CUET UG Maths Previous Year Question Paper 2024

(1) CUET UG Maths Question Paper 2024

1. The second order derivative of which of the following functions is 5^x?

(1) 5^x log_e5

(2) 5^x (log_e5)²

(3) $\frac{5^x}{{\log }_{e}5}$

(4)$\frac{5^x}{{\left({\log }_{e}5\right)}^2}$

Answer - (4)$\frac{5^x}{{\left({\log }_{e}5\right)}^2}$

2. The degree of the differential equation ${\left(1-{\left(\frac{dy}{dx}\right)}^2\right)}^{3/2}=k\frac{d^{2}y}{d{x}^2}$is:

(1) 1

(2) 2

(3) 3

(4) $\frac{3}{2}$

Answer- (2) 2

3. $\int \frac{\mathrm{\pi }}{x^{n+1}-x}dx=$

(1) $\frac{\mathrm{\pi }}{n}{\log }_e\left|\frac{x^n-1}{x^n}\right|+C$

(2) ${\log }_e\left|\frac{x^n+1}{x^n-1}\right|+C$

(3) $\frac{\mathrm{\pi }}{n}{\log }_e\left|\frac{x^n+1}{x^n}\right|+C$

(4) ${\mathrm{\pi log}}_e\left|\frac{x^n}{x^n-1}\right|+C$

Answer- (1) $\frac{\mathrm{\pi }}{n}{\log }_e\left|\frac{x^n-1}{x^n}\right|+C$

4. The value of ${\int }_0^1\frac{a-b{x}^2}{{\left(a+b{x}^2\right)}^2}dx$is:

(1) $\frac{a-b}{a+b}$

(2) $\frac{1}{a-b}$

(3) $\frac{a+b}{2}$

(4) $\frac{1}{a+b}$

Answer - (4) $\frac{1}{a+b}$

5. If A and B are symmetric matrices of the same order, then AB – BA is a :

(1) symmetric matrix

(2) zero matrix

(3) skew symmetric matrix

(4) identity matrix

Answer- (3) skew symmetric matrix

6. If A is a square matrix of order 4 and |A|= 4, then |2A| will be :

(1) 8

(2) 64

(3) 16

(4) 4

Answer- (2) 64

7. If ${\left[A\right]}_{3\times 2}{\left[B\right]}_{x\times y}={\left[C\right]}_{3\times 1}$, then :

(1) x = 1, y = 3

(2) x = 2, y = 1

(3) x = 3, y = 3

(4) x = 3, y = 1

Answer- (2) x = 2, y = 1