NDA Mathematics 16 April 2023
Paper was held on Sun, Apr 16, 2023 8:30 AM
View Questions

## Mathematics

If&nbsp;ω is a non-real cube root of 1, then what is the value of&nbsp;&nbsp;$\left|\frac{1-\omega}{\omega+\omega^2}\rig View Question &nbsp;What is the number of 6-digit numbers that can be formed only by using 0, 1, 2, 3, 4 and 5 (each once); and divisi View Question What is the binary number equivalent to decimal number 1011 ? View Question Let A be a matrix of order 3 × 3 and |A| = 4. If |2adj(3A)| = 2α&nbsp;3β, then what is the value of (α +&nbsp;β)?&nbsp; View Question If&nbsp;α and&nbsp;β are the distinct roots of equation x2&nbsp;- x&nbsp;+ 1 = 0, then what is the value of&nbsp;$\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&nbsp;: 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&nbsp;&nbsp;
View Question
Let AX = B be a system of 3 linear equations with 3-unknowns. Let X1&nbsp;and X2&nbsp;be its two distinct solutions. If
View Question
What is the sum of the roots of the equation&nbsp;$\left|\begin{array}{ccc} 0 &amp; x-a &amp; x-b \\ 0 &amp; 0 &amp; x-c View Question If 2 - i√3 where&nbsp;i = √-1 is a root of the equation x2&nbsp;+ ax + b = 0, then what is the value of (a + b)?&nbsp; View Question If&nbsp;$z=\frac{1+i √{3}}{1-i √{3}}$&nbsp;where i =&nbsp;√-1&nbsp;then&nbsp;what is the argument of z ? View Question If a, b, c are in AP, then what is&nbsp;$\left|\begin{array}{lll} x+1 &amp; x+2 &amp; x+3 \\ x+2 &amp; x+3 &amp; x+4 \\
View Question
If logxa, ax and logbx are in GP, then what is x equal to ?&nbsp;
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 ?&nbsp;
View Question
The first and the second terms of an AP are&nbsp;$\frac{5}{2}$ 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 ?&nbsp;
View Question
How many real numbers satisfy the equation |x - 4| + |x - 7| = 15 ?
View Question
A mapping f : A&nbsp;→ B defined as&nbsp;$f(x)=\frac{2 x+3}{3 x+5}, x \in A$&nbsp;If f is to be onto, then what are A an
View Question
α and&nbsp;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&nbsp;$\left(x^{-\frac{8}{3}}+x^2 \log _{10} x\right)^8$&nbsp;is 5600, the
View Question
How many terms are there in the expansion of (3x - y)4(x + 3y)4 ?&nbsp;&nbsp;
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.&nbsp;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) ?&nbsp;
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&nbsp;θ ?&nbsp;
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 ?&nbsp;
View Question
If c = 8, what is the area of the&nbsp;triangle ?
View Question
At what value of x does the function&nbsp;attain minimum value ?
View Question
What is the minimum value of the&nbsp;function ?
View Question
If the sum S is divided by 8, what is the remainder ?&nbsp;&nbsp;
View Question
If the sum S is divided by 60, what is the remainder ?
View Question
What is the value of n ?&nbsp;
View Question
What is the length of the smallest side ?
View Question
The given equation can be reduced to&nbsp;
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 ?&nbsp
View Question
What is the HM of the roots of the equation ?&nbsp;
View Question
What is the GM of the roots of the equation ?
View Question
If&nbsp;Δ(a, b, c,&nbsp;α) = 0&nbsp;for every&nbsp;α &gt; 0, then which one of the following is correct ?&nbsp;
View Question
If Δ(7, 4, 2,&nbsp;α) = 0, then&nbsp;α is a root of which one of the following equations ?&nbsp;
View Question
What is the least value of m(θ) ?
View Question
Under what condition does m attain the least value ?&nbsp;
View Question
What is the equation of diagonal through origin ?&nbsp;
View Question
What is the equation of other diagonal ?&nbsp;&nbsp;
View Question
What is PE + PF equal to ?
View Question
Consider the following points : 1.&nbsp;$\left(\frac{\sqrt{3}}{2}, 0\right)$ 2.&nbsp;$\left(\frac{\sqrt{3}}{2}, \frac{ View Question What is the area of minor segment ? View Question What is the area of major segment ? View Question What is u + v + w equal to ?&nbsp; View Question P(x, y, z) is any point on the sphere, then what is PA2 + PB2 equal to ?&nbsp;&nbsp; View Question What is the value of k?&nbsp; View Question What are the direction ratios of a line which is perpendicular to both the lines ? View Question What is&nbsp;$\vec{b}$&nbsp;equal to ? View Question What is the angle between&nbsp;$(\vec{a}+\vec{b})$&nbsp;and&nbsp;$\vec{c}$&nbsp;? View Question What is cosα equal to ?&nbsp; View Question What is cos2β + cos2γ equal to ?&nbsp; View Question Consider the following points : 1.&nbsp;(-1, -3, 1) 2.&nbsp;(-1, 3, 2) 3.&nbsp;(-2, 5, 3) Which of the above points View Question What is the magnitude of&nbsp;$\overrightarrow{A B}$&nbsp;? View Question ‘What is the value of Q ?&nbsp; View Question What is the value of R ?&nbsp; View Question What is f'(0) equal to ?&nbsp;&nbsp; View Question What is the order of the differential equation ? View Question What is the degree of the differential equation ?&nbsp; View Question What is f(0) equal to ? View Question What is&nbsp;$\lim _{x \rightarrow 0} \frac{f(x)}{x}$&nbsp;equal to ?&nbsp; View Question What is&nbsp;$\lim _{x \rightarrow 0} \frac{f(x)}{x^2}$&nbsp;equal to ?&nbsp; View Question What is&nbsp;$f\left(\frac{\pi}{2}\right)$&nbsp;equal to ? View Question What is$f\left(\frac{\pi}{4}\right)$equal to ?&nbsp; View Question What is the value of&nbsp;$\frac{I_1+I_2}{I_1-I_2} $&nbsp;? View Question What is the value of&nbsp;$8 I_1^2$View Question What is the value of I2&nbsp;? View Question What is l equal to when a &lt; 0 &lt; b ?&nbsp; View Question What is l equal to when a &lt; b &lt; 0 ?&nbsp; 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 ?&nbsp; View Question What is the derivative of fof(x), where 1 &lt; x &lt; 2 ? View Question What is the value of p ? View Question What is the value of q ?&nbsp;&nbsp; View Question Consider the following statements : 1. f(x) = In x is increasing in (0, ∞) 2.$g(x)=e^x+e^{\frac{1}{x}} $is decreasin View Question What is the derivative of sin2 x with respect to cos2x ?&nbsp;&nbsp; View Question For what value of m with m &lt; 0, is the area bounded by the lines y = x, y = mx and x = 2 equal to 3 ? View Question What is the derivative of cosec(x°) ?&nbsp;&nbsp; View Question A solution of the differential equation$\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=0 $&nbsp;is View Question If f(x) = x2&nbsp;+ 2 and g(x) = 2x - 3, then what is (fog)(1) equal to ? View Question What is the range of the function f(x) = x + |x| if the domain is the set of real numbers ?&nbsp;&nbsp; View Question If f(x) = x(4x2&nbsp;- 3), then what is f(sinθ) equal to ?&nbsp;&nbsp; View Question What is&nbsp;$\lim\limits_{x \rightarrow 5} \frac{5-x}{|x-5|}$&nbsp;equal to ? View Question What is&nbsp;$\lim\limits_{x \rightarrow 1} \frac{x^9-1}{x^3-1}$&nbsp;equal to ? View Question The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 2 View Question Let A and B be two independent events such that P(A̅) = 0.7, P(B̅) = k, P(A&nbsp;∪ B) = 0.8, what is the value of k ? View Question A biased coin with the probability of getting head equal to&nbsp;$\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 ?&nbsp; 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,&nbsp;1, 1, 2, 1, 4, 6, 5, 4 &nbsp;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&nbsp;$5 P=4 Q=\frac{R}{2}$&nbsp;then what is&nbsp; 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&nbsp;what is n/H equal to ?&nbsp; View Question Let P be the median, Q&nbsp;be the mean and R be the mode of observations x1,&nbsp;x2,&nbsp;x3, .....xn. Let&nbsp;$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 ?&nbsp;
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&nbsp;\$n+\frac{50}{n}&lt;50
View Question
EXAM MAP
Medical
NEET