 : 20

B : C = 5 : 6 = 20 : 24

C : D = 8 : 9 = 24 : 27

A : B : C : D = 15 : 20 : 24 : 27

Share of C = 24/(15 + 20 + 24 + 27) × 12384 = Rs. 3456

∴ The share of C is Rs. 3456.

Steps 1 & 2: Understand Question and Draw Inferences

Given equation is

x²+bx+c=0 …………….. (I)

Let us suppose that the roots of this equation are p and q.

Given that b and c are constants, we need to find the value of c.

We know that for a quadratic equation

ax²+bx+c=0

Sum of roots = −b/a

Product of roots = c/a

In the given equation, a = 1

Therefore,

Sum of roots = -b

Product of roots = c

Step 3: Analyze Statement 1

It is given that the sum of roots of (I) is zero.

So, we have:

-b = p + q = 0

• b = 0 ………….. (II)

We cannot find the value of c from this information.

Statement 1 alone is not sufficient to arrive at a unique answer.

Step 4: Analyze Statement 2

Now let us look at statement 2.

Writing it in equation form, we have:

p²+q²=18

We know that

p²+q²=(p+q)²−2pq

• p²+q²=(−b)²−2c

• (−b)²−2c=18
• b²−2c=18 ………….. (III)

But we need the value of b here to find the value of c.

Statement 2 alone is not sufficient to arrive at a unique answer.

Step 5: Analyze Both Statements Together (if needed)

Now, let us look at both the statements together.

From statement 1, we have

b = 0

From statement 2, we have

b² - 2c = 18

Combining both of these, we get:

-2c = 18

• c = -9

Answer: Option (C)

• Given, x² + 9 = 6x
• ⇒ x² - 6x + 9 = 0
• ⇒ x² -3x -3x + 9 = 0
• ⇒ x ( x - 3) - 3 ( x - 3) = 0 
• Taking (x-3) common from the equation , we get
• ⇒ (x - 3) (x - 3) = 0
• ⇒ x = 3

Let the first of the eight consecutive odd numbers be a. Then the numbers are a, a+2, a+4, a+6, a+8, a+10, a+12, a+14.

Their sum is 8a + (2+4+6+8+10+12+14) = 8a + 56. This equals 656, so

8a + 56 = 656 → 8a = 600 → a = 75.

The largest odd number = a + 14 = 75 + 14 = 89.

For the four consecutive even numbers let the first be n. Then the numbers are n, n+2, n+4, n+6.

Their average is n + 3. Given this average is 87, so n + 3 = 87 → n = 84.

The largest even number = n + 6 = 84 + 6 = 90.

Therefore the sum of the largest even and largest odd numbers = 90 + 89 = 179.

1m = 100 cm 3m = 3×100 cm = 300cm

Total surface area of cube = 6a²

Curved surface area of cube = 4a² 

Volume of cube = a³

There are 2 symmetry lines of a rectangle which are from its length and breadth. These two lines cut the rectangle in two similar halves which are mirror images of each other. If a rectangle is folded along its line of symmetry, it superimposes perfectly.

In the given pictograph one image represents 10 people.

Green and Black colour has equal number of images i.e. 3. Therefore, these 2 colours are are liked by same number of people.

Area of square having sides 5 cm = 5² = 25 cm²

Area of smaller square having sides 1 cm = 1² = 1 cm²

Then area of 4 squares will be 4 cm²

Area of shaded portion will be =  Area of square having sides 5 cm - area of 4  smaller squares (Unshaded portion)

 Area of shaded portion = 25 cm² - 4 cm²

 Area of shaded portion = 21 cm²

• In △PAB

  ⇒  ∠PAB=40o         [ Given ]

  ⇒  ∠BPA=90o      [ angle inscribed in a semi-circle ]

  ⇒  ∠PAB+∠PBA+∠BPA=180o

  ∴   40o+∠PBA+90o=180o

  ∴   ∠PBA=180o−130o

  ∴   ∠PBA=50o

  ⇒  ∠PBA=∠PCA=50o     [ angles inscribed in a same arc PA ] 

  ∴   ∠PCA=50o

∴ H.C.F. of 120 & 144 =24