List of top Mathematics Questions asked in CUET (UG)

If the planes \(\overrightarrow{r}.(2\hat{i}-\lambda\hat{j}+3\hat{k})=0\) and \(\overrightarrow{r}.(\lambda\hat{i}+5\hat{j}-\hat{k})=5\) are perpendicular to each other ,then value \(\lambda^2+\lambda \) is :

which is the true of the following ?
(A)Any vector \(\overrightarrow{r}\) in space can be written as \((\overrightarrow{r}.\hat{i})\hat{i}+(\overrightarrow{r}.\hat{j})\hat{j}+(\overrightarrow{r}.\hat{k})\hat{k}\) 
(B)If  \(\overrightarrow{a}\)  is perpendicular to  \(\overrightarrow{b}\)\(|\overrightarrow{a}+\overrightarrow{b}|^2=|\overrightarrow{a}|^2+|\overrightarrow{b}|^2\) 
 
(C)If \(|\overrightarrow{a}|=2,|\overrightarrow{b}|=1 \) and \(\overrightarrow{a}.\overrightarrow{b}=1 \) ,the value of \((3\overrightarrow{a}-5\overrightarrow{b}).(2\overrightarrow{a}+7\overrightarrow{b})\) ia 1
(D) \(\overrightarrow{a}=5\hat{i}-\hat{j}-3\hat{k}\) and \(\overrightarrow{b}=\hat{i}+3\hat{j}-5\hat{k}\), is the angle between \(\overrightarrow{a}+\overrightarrow{b}\) and \(\overrightarrow{a}-\overrightarrow{b}\) is \(60\degree\)
Choose the correct answer from the options given below:
 

Solution of a differential equation  \((1+ y2)dx=(\tan^{-1}y - x)dy\) is :

Let \(\overrightarrow a = 4\hat i -\hat j + 3\hat k\) and \(\overrightarrow b = -2\hat i + \hat j-2\hat k\). Then
(A) \(\overrightarrow a\) is a unit vector
(B) \(\overrightarrow a\times \overrightarrow b=-\hat i + 2\hat j + 2\hat k\)
(C) \(\overrightarrow a\) and \(\overrightarrow b\) are parallel vectors
(D) \(\overrightarrow a\) and \(\overrightarrow b\)are neither parallel nor perpendicular vectors
Choose the correct answer from the options given below :

Let \(\overrightarrow a\) and \(\overrightarrow b\) be two unit vectors. If the vectors \(\overrightarrow c=5\overrightarrow a-4\overrightarrow b\) and \(\overrightarrow d = \overrightarrow a+2\overrightarrow b\) perpendicular to each other, then the angle between \(\overrightarrow a\) and \(\overrightarrow b\) is:

If the straight lines \(x=1+s, y = -3-s, z=1+λs\) and \(x = \frac{t}{2},y=1+t, z=2-t\) with parameters s and t respectively, are coplanar, then \(λ\) is equal to:

If x is the least positive integer satisfying 100 ≡ x(mod 6), then (2x+1) is equal to :

If the matrix \(A =\begin{bmatrix}x&-2 &-5y\\ 2&0& -9 \\10& 3z &0\end{bmatrix}\)is skew-symmetric, then the value of \((2x-3y+4z)\) is:

Match List I with List II

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A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If P(X=1)=0.4, P(X=4)=P(X=2) and P(X=3)=2P(X=2), then P(X=0) is:

Consider the following data:

The equation of the straight line trend by the method of least squares is :

A car costing ₹8,00,000 has scrap value of ₹3,00,000. If the book value of car at the end of fourth year is ₹6,00,000, then the useful life of the car is:

In the equation of trend line \(y_t=a+bx\), a and b represent:

The area of a triangle is 9y cm². Find the value of y if its area is equal to the area of an equilateral triangle having side 6 cm.

If three vertices of a rhombus taken in order are (2, -1), (3, 4) and (-2, 3), then the fourth vertex is :

The mean and the median of a certain data are 13.3 and 13.5 respectively. Find the mode.

A man was allotted a work for 30 days on the condition that he would get ₹ 10 per day as wage if he reports for work and if he remains absent he would have to pay ₹ 2 as penalty for the day. Ultimately he got ₹ 216. For how many days he remained absent ?

In the figure, O is centre of the circle. What is the measure of ∠ABC ?

If perimeter of a rhombus is 104 cm and length of one of its diagonals is 48 cm, then area of the rhombus (in cm²) is:

Find the median of the following data: \(42, 19, 46, 17, 8, 35, 26, 39, 29\)

Find the average of squares of first five natural numbers.

A thief is spotted by a policeman from a distance of \(200 \)meters. The policeman starts chasing at a speed of \( 10 \frac{km}{h}\) while the thief is running at a speed of \( 8\frac{km}{h}\). After how much time (in minutes) will the thief be caught?

A ladder 25 feet long is leaning against a wall such that it touches 24 feet high window. How far is the foot of the ladder from the wall?

If the points (2, -3), (λ, -1) and (0, 4) are collinear, then the value of λ is :

If \(f(x)=\begin{cases} 2x+8, & 1\le x\le2 \\ 6x, & 2\lt x \lt4\end{cases}\), then \(\int_1^4f(x)\) is :