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Full Syllabus Mock Test

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Q1 Logical Reasoning
If 2x = 10 gives x = 5, then 4x = 20 gives x = ___ ?
x = 20 ÷ 4 = 5.
Q2 Mathematical Reasoning
What is the volume of a cube of side 5 cm?
5³ = 125 cm³.
Q3 Everyday Mathematics
A rope piece is ¾ m long. How long are 4 such pieces?
¾ × 4 = 3 m.
Q4 Mathematical Reasoning
Solve: 5x = 2x + 12.
3x = 12, so x = 4.
Q5 Mathematical Reasoning
Between which integers does −5/4 lie?
−5/4 = −1.25 lies between −2 and −1.
Q6 Everyday Mathematics
In a class of 40, 10 like cricket. What pie-chart angle represents cricket?
(10/40) × 360 = 90°.
Q7 Logical Reasoning
5x + 10 = 5( ? )
5(x + 2).
Q8 Logical Reasoning
In direct proportion, x/y is ___ ?
In direct proportion the ratio stays constant.
Q9 Logical Reasoning
The probability of a certain event is ___ ?
A certain event has probability 1.
Q10 Mathematical Reasoning
What is the amount on ₹2000 at 10% compound interest for 2 years?
Year 1: 2200, year 2: 2420.
Q11 Achievers Section
The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The largest is ___ ?
Parts = 10; 360 ÷ 10 = 36, so the largest is 4 × 36 = 144°.
Q12 Everyday Mathematics
A car covers 100 km in 2 hours. At the same speed, how far in 5 hours?
Direct: 50 km/hr × 5 = 250 km.
Q13 Logical Reasoning
a² − b² factorises as ___ ?
Difference of squares: (a + b)(a − b).
Q14 Everyday Mathematics
The diagonals of a rectangle are ___ ?
A rectangle has equal diagonals.
Q15 Everyday Mathematics
1 pen costs ₹10. On a cost-quantity graph, what is the cost of 4 pens?
4 × 10 = ₹40.
Q16 Mathematical Reasoning
Expand: (x + 3)².
x² + 6x + 9.
Q17 Mathematical Reasoning
On y = x + 1, what is y when x = 4?
y = 4 + 1 = 5.
Q18 Mathematical Reasoning
The probability of an impossible event is ___ ?
An impossible event has probability 0.
Q19 Logical Reasoning
A 100% increase means the value ___ ?
Adding 100% doubles the value.
Q20 Everyday Mathematics
A father is three times as old as his son and 30 years older. The son's age is ___ ?
x + 30 = 3x, so x = 15.
Q21 Everyday Mathematics
Write 4,500,000 in standard form.
4,500,000 = 4.5 × 10⁶.
Q22 Mathematical Reasoning
Divide 12x³ by 3x.
12 ÷ 3 = 4 and x³ ÷ x = x², so 4x².
Q23 Logical Reasoning
A discount reduces the ___ ?
A discount is taken off the marked price.
Q24 Everyday Mathematics
A man walks 5 km North, then 5 km East. In which direction is he from the start?
North and East combine to North-East.
Q25 Achievers Section
What is the volume of a cylinder with radius 7 cm and height 5 cm (π = 22/7)?
(22/7) × 49 × 5 = 770 cm³.
Q26 Mathematical Reasoning
What is 8³?
8 × 8 × 8 = 512.
Q27 Logical Reasoning
Probability values range from 0 to ___ ?
Probability ranges from 0 to 1.
Q28 Mathematical Reasoning
What is 72 − 27?
72 − 27 = 45 = 9 × 5.
Q29 Logical Reasoning
(a + b)² = a² + 2ab + ___ ?
(a + b)² = a² + 2ab + b².
Q30 Mathematical Reasoning
What is the reverse of 58?
Swapping the digits gives 85.
Q31 Mathematical Reasoning
What pie-chart angle represents 25% of the data?
(25/100) × 360 = 90°.
Q32 Logical Reasoning
In a 3-set Venn diagram, items common to all sets lie in the ___ ?
The centre overlap belongs to all three sets.
Q33 Logical Reasoning
The coordinates of the origin are ___ ?
The origin is (0, 0).
Q34 Achievers Section
A point (a, 0) lies on which axis?
Since y = 0, the point is on the x-axis.
Q35 Mathematical Reasoning
A rhombus has diagonals 10 cm and 12 cm. Its area is ___ ?
½ × 10 × 12 = 60 sq cm.
Q36 Logical Reasoning
1 cm³ equals ___ ?
1 cm³ = 1 mL.
Q37 Mathematical Reasoning
What is √256?
16 × 16 = 256.
Q38 Everyday Mathematics
5 taps fill a tank in 8 hours. How long for 10 taps?
Inverse: 5 × 8 = 40, so 40 ÷ 10 = 4 hours.
Q39 Mathematical Reasoning
Decrease 80 by 25%.
25% of 80 = 20, so 80 − 20 = 60.
Q40 Logical Reasoning
ab + ba is always divisible by ___ ?
ab + ba = 11(a + b), a multiple of 11.
Q41 Logical Reasoning
Which of these is a perfect cube?
64 = 4³.
Q42 Mathematical Reasoning
What is the amount on ₹1000 at 10% compound interest for 2 years?
CI ₹210, so amount ₹1210.
Q43 Mathematical Reasoning
3 kg cost ₹90. What do 5 kg cost?
₹30 per kg × 5 = ₹150.
Q44 Mathematical Reasoning
Factorise x² − 16.
Difference of squares: (x + 4)(x − 4).
Q45 Achievers Section
If A = 1, B = 2, …, Z = 26, what is the sum of the letters in 'CAB'?
C + A + B = 3 + 1 + 2 = 6.
Q46 Mathematical Reasoning
4 workers finish in 6 days. How long for 8 workers?
4 × 6 = 24, so 24 ÷ 8 = 3 days.
Q47 Achievers Section
By how much does CI exceed SI on ₹1000 at 10% for 2 years?
CI ₹210 − SI ₹200 = ₹10.
Q48 Logical Reasoning
Which of these is a perfect square?
64 = 8².
Q49 Mathematical Reasoning
Each exterior angle of a regular pentagon is ___ ?
360 ÷ 5 = 72°.
Q50 Everyday Mathematics
A cube has volume 64 cm³. What is its side?
∛64 = 4 cm.
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