NMTC Kaprekar Sub-Junior 2019 Solved Question Paper PDF

For the following questions answer them individually

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 1

If $$4921 \times D = ABBBD$$, then the sum of the digits of $$ABBBD \times D$$ is

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 2

What is the 2019th digit to the right of the decimal point, in the decimal representation of $$\frac{5}{28}$$?

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 3

If $$X$$ is a 1000 digit number, $$Y$$ is the sum of its digits, $$Z$$ the sum of the digits of $$Y$$ and $$W$$ the sum of the digits of $$Z$$, then the maximum possible value of $$W$$ is

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 4

Let $$x$$ be the number $$0.000\ldots001$$ which has 2019 zeroes after the decimal point. Then which of the following numbers is the greatest?

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 5

Where A, B, C, D, E are distinct digits satisfying this addition fact, then E is

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 6

In a 5 x 5 grid having 25 cells, Janani has to enter 0 or 1 in each cell such that each sub square grid of size 2 x 2 has exactly three equal numbers. What is the maximum possible sum of the numbers in all the 25 cells put together?

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 7

$$ABCD$$ is a square. $$E$$ is one fourth of the way from $$A$$ to $$B$$ and $$F$$ is one fourth of the way from $$B$$ to C. $$X$$ is the centre of the square. Side of the square is 8 cm. Then the area of the shaded region in the figure in $$\text{cm}^2$$ is

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 8

$$ABCD$$ is a rectangle with $$E$$ and $$F$$ are midpoints of $$CD$$ and $$AB$$ respectively and $$G$$ is the mid-point of $$AF$$. The ratio of the area of $$ABCD$$ to area of $$AECG$$ is

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 9

each alphabet represents a different digit, what is the maximum possible value of FLAT?

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 10

How many positive integers smaller than 400 can you get as a sum of eleven consecutive positive integers?

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 11

Let $$x, y$$ and $$z$$ be positive real numbers and let $$x \geq y \geq z$$ so that $$x+y+z=20.1$$. Which of the following statements is true?

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 12

A sequence $$\{a_n\}$$ is generated by the rule, $$a_n = a_{n-1} - a_{n-2}$$ for $$n \geq 3$$. Given $$a_1 = 2$$ and $$a_2 = 4$$, then sum of the first 2019 terms of the sequence is given by

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 13

There are exactly 5 prime numbers between 2000 and 2030. Note $$2021 = 43 \times 47$$ is not a prime number. The difference between the largest and the smallest among these is

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 14

Which of the following geometric figures is possible to construct?

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 15

If $$y^{10} = 2019$$, then

NMTC KAPREKAR Sub-Junior 2019 Solved PDF - Question 16

A sequence of all natural numbers whose second digit (from left to right) is 1, is written in strictly increasing order without repetition as follows. $$11, 21, 31, 41, 51, 61, 71, 81, 91, 110, 111, \ldots$$ Note that the first term of the sequence is 11. The third term is 31, eighth term is 81 and tenth term is 110. The 100th term of the sequence will be