CTET (Central Teacher Eligibility Test) Practice Test: Mathematics - 3

Steps 1 & 2: Understand Question and Draw Inferences

Given equation is

 ax²+bx+c=0

It is also given that a, b and c are constants and that a≠0.

We need to find the value of b.

Step 3: Analyze Statement 1

It is given that 3 and 4 are the roots of the equation.

We know that for a quadratic equation
ax²+bx+c=0

Sum of roots = −b/a

Product of roots = c/a

Therefore, we have:

−ba  = 3 + 4 = 7………..(I)

c/ a  = 3 * 4 = 12 …………(II)

Note that these are two linear equations in three variables. So we cannot solve exclusively for b.

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

Step 4: Analyze Statement 2

It is given that the product of roots is 12.

Therefore, we have:

c/a  = 12 …….(III)

Notice that (III) is a single linear equation in two variables. Moreover, it doesn’t provide any information about b.

So 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.

Statement 1 gives us (I) and (II)

Statement 2 gives us (III).

However, notice that (III) is essentially same as (II).

In other words, we are simply left with (I) and (II) (essentially the same situation as in statement 1).

Therefore statement 1 and statement 2 combined together are not sufficient to arrive at a unique answer.

Answer: Option (E)

 U appears the same in mirror too.

The below given steps will be followed to construct the required triangle.

Step I:
Draw line segment AB of 12 cm. Draw a ray AX making 90deg with AB.
Step II:
Cut a line segment AD of 18 cm (as the sum of the other two sides is 18) from ray AX.
Step III:
Join DB and make an angle DBY equal to ADB.
Step IV:
Let BY intersect AX at C. Join AC, BC.

ΔABC is the required triangle.

Since diagonals of a rhombus bisect each other at right angle .

∴ In △AOB , we have 

∠OAB + ∠x + 90° = 180° 

∠x = 180° -  90° - 35° [∵ ∠OAB = 35°]

= 55° 

Also, ∠DAO = ∠BAO = 35°  

∴ ∠y + ∠DAO + ∠BAO + ∠x = 180°  

⇒ ∠y + 35° + 35° + 55° =  180°  

⇒ ∠y = 180° - 125° = 55°

Hence the values of x and y are x =  55°, y =  55°.    

Of the given options 973572 is an even number.

= (-8) - 3

= -8 - 3 

= - 11

try to  convert this statment in mathematical equation and you will get your answer

The minimum number of shirts, that is, 10 shirts were sold on Tuesday. 

1 is a factor of every number.

When two factors are multiplied we get a product.

Base area = length * breadth = 20 sq.cm
Now,
Volume of cuboid = length * breadth * height
Volume = 20 * height
200 = 20 * height
Height = 200 / 20 = 10 cm.

The Hindu-Arabic numeral for CD is 400.Explanation:

- In Roman numerals, CD represents the number 400.
- C represents 100 and D represents 500 in Roman numerals.
- When a smaller number is placed before a larger number in Roman numerals, it is subtracted from the larger number.
- So, CD represents 500 - 100 = 400.

Concept:

Counting the whole numbers within the given range.

Solution:

⇒ The sequence of whole numbers between 0 and 10 is: 1, 2, 3, 4, 5, 6, 7, 8, 9

⇒ We simply need to count these numbers.

⇒ There is 1 one. ⇒ There is 1 two. ⇒ There is 1 three. ⇒ There is 1 four. ⇒ There is 1 five. ⇒ There is 1 six. ⇒ There is 1 seven. ⇒ There is 1 eight. ⇒ There is 1 nine.

by adding all the counts, we get 9 whole numbers between 0 and 10.

Hence, the correct answer is "9".

In the pictograph, 1 image equals 1 Absentee. 

On Saturday there are 8 such images, which is higher than all the other days in the week. 

Therefore, on Saturday the maximum number of students were absent.

The probability of an impossible event is 0, as there is no chance of that event ever happening. 

Reflex angles are those that "bend back" on themselves, creating an angle larger than a straight line (180°) but not completing a full circle (360°). Therefore, 270° fits the definition of a reflex angle.

So, the correct answer is 270°.

• Since the lines, AB and CD are parallel to each other, and the lines RD and AN are parallel, it means that the triangles RBF and NCI are similar to each other. Since the ratio of CN : BR = 1.333, if we take BR as 3, we will get CN as 4.
• This means that the ratio of BF : CI would also be 3 : 4.
  Also, the ratio of BR : RS : ST : TA = BF : FG : GH : HI = 3 : 5 : 2 : 7 (given).

Hence, the correct answer is 3 : 5 : 2 : 7 : 4 

• 
• 1248 + M = 312 x 5
• M = 1560 - 1248 = 312

Natural numbers are naturally occurring counts of an object 1,2,3,4,…forming an infinite list in which the first number is 1 and every next number is equal to the preceding number +1.

Whole number include the set of all Natural numbers and also 0.

Let N and W elements of natural and whole numbers.

N={1,2,3,4,....∞}

W={0,1,2,3,4,...∞}

So, here we can say N is subset of W.

∴ N⊂W is correct statement.

In the given pictograph one image represents 10 people. 

Therefore, the number of people who prefer yellow colour are 6 x 10 = 60.

Since the angle between the two tangents drawn from an external point to a circle in supplementary of the angle between the radii of the circle through the point of contact.
∴ ∠PTQ = 180^∘−110^∘ = 70^∘

179^∘ 90^∘, 179^∘ 180^∘  So it is obtuse.

Hence the option A is correct

odd numbers – x-2, x, x+2 ; even numbers – y-2, y, y+2
3x + 3y = 231
x + y = 77
(y – 2) – (x – 2) = 11
y – x = 11
x = 33, y = 44
sum of the largest even number and odd number = 46 + 35 = 81

Given: SQ = 6 cm and RQ = 4 cm.

To find the length of OR, we can use the properties of the right triangle OQR, where:

• OQ is the radius of the circle.
• Since SQ = 6 cm, then OQ = OS = 6/2 = 3 cm.
• Angle Q is a right angle (90°).

Using the Pythagorean theorem in triangle OQR:

• OR² = QR² + OQ²
• Substituting the known values: OR² = (4 cm)² + (3 cm)²
• Calculating: OR² = 16 + 9 = 25
• Thus, OR = √25 = 5 cm.

The final result is that OR is equal to 5 cm.

• Imagine a circle on the corner of the rectangle. 
• 3 quarters of the circle lie outside the rectangle and 1 quarter lies inside. 
• Hence, Required ratio = 3 : 1