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Class 10 Exam  >  Class 10 Tests  >  NTSE for Class 10  >  National Level Solved Paper (MAT) - 2016 - Class 10 MCQ

National Level Solved Paper (MAT) - 2016 - Class 10 MCQ


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30 Questions MCQ Test NTSE for Class 10 - National Level Solved Paper (MAT) - 2016

National Level Solved Paper (MAT) - 2016 for Class 10 2024 is part of NTSE for Class 10 preparation. The National Level Solved Paper (MAT) - 2016 questions and answers have been prepared according to the Class 10 exam syllabus.The National Level Solved Paper (MAT) - 2016 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for National Level Solved Paper (MAT) - 2016 below.
Solutions of National Level Solved Paper (MAT) - 2016 questions in English are available as part of our NTSE for Class 10 for Class 10 & National Level Solved Paper (MAT) - 2016 solutions in Hindi for NTSE for Class 10 course. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free. Attempt National Level Solved Paper (MAT) - 2016 | 100 questions in 120 minutes | Mock test for Class 10 preparation | Free important questions MCQ to study NTSE for Class 10 for Class 10 Exam | Download free PDF with solutions
National Level Solved Paper (MAT) - 2016 - Question 1
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If x + y + z = 0, then value of

Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 1

Given x + y + z = 0    ...(i)

(From equation (i)
x = – (y + z),
y = – (x + z)
z = – (x + y))

National Level Solved Paper (MAT) - 2016 - Question 2
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If sin A + cos A = √2 sin (90° – A) then value of ( √2+ 1) tan A will be

Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 2

Given sin A + cos A = √2 cos A

sin A = √2 cos A – cos A

sin A = ( √2 – 1) cos A

tan A = √2 – 1

( √2 + 1) tan A = ( √2 + 1)( √2 – 1)

( √2 + 1) tan A = 1

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National Level Solved Paper (MAT) - 2016 - Question 3
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If the point (K, 2)is equidistant from the point (5, –2) and (1, –2) then value of K2 + 7 will be

Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 3

Using distance formula

(k – 5)2 + (4)2 = (k – 1)2 + (4)2

⇒ (k – 5)2 – (k – 1)2 = 0

⇒ (k – 5)2 = (k –1 )2

⇒ k – 5 = |k–1|

⇒ k = 5 = –k + 1

∴ 2k = 6

⇒ k = ± 3

⇒ k2 + 7 = (± 3)2 + 7 = 16

National Level Solved Paper (MAT) - 2016 - Question 4
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If each side of a cube is increased by 40%, then how much percent its total surface area will be increased.
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 4

Using formula

National Level Solved Paper (MAT) - 2016 - Question 5
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If sum of squares of zeros of a quadratic polynomial g(y) = y2 – 6y + p is 10. What will be the value of p.
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 5

Given quadratic polynomial

According to question

National Level Solved Paper (MAT) - 2016 - Question 6
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A train cross a pole in 12 seconds. If the speed of the train is 54 km/hr then length of train will be
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 6

Here speed of the train
= 54 km/hr

∴ Length of train
= speed of the tran × total time
= (15 × 12) m = 180 m
∴ The length of a train is 180 m

National Level Solved Paper (MAT) - 2016 - Question 7
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If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number is
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 7

From given question

x + y = 9    ...(i )

(10x + y) – (10y + x) = 45

9 (x – y) = 45

x – y = 5     ...(ii )

Solving equations (i ) and (ii ), we get

∴  x = 7, y = 2

So the number

= 10x + y

= 10 x 7 + 2

= 72

∴ 72 is the number

National Level Solved Paper (MAT) - 2016 - Question 8
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How many numbers between 10 and 90 are divisible by 8 completely
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 8

Number between 10 and 90, which are divisible by 8.

First term (a) = 16

Last term (tn) = 88

∴ tn = a + (n – 1)d

88 = 16 + (n – 1)8

72 = (n – 1)8

∴ n = 1 + 9

= 10

National Level Solved Paper (MAT) - 2016 - Question 9
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Value of x will be
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 9

Given


National Level Solved Paper (MAT) - 2016 - Question 10
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Simplify
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 10

Given expression is

National Level Solved Paper (MAT) - 2016 - Question 11
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Vinod has some cows and some hens in his shed. The total number of legs is 92 and total number of heads is 29. Then the number of hens in his shed is
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 11

Let the total number of hens be ‘x’.

∴ Total number of cows is (29 – x).

