List of top Questions asked in CUET (UG)

If the lines \(\frac{x-1}{-3} = \frac{y-2}{2 \lambda} = \frac{z-3}{2}\) and \(\frac{x-1}{3 \lambda} = \frac{y-1}{2} = \frac{z-6}{-5}\) are perpendicular. Then the value of \(\lambda\) is:
The general solution of the differential equation ydx + xdy = 0 is:
Two tailors A and B earn ₹150 and ₹200 per day respectively. A can stitch 6 shirts and 4 pants per day, while B can stitch 10 shirts and 4 pants per day. If the tailors A and B work for x and y days respectively. To maximize the earning for producing at least 60 shirts and 32 pants, the LPP is:
Let a pair of dice be thrown and the random variable X be the sum of numbers on the two dice. Then.
Match List I with List II.
List IList II
A. P (X = 2)I. \(\frac{4}{36}\)
B. P (X = 4)II. \(\frac{5}{36}\)
C. P (X - 5)III. \(\frac{1}{36}\)
D. P (X - 6)IV. \(\frac{3}{36}\)

Choose the correct answer from the options given below:
For two events A and B
Match List I with List II
List IList II
A. \(P (\bar{\bigwedge} \cap \bar{B}) = P(\bar{\bigwedge}) . P(\bar{B})\)I. \(P(A/B) \geq P(A)\)
B. \(A \subset B \) and \(P(B) \neq0\)II. \(P(A) = P(B)\)
C. \(P(A \bigcup B) = P(A) + P(B)\)III. A and B are independent events
D. \(P(A|B) = P (B|A)\)IV. A and B are mutually exclusive events

Choose the correct answer from the options given below:
Match List I with List II
List IList II
A. The region represented by \(x \geq 0, y \geq 0\)I. no feasible region
B. The region represented by the inequalities \(2x + y \geq 3, x + 2y \geq 6, x,y \geq 0\)II. 1st quadrant
C. The region represented by the inequalities \(x + 2y \leq 8, 3x + 2y \leq 12, x,y \geq 0\)III. unbounded
D. The region represented by the inequalities \(x + y \leq 2, 3x + 5y \geq 15, x,y \geq 0\)IV. bounded

Choose the correct answer from the options given below:
The area of the region bounded by the curves \(x^2=4y\), the line x = 3 and x axis is:
The area of the region enclosed between the parabolas \(y^2 = x + 1\) and \(y^2 = x + 1\) is:
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is:
The straight line \( \frac{x+2}{3} = \frac{z-3}{ -2}, y-2 \) is
The value of \(\int_0^{\frac{\pi}{2}} log (\frac{5 + 4 sinx}{5 + 4 cosx})dx\) is:
The value of \(\lambda\), for which the projection of \(\vec{a} = \lambda \hat{i} + \hat{j} +4 \hat{k}\) on \(\vec{b} =2\hat{i} +6 \hat{j} +3\hat{k}\) is 4 units
For any two non zero vectors \(\vec{a}\) and \(\vec{b}\)
A. If \(|\vec{a}| = |\vec{b}|\)then \(\vec{a} = \vec{b}\)
B. If \(\vec{a} = \vec{b}\) then \(|\vec{a}| = |\vec{b}|\)
C. \(\vec{a} . \vec{b}=\vec{b} . \vec{a}\)
D. \(\vec{a} \times \vec{b}=\vec{b} \times \vec{a}\)
E. area of the parallelogram = \(\frac{1}{2} |\vec{a} \times \vec{b}|\). where \(\vec{a}\) and \(\vec{b}\) represent resent the diagonals of the parallelogram.
Choose the correct answer from the options given below:
If f(x)= \(\frac{\sqrt{4} + x - 2}{x}, If \ x \neq 0 \\ k \ If \ x \neq 0\) ,is continuous at x = 0, then the value of k is:
The absolute maximum value of the function f(x)=sinx + cosx, x \(\in\)[0, \(\pi\)] is:
If \(x = \sqrt{a^{sin^{-1} t}}\), \(y = \sqrt{a^{ cos^{-1}t}}\) then \(\frac{dy}{dx}\) is:
The function f(x) = \(|x - 1|\) is
The radius of a spherical ball is increasing at the rate of 1 m/sec. At the radius equal to 3m, the volume of the ball is increasing at the rate given by:
\(\int \frac{cos x - sin x}{1 + sin2x} dx\) is equal to:
The value of b for which the function f(x) = sinx - bx + C, where b and e are constants is decreasing for \(x \in R\) is given by
If \(A= \begin{bmatrix}1 & 0 \\[0.3em]-1 & 5 \\[0.3em] \end{bmatrix}\) and \(I= \begin{bmatrix}1& 0\\[0.3em]0& 1\\[0.3em] \end{bmatrix}\) then the value of k so that \(A^2 = 6A + kI\) is given by:
If A = \(\begin{bmatrix}2a & 0& 0\\[0.3em]0& 2a& 0\\[0.3em]0&0 & 2a\\[0.3em] \end{bmatrix}\), then the value of \(|adj A|\)is:
If, A = \(\begin{bmatrix}a& d& l\\[0.3em]b& e& m\\[0.3em]c& f& n\\[0.3em] \end{bmatrix}\)and B = \(\begin{bmatrix}l& m& n\\[0.3em]a& b& c\\[0.3em]d& e& f\\[0.3em]  \end{bmatrix}\), then
If A is a non-identity invertible symmetric matrix, then \(A^{-1}\) is:
If A is a skew-symmetric matrix of order n. then