List of top Questions asked in CUET (UG)

Which one of the following is not an Arithmetic progression ?

Arun covers first 28 kms of his journey in 45 minutes and the remaining 32 kms in 35 minutes. What is his average speed in m/s ?

Four men can do a work in 10 days and 5 women can do the same work in 12 days. How many women must work with 3 men to do the same work in 8 days ?

In △ABC, BD is the internal bisector of ∠B meeting AC at D. If CD = 7 cm and AC = 10.5 cm, then AB : BC is

Two balls are chosen randomly from an urn containing 8 white balls and 4 black balls by a player. Suppose that he wins ₹30 for each black ball selected and loses ₹15 for each white ball selected. The expected value of winning amount is :

Consider the following statements :
A. Cost of living at two different cities can be compared with volume index.
B. When the prices of rice are to be compared we use price index.
C. In Laspeyre's price index number weight is considered as price in current year.
D. Purchasing power of money can be assessed through consumer price index.
E. Fisher Index number is called ideal index number.
Choose the correct answer from the options given below :

Consider the following statements with respect to probability distributions :
A. When mean (μ) = 1 and standard deviation (σ) = 0 for a data set, normal distribution is called standard normal distribution.
B. In a normal distribution of data, z is given by \(z=\frac{\mu-x}{\sigma}\)
C. P('t' success) is the (r + 1)^th term in the binomial expansion of (q + p)ⁿ.
D. In a random experiment, a collection of trials is called Bernoulli, if trials are department by nature.
E. When a random variable whose value is obtained by measuring and it takes many values between two values, it is called a continuous random variable.
Choose the correct answer from the options given below :

For a discrete random variable X, whose probability distribution is defined as :
\(P(x)=\begin{cases} 2k(x+1) ;& x = 0,1 \\ 3kx; &  x=2 \\ k(5-x) & x=3 \end{cases}\)
The value of mean will be

A die is thrown n times. A random variable X denotes the number of times, the number on the dice is greater than 4 and P(X = 1) = 2P(X = 2). The value of n is :

Match List I with List II:

List I		List II
A.	Marshall Edgeworth's Index Number	I.	\(\frac{\sum p_1q_0}{\sum p_0q_0}\times100\)
B.	Laspeyre's Index Number	II.	\(\sqrt{\frac{\sum p_1q_0}{\sum p_0q_0}\times\frac{\sum p_1q_1}{\sum p_0q_1}}\times100\)
C.	Fisher's Ideal Index Number	III.	\(\frac{\sum p_1q_1}{\sum p_0q_1}\times100\)
D.	Paasche's Index Number	IV.	\(\frac{\sum p_1(q_0+q_1)}{\sum p_0(q_0+q_1)}\times100\)

If f(x) is a function which is derivable in an interval 1 containing a point c, then match List I with List II.

List I		List II
A.	f(x) has second order derivate at x = c such that f'(c) = 0 and f'(c) < 0; then	I.	point of inflexion of f(x)
B.	Necessary condition for point x = c to be extreme point of f(x) is	II.	‘c’ is point of local minima of f(x)
C.	If f'(x) does not change its sign as x crosses the point x = c then it is called a	III.	c is a critical point of f(x)
D.	f(x) has second order derivate at x = c such that f'(c) and f'(c) > 0; then	IV.	‘c’ is point of local maxima of f(x)

Choose the correct answer from the options given below :

If the transpose of matrix A is matrix B, where \(A=\begin{bmatrix} 2a & 1 & 3b \\ 1 & 2 & 4c \\ 5 & 6 & 0 \end{bmatrix}\)and \(B=\begin{bmatrix} 4 & 1 & 5 \\ 1 & 2 & 6 \\ 9 & 3 & 0 \end{bmatrix}\)then the value of 3a + 2b + 4c is :

If \(x\sqrt{1+y}+y\sqrt{1+x}=0;x\ne y\), then the value of \(\frac{d^2y}{dx^2}+2\frac{dy}{dx}\) at x = 1 is :

If \(y=\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+}}}}.....+\) then \(\frac{dy}{dx}\) is :

For the function f(x) = 2e^5x + 10, which of the following is the most appropriate option.

The price per unit of a commodity produced by a company is given by P = 92 - 2x², where x is the quantity demanded. The marginal revenue of producing 3 units of such a commodity shall be :

If A is a symmetric matrix and n ∈ N, then Aⁿ is :

The solution set of inequalities :
x + 3 ≤ 0 and 2x + 5 ≤ 0; if x ∈ R is :

₹3,60,000, ₹4,20,000 and ₹4,80,000 were invested by three friends A, B and C respectively in a business. If they earned a net profit of ₹2,10,000, the share of B's profit is :

The ratio of speeds of a motor boat and that of current of water is 35:6. The boat goes against the current in 6 hours 50 minutes. The time taken by boat to come back is :

A tank can be filled by two pipes A and B in 18 minutes and 24 respectively. Another tap C can empty the full tank in 36 mintues. If the tap C is opened 6 minutes after the pipes A and B are opened, the tank will become full in a total of :

If \(\vec{a}\) and \(\vec{b}\) are two non zero vectors such that \(|\vec{a}|\)=10, \(|\vec{b}|=2\) and \(\vec{a}.\vec{b}=12\), then value of \(|\vec{a}\times\vec{b}|\) is :

If xy = e^(x-y), then the value of \(\frac{dy}{dx}\) at (1, 1) is :

The direction cosines of a line which makes equal angles with the co-ordinate axes is/are :

The maximum value of the function y = 2 - |x - 3| is :