NDA I - Mathematics Question Paper 2018 - Defence MCQ

What is the principal argument of (−1 − i), where 

Let α and β be real numbers and z be a complex number. If z² + αz + β = 0 has two distinct non-real roots with real roots Re(z) = 1, then it is necessary that

Let A and B be subsets of X and C = (A ∩ B′) ∪ (A′ ∩ B), where A’ and B’ are complements of A and B respectively in X. What is C equal to?

How many numbers between 100 and 1000 can be formed with the digits 5, 6, 7, 8, 9 if the r epetition of digits is not allowed?

The number of non-zero integral solutions of the equation |1 − 2i|^x − 5^x i

If the ratio of AM to GM of two positive numbers a and b is 5:3, then a:b is equal to

If coefficients of a^m and aⁿ in the expansion of (1 + a)^m+n are α and β, then which one of the following is correct?

If x + log₁₅(1 + 3^x) = x log₁₅5 + log₁₅12, where x is an integer, then what is x equal to?

How many four-digit numbers divisible by 10 can be formed using 1, 5, 0, 6, 7 without repetition of digits?

In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only, and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.

Q. What is the number of students who are good in either Hindi or Mathematics but not in English?

In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only, and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.

Q. What is the number of students who are good in Hindi and Mathematics but not in English?

If α and β are different complex numbers with |α| = 1, then what is 

The equation |1 − x| + x² = 5 has

The binary number expression of the decimal number 31 is

What is i¹⁰⁰⁰ + i¹⁰⁰¹ + i¹⁰⁰² + i¹⁰⁰³ equal to 

What is equal to (n ≠ 1)?

The modulus-amplitude form of 

What is the number of non-zero terms in the expansion of  (after simplification)?

What is the greatest integer among the following by which the number 5⁵ + 7⁵ is divisible?

If x = 1 − y + y² − y³ + … up to infinite terms, where |y| < 1, then which one of the following is correct?

What is the inverse of the matrix A = 

If A is a 2 × 3 matrix and AB is a 2 × 5 matrix, then B must be a

and A² − kA − I2 = O, where I2 is the 2 × 2 identity matrix, then what is the value of k?

What is the number of triangles that can be formed by choosing the vertices from a set of 12 points in a plane, seven of which lie on the same straight line?

What is C(n, r) + 2C (n, r − 1) + C(n, r) equal to?

Let [x] denote the greatest integer function. What is the number of solutions of the equation x² + 4x + [x] = 0 in the interval [0,2]?

A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance?