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

 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 divisible by 6 ? 

What is the binary number equivalent to decimal number 1011 ?

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

If α and β are the distinct roots of equation x2 - x + 1 = 0, then what is the value of $\left|\frac{\alpha^{100}+\beta^{100}}{\alpha^{100}-\beta^{100}}\right|$ ?

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

1. Its diagonal entries are equal but nonzero

2. The sum of its non-diagonal entries is zero

Select the correct answer using the code given below : 

Consider the following statements in respect of square matrices A, B, C each of same order n :

1. AB = AC ⇒ B = C if A is non-singular

2. If BX = CX for every column matrix X having n rows then B = C

Which of the statements given above is/are correct ?  

The system of linear equations

x + 2y + z = 4, 2x + 4y + 2z = 8 and 3x + 6y + 3z = 10 has  

What is the sum of the roots of the equation $\left|\begin{array}{ccc} 0 & x-a & x-b \\ 0 & 0 & x-c \\ x+b & x+c & 1 \end{array}\right|=0 $ ?

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)? 

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

If a, b, c are in AP, then what is $\left|\begin{array}{lll} x+1 & x+2 & x+3 \\ x+2 & x+3 & x+4 \\ x+a & x+b & x+c \end{array}\right|$ equal to ?

If log_xa, a^x and log_bx are in GP, then what is x equal to ? 

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 ? 

The first and the second terms of an AP are $\frac{5}{2}$ and $\frac{23}{12}$ respectively. If n^th term is the largest negative term, what is the value of n ? 

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 lie in the interval (0, 5) ? 

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 ?

Consider the following statements :

1. (25)! + 1 is divisible by 26

2. (6)! + 1 is divisible by 7

Which of the above statements is/are correct ? 

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

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

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 and B equal to ?

α and β are distinct real roots of the quadratic equation x² + ax + b = 0. Which of the following statements is/are sufficient to find α ? 

1. α + β = 0, α² + β² = 2

2. αβ² = -1, a = 0

Select the correct answer using the code given below :

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

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

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 ?  

Consider the following statements for a fixed natural number n:

1. C(n, r) is greatest if n = 2r

2. C(n, r) is greatest if n = 2r - 1 and n = 2r + 1 

Which of the statements given above is/are correct ?

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

Let x be the number of permutations of the word ‘PERMUTATIONS’ and y be the number of permutations of the word ‘COMBINATIONS’. Which one of the following is correct ? 

5-digit numbers are formed using the digits 0, 1, 2, 4, 5 without repetition. What is the percentage of numbers which are greater than 50,000 ?

What is cos 2β equal to ?

What is the value of sec²γ?

If x is the distance of P from the bottom of the pillar, then consider the following statements :

1. x can take two values which are in the ratio 1 : 3

2. x can be equal to the height of the flagstaff

Which of the statements given above is/are correct? 

What is a possible value of tan θ ? 

What is the perimeter of the triangle ?

Consider the following statements :

1. ABC is right angled triangle

2. The angles of the triangle are in AP

Which of the statements given above is/are correct ? 

What is the minimum value of x ?

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

What is the nature of the triangle ? 

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

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

What is the minimum value of the function ?

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

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

What is the value of n ? 

What is the length of the smallest side ?

The given equation can be reduced to 

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 ? 

What is the HM of the roots of the equation ? 

What is the GM of the roots of the equation ?

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

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

What is the least value of m(θ) ?

Under what condition does m attain the least value ? 

What is the equation of diagonal through origin ? 

What is the equation of other diagonal ?  

What is PE + PF equal to ?

Consider the following points :

1. $\left(\frac{\sqrt{3}}{2}, 0\right)$

2. $\left(\frac{\sqrt{3}}{2}, \frac{1}{4}\right)$

3. $\left(\frac{\sqrt{3}}{2},-\frac{1}{4}\right)$

Which of the above points lie on latus rectum of ellipse ?

What is the area of minor segment ?

What is the area of major segment ?

What is u + v + w equal to ? 

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

What is the value of k? 

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

What is $\vec{b}$ equal to ?

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

What is cosα equal to ? 

What is cos2β + cos2γ equal to ? 

Consider the following points :

1. (-1, -3, 1)

2. (-1, 3, 2)

3. (-2, 5, 3)

Which of the above points lie on the line joining A and B ?  

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

‘What is the value of Q ? 

What is the value of R ? 

What is f'(0) equal to ?  

What is the order of the differential equation ?

What is the degree of the differential equation ? 

What is f(0) equal to ?

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

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

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

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

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

What is the value of $8 I_1^2$

What is the value of I₂ ?

What is l equal to when a < 0 < b ? 

What is l equal to when a < b < 0 ? 

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

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

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

What is the value of p ?

What is the value of q ?  

Consider the following statements :

1. f(x) = In x is increasing in (0, ∞)

2. $g(x)=e^x+e^{\frac{1}{x}} $ is decreasing in (0, ∞)

Which of the statements given above is/are correct ?  

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

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 ?

What is the derivative of cosec(x°) ?  

A solution of the differential equation

$\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=0 $ is

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

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

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

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

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

The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 20. What are the other two observations ?

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 ?

A biased coin with the probability of getting head equal to $\frac{1}{4}$ is tossed five times. What is the probability of getting tail in all the first four tosses followed by head ? 

A coin is biased so that heads comes up thrice as likely as tails. In four independent tosses of the coin, what is probability of getting exactly three heads ?

Let X and Y be two random variables such that X + Y = 100. If X follows Binomial distribution with parameters n = 100 and p = $\frac{4}{5}$, what is the variance of Y?  

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 ? 

The central angles p, q, r and s (in degrees) of four sectors in a Pie Chart satisfy the relation 9p = 3q = 2r = 6s. What is the value of 4p - q ? 

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 of lowest 8 observations and highest 4 observations respectively, then what is (2m + M) equal to ?  

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

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 mode of data so obtained ?  

Consider the following frequency distribution :

x	1	2	3	5
f	4	6	9	7

What is the value of median of the distribution ?  

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 observations, then what is the value of 4M - N ? 

Let P, Q, R represent mean, median and mode. If for some distribution $5 P=4 Q=\frac{R}{2}$ then what is $\frac{P+Q}{2 P+0.7 R}$ equal to ?

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

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

Let P be the median, Q be the mean and R be the mode of observations x_1, x_2, x₃, .....x_n. Let $S=\sum\limits_{i=1}^n\left(2 x_i-a\right)^2$ S takes minimum value, when a is equal to

One bag contains 3 white and 2 black balls, another bag contains 2 white and 3 black balls. Two balls are drawn from the first bag and put it into the second bag and then a ball is drawn from the second bag. What is the probability that it is white ? 

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

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

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