NDA Mathematics 16 April 2023

Paper was held on
Sun, Apr 16, 2023 8:30 AM

## Mathematics

If ω is a non-real cube root of 1, then what is the value of $\left|\frac{1-\omega}{\omega+\omega^2}\rig

View Question What is the number of 6-digit numbers that can be formed only by using 0, 1, 2, 3, 4 and 5 (each once); and divisi

View Question What is the binary number equivalent to decimal number 1011 ?

View Question Let A be a matrix of order 3 × 3 and |A| = 4. If |2adj(3A)| = 2α 3β, then what is the value of (α + β)?

View Question If α and β are the distinct roots of equation x2 - x + 1 = 0, then what is the value of $\left|

View Question Let A and B be symmetric matrices of same order, then which one of the following is correct regarding (AB - BA) ?
1. It

View Question Consider the following statements in respect of square matrices A, B, C each of same order n :
1. AB = AC ⇒ B = C

View Question The system of linear equations
x + 2y + z = 4, 2x + 4y + 2z = 8 and 3x + 6y + 3z = 10 has

View Question Let AX = B be a system of 3 linear equations with 3-unknowns. Let X1 and X2 be its two distinct solutions. If

View Question What is the sum of the roots of the equation $\left|\begin{array}{ccc} 0 & x-a & x-b \\ 0 & 0 & x-c

View Question If 2 - i√3 where i = √-1 is a root of the equation x2 + ax + b = 0, then what is the value of (a + b)?

View Question If $z=\frac{1+i √{3}}{1-i √{3}}$ where i = √-1 then what is the argument of z ?

View Question If a, b, c are in AP, then what is $\left|\begin{array}{lll} x+1 & x+2 & x+3 \\ x+2 & x+3 & x+4 \\

View Question If logxa, ax and logbx are in GP, then what is x equal to ?

View Question If $2^{\frac{1}{c}}, 2^{\frac{b}{a c}}, 2^{\frac{1}{a}}$ are in GP, then which one of the following is correct ?

View Question The first and the second terms of an AP are $\frac{5}{2}$ and $\frac{23}{12}$ respectively. If nth term is the larg

View Question For how many integral values of k, the equation x2 - 4x + k = 0, where k is an integer has real roots and both of them l

View Question In an AP, the first term is x and the sum of the first n terms is zero. What is the sum of next m terms ?

View Question Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above

View Question If z is a complex number such that $\frac{z-1}{z+1}$ is purely imaginary, then what is |z| equal to ?

View Question How many real numbers satisfy the equation |x - 4| + |x - 7| = 15 ?

View Question A mapping f : A → B defined as $f(x)=\frac{2 x+3}{3 x+5}, x \in A$ If f is to be onto, then what are A an

View Question α and β are distinct real roots of the quadratic equation x2 + ax + b = 0. Which of the following statements is/are

View Question If the sixth term in the binomial expansion of $\left(x^{-\frac{8}{3}}+x^2 \log _{10} x\right)^8$ is 5600, the

View Question How many terms are there in the expansion of (3x - y)4(x + 3y)4 ?

View Question p, q, r and s are in AP such that p + s = 8 and qr = 15. What is the difference between largest and smallest numbers ?&n

View Question Consider the following statements for a fixed natural number n:
1. C(n, r) is greatest if n = 2r
2. C(n, r) is gr

View Question m parallel lines cut n parallel lines giving rise to 60 parallelograms. What is the value of (m + n) ?

View Question Let x be the number of permutations of the word ‘PERMUTATIONS’ and y be the number of permutations of the word ‘COMBINAT

View Question 5-digit numbers are formed using the digits 0, 1, 2, 4, 5 without repetition. What is the percentage of numbers which ar

View Question What is cos 2β equal to ?

View Question What is the value of sec2γ?

View Question If x is the distance of P from the bottom of the pillar, then consider the following statements :
1. x can take two val

View Question What is a possible value of tan θ ?

View Question What is the perimeter of the triangle ?

View Question Consider the following statements :
1. ABC is right angled triangle
2. The angles of the triangle are in AP
Which of

View Question What is the minimum value of x ?

View Question At what value of A does x attain the minimum value ?

View Question What is the nature of the triangle ?

View Question If c = 8, what is the area of the triangle ?

View Question At what value of x does the function attain minimum value ?

View Question What is the minimum value of the function ?

View Question If the sum S is divided by 8, what is the remainder ?

View Question If the sum S is divided by 60, what is the remainder ?

View Question What is the value of n ?

View Question What is the length of the smallest side ?

View Question The given equation can be reduced to

View Question If sin2x = a - b√c, where a and b are natural numbers and c is prime number, then what is the value of a - b + 2c ? 

View Question What is the HM of the roots of the equation ?

View Question What is the GM of the roots of the equation ?

View Question If Δ(a, b, c, α) = 0 for every α > 0, then which one of the following is correct ?

View Question If Δ(7, 4, 2, α) = 0, then α is a root of which one of the following equations ?

View Question What is the least value of m(θ) ?

View Question Under what condition does m attain the least value ?

View Question What is the equation of diagonal through origin ?

View Question What is the equation of other diagonal ?

View Question What is PE + PF equal to ?