According to question

2x + 4(29 – x) = 92

2x + 116 – 4x = 92

∴ 2x = 24

∴ x = 24

Hence the number of hens is 24

National Level Solved Paper (MAT) - 2016 - Question 12
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Parth can row 16 km downstream and 8 km upstream in 6 hours. He can row 6 km upstream and 24 km downstream in 6 hours. Find the speed of Parth in still water
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 12

From given question

Solving equations (i ) and (i i ), we get

x = 1/8

y = 1/2

Now e + f = 8 {e represents Parth’s speed}
e – f = 2 {f represents speed of stream}

⇒ e = 5 km/hr

National Level Solved Paper (MAT) - 2016 - Question 13
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Value of
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 13

National Level Solved Paper (MAT) - 2016 - Question 14
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Find the angle between the two hands of a clock at 15 minutes past 4 O' clock (Minute hand and hour hand)
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 14

At 4:15, angle between hands

= (4 × 30°) – (5.5 × 15°)

= 120° – 82.5

= 37.5°

So the angle between two hands of a clock is 37.5°.

National Level Solved Paper (MAT) - 2016 - Question 15
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If  then what will be the value of 
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 15

Given

Now

National Level Solved Paper (MAT) - 2016 - Question 16
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The traffic signals at four road crossing change every 30 second, 1 minute, 45 seconds and 75 seconds respectively. If they change simultaneously at 9 AM, at what time will they change simultaneously again.
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 16

LCM of 30 sec, 1 min , 45 sec and 75 sec

= 15 min

∴ At 9:15 AM, they will simultaneously change again.

National Level Solved Paper (MAT) - 2016 - Question 17
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If A:B = 2:3, B:C = 2:4, and C:D = 2:5 then A:D is equal to
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 17

The equired ratio of A : D is

National Level Solved Paper (MAT) - 2016 - Question 18
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In the adjoining figure, ABCD is a square of 7cm side length. is an arc of a circle of radius AB, what is the area of the shaded region?
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 18

∴ B = 28/2 = 14

⇒ Shaded area = 28 cm2

National Level Solved Paper (MAT) - 2016 - Question 19
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Width of a room is half of its height and height of room is 3/2 times of its length. If cost of flooring carpet on floor at the rate of Rs 4/m2 is Rs 432, then what will be height of room?
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 19

National Level Solved Paper (MAT) - 2016 - Question 20
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Which number in the following will completely divide 315 + 316 + 317
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 20

Given

⇒ Divisible by 13.

National Level Solved Paper (MAT) - 2016 - Question 21
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What will be the difference between simple interest and compound interest on sum of Rs 6000 in 2 years at the rate of interest of 5% p.a.
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 21

Using formula

National Level Solved Paper (MAT) - 2016 - Question 22
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Value of (3.5)3 – (2.5)3 is
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 22

(3.5)3 – (2.5)3

= (3.5 – 2.5) ((3.5)2 + (2.5)2 + 3.5 x 2.5)

= 1 x (12.25 + 6.25 + 8.75)

= 27.25

National Level Solved Paper (MAT) - 2016 - Question 23
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If  , then what is the value of x?
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 23

Given

squaring on both sides, we get

National Level Solved Paper (MAT) - 2016 - Question 24
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In the adjoining figure, ΔABC, is circumscribing a circle. Then the length of BC is
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 24

⇒ BC = 10 cm(Tangents from a point to the circle are of equal length)

National Level Solved Paper (MAT) - 2016 - Question 25
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The selling price of 5 articles is the same as the cost price of 3 article. The gain or loss percent is
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 25

From given question

SP of 5 = CP of 3

5 SP = 3 CP

National Level Solved Paper (MAT) - 2016 - Question 26
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If the first half of the English alphabet is reversed and so is the 2nd half, then which letter is7th to the right of the 12th letter from the left side?
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 26

The required sequence of the alphabet is:

So the letter is 7th to the right of 12th letter from the left side is U.

National Level Solved Paper (MAT) - 2016 - Question 27
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If in a certain code language ‘THREAT’ is written as ‘RHTTAE’ then how will ‘PEARLY’ be written in that code?
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 27

Logic : First half is reversed, then second half of reversed.

National Level Solved Paper (MAT) - 2016 - Question 28
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What comes in place of question mark ‘?’

4, 6, 16, 62, 308, ?
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 28

National Level Solved Paper (MAT) - 2016 - Question 29
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In a group of five persons Kamal is the tallest while Leela is the shortest. Rashi is shorter than Kamal but taller than Vinita and Priti. Priti is second shortest person in the group. Who is the third tallest?
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 29

The arrangement is:

Kamal, Rashi, Vinita, Preeti, Leela

∴ 3rd in order of height is Vinita.

National Level Solved Paper (MAT) - 2016 - Question 30
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Which is the following diagram best depicts the relationship between Males, Husbands andDoctors?
Detailed Solution for National Level Solved Paper (MAT) - 2016 - Question 30

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