CTET (Central Teacher Eligibility Test) Practice Test: Mathematics - 1

Hence the option B is correct

• Smallest 4-digit number: The smallest 4-digit number starts with 1, so the number must be in the form of 1XXX.


• Having three different digits: Since the number must have three different digits, the last three digits must be different from each other.


• Possible combinations: The possible combinations for the last three digits are 012, 021, 102, 120, 201, 210.


• Choosing the smallest: Among the given options, the smallest number with three different digits is 1002.

• In a rhombus, all sides are equal.

• The diagonals bisect each other at right angles and bisect opposite angles.

• However, the diagonals are generally not equal (they are only equal in a square, which is a special type of rhombus).

There 29 numbers between 38 and 68 . Hence the number of whole numbers between 38 and 68 are 29

The opposite of any negative number is it's positive counterpart. Therefore, opposite of -7 would be 7.

Area of Rectangle = Length * Breadth.
Area of Rhombus Using DiagonalsA = ½ × d₁ × d₂
Area of quadrilateral willl be calculated based on which type of quadriateral it is-
Area of trapezium willl be 1/2 (sum of Parallel sides )*height.

let the number be 100a + 10b + c
(100a + 10b +c) – (100a + 10c +b) = 36
b – c = 4

⇒ In ∠PRQ, Q is a vertex of an angle.

⇒ RP and RQ are two rays of an angle.

⇒ So, RP and RQ​ are two arms of ∠PRQ.

A: 2 × 2 × 7 = 28

B: 2 × 2 × 5 = 20

C: 2 × 2 × 5 × 7 = 140

D: 2 × 2 × 5 × 7 × 3 = 420

a + b = 6
(10a + b) – (10b +a) = 36, a – b = 4
We get a = 5 and b = 1
So number is 51

Let point of contact of RS be A, point of contact of QR be B, point of contact of PQ be C and point of contact of PS be D. Also let AS = x and AR = y
Now, AS = SD = x [Tangents from an external point]

PD = 4.2 - x
But PD = PC= 4.2 - x
And QC = 6.5 - PC = 6.5 - 4.2 + x = 2.3 + x .........(i)  
Now, again, AR = BR = y [Tangents from an external point]
⇒ QB = 7.3 -  y
But QB = QC [Tangents from an external point]

The given equation, 6×(7×3)=(6×7)×36×(7×3)=(6×7)×3, illustrates the Associative Property of multiplication. The Associative Property states that when multiplying three or more numbers, the product is the same, regardless of how the numbers are grouped. In this case, you can rearrange the grouping of the numbers without changing the result of the multiplication.

1m³ = 1000 L and 1m³=1000000cm³ and 1000L= 1000000ml
So 1000000cm³ = 1000000ml which is 1ml = 1cm³

just placed them in descending order 

The first few twin prime pairs are: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), … ... Five is the only prime in two distinct pairs.

Area of Rectangle = product of length and breadth (L * B)
Area of Parallelogram = A = ½ × d₁ × d₂ sin (y) where d1 & d2 are diagonal and y is the angle of intersection of diagonal.
 
Area of Trapezium = 1/2(sum of parallel sides)*height. 

100cm = 1m

1cm = (1/100)m

805cm in m = (805/100)m

Formula used: Divide the length value by 100
Correct option is D. 8.05 m

• Rounded off to the nearest thousands: To round off the number 85642 to the nearest thousands, we look at the hundreds place. Since the hundreds place digit is less than 5 (4), we keep the thousands place (8) the same and change all digits after the thousands place to zero.


• So, 85642 rounded off to the nearest thousands is 86000.

To show: ∠PSR + ∠PQR = 180°
∠SPQ + ∠SRQ = 180°

In △DSA,

∠DAS + ∠ADS + ∠DSA = 180° (angle sum property)

+ ∠ SA = 180° (since RD and AP are bisectors of ∠D and ∠A)

∠DSA = 180°
∠PSR = 180°−

(∵ ∠DSA = ∠PSR are vertically opposite angles)

Similarly,

∠PQR = 180°− 

Adding (i) and (ii), we get, ∠PSR + ∠PQR = 180°
=360° − 1/2 ​× (∠A + ∠B + ∠C + ∠D)
 

=360°− 1/2​ × 360° = 180° ∴ ∠PSR + ∠PQR = 180°

In quadrilateral PQRS,

∠SPQ + ∠SRQ + ∠PSR + ∠PQR = 360°
=> ∠SPQ + ∠SRQ + 180° = 360°
=> ∠SPQ + ∠SRQ = 180°

Hence, showed that opposite angles of PQRS are supplementary.

The quantity that a container holds is called its "capacity" or "volume."

Hence option C is correct.

MMM is 3000 in Roman numerals. To convert 3000 to Roman Numerals, first write 3000 in expanded form, i.e. 3000 = 1000 + 1000 + 1000, then replace the changed numbers with corresponding roman numerals to get 3000 = M + M + M = MMM.