View Question Consider the following points :
1. $\left(\frac{\sqrt{3}}{2}, 0\right)$
2. $\left(\frac{\sqrt{3}}{2}, \frac{

View Question What is the area of minor segment ?

View Question What is the area of major segment ?

View Question What is u + v + w equal to ?

View Question P(x, y, z) is any point on the sphere, then what is PA2 + PB2 equal to ?

View Question What is the value of k?

View Question What are the direction ratios of a line which is perpendicular to both the lines ?

View Question What is $\vec{b}$ equal to ?

View Question What is the angle between $(\vec{a}+\vec{b})$ and $\vec{c}$ ?

View Question What is cosα equal to ?

View Question What is cos2β + cos2γ equal to ?

View Question Consider the following points :
1. (-1, -3, 1)
2. (-1, 3, 2)
3. (-2, 5, 3)
Which of the above points

View Question What is the magnitude of $\overrightarrow{A B}$ ?

View Question ‘What is the value of Q ?

View Question What is the value of R ?

View Question What is f'(0) equal to ?

View Question What is the order of the differential equation ?

View Question What is the degree of the differential equation ?

View Question What is f(0) equal to ?

View Question What is $\lim _{x \rightarrow 0} \frac{f(x)}{x}$ equal to ?

View Question What is $\lim _{x \rightarrow 0} \frac{f(x)}{x^2}$ equal to ?

View Question What is $f\left(\frac{\pi}{2}\right)$ equal to ?

View Question What is $f\left(\frac{\pi}{4}\right)$ equal to ?

View Question What is the value of $\frac{I_1+I_2}{I_1-I_2} $ ?

View Question What is the value of $8 I_1^2$

View Question What is the value of I2 ?

View Question What is l equal to when a < 0 < b ?

View Question What is l equal to when a < b < 0 ?

View Question What is the derivative of f(x) at x = 0.5 ?

View Question What is the derivative of f(x) at x = 2 ?

View Question What is the derivative of fof(x), where 1 < x < 2 ?

View Question What is the value of p ?

View Question What is the value of q ?

View Question Consider the following statements :
1. f(x) = In x is increasing in (0, ∞)
2. $g(x)=e^x+e^{\frac{1}{x}} $ is decreasin

View Question What is the derivative of sin2 x with respect to cos2x ?

View Question For what value of m with m < 0, is the area bounded by the lines y = x, y = mx and x = 2 equal to 3 ?

View Question What is the derivative of cosec(x°) ?

View Question A solution of the differential equation
$\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=0 $ is

View Question If f(x) = x2 + 2 and g(x) = 2x - 3, then what is (fog)(1) equal to ?

View Question What is the range of the function f(x) = x + |x| if the domain is the set of real numbers ?

View Question If f(x) = x(4x2 - 3), then what is f(sinθ) equal to ?

View Question What is $\lim\limits_{x \rightarrow 5} \frac{5-x}{|x-5|}$ equal to ?

View Question What is $\lim\limits_{x \rightarrow 1} \frac{x^9-1}{x^3-1}$ equal to ?

View Question The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 2

View Question Let A and B be two independent events such that
P(A̅) = 0.7, P(B̅) = k, P(A ∪ B) = 0.8, what is the value of k ?

View Question A biased coin with the probability of getting head equal to $\frac{1}{4}$ is tossed five times. What is the probabi

View Question A coin is biased so that heads comes up thrice as likely as tails. In four independent tosses of the coin, what is proba

View Question Let X and Y be two random variables such that X + Y = 100. If X follows Binomial distribution with parameters n = 100 an

View Question If two lines of regression are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, then what is the value of x when y = -3 ?

View Question The central angles p, q, r and s (in degrees) of four sectors in a Pie Chart satisfy the relation 9p = 3q = 2r = 6s. Wha

View Question The observations 4, 1, 4, 3, 6, 2, 1, 3, 4, 5, 1, 6 are outputs of 12 dices thrown simultaneously. If m and M are means

View Question A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ?

View Question A die is thrown 10 times and obtained the following outputs :
1, 2, 1, 1, 2, 1, 4, 6, 5, 4
What will be the

View Question Consider the following frequency distribution :
x
1
2
3
5
f
4
6
9
7
W

View Question For data -1, 1, 4, 3, 8, 12, 17, 19, 9, 11; if M is the median of first 5 observations and N is the median of last five

View Question Let P, Q, R represent mean, median and mode. If for some distribution $5 P=4 Q=\frac{R}{2}$ then what is

View Question If G is the geometric mean of numbers 1, 2, 22, 23,.....2n-1, then what is the value of 1 + 2log2G ?

View Question If H is the harmonic mean of numbers 1, 2, 22, 23, ......2n-1 what is n/H equal to ?

View Question Let P be the median, Q be the mean and R be the mode of observations x1, x2, x3, .....xn. Let $S=\su

View Question One bag contains 3 white and 2 black balls, another bag contains 2 white and 3 black balls. Two balls are drawn from the

View Question Three dice are thrown. What is the probability that each face shows only multiples of 3 ?

View Question What is the probability that the month of December has 5 Sundays ?

View Question A natural number n is chosen from the first 50 natural numbers. What is the probability that $n+\frac{50}{n}<50

View Question