CUET Mathematics 2024 16 May Shift 1 PYQs

$8 a+4=b$

$a=2 b$

$\mathrm{b}=2 \mathrm{a}$

$8 b+4=a$

$0$

$4 t$

$\frac{4 e^{2 t}}{t}$

$\frac{e^{2 t}(4 t-1)}{t^{2}}$

$60$

$50$

$40$

$80$

$34$ sq units

$20$ sq units

$24$ sq units

$16$ sq units

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{1}{9}$

$\frac{1}{18}$

$\frac{\pi}{n} \log _{e}\left|\frac{x^{n}-1}{x^{n}}\right|+C$

$\quad \log _{e}\left|\frac{x^{n}+1}{x^{n}-1}\right|+C$

$\frac{\pi}{n} \log _{e}\left|\frac{x^{n}+1}{x^{n}}\right|+C$

$\pi \log _{e}\left|\frac{x^{n}}{x^{n}-1}\right|+C$

$\frac{a-b}{a+b}$

$\frac{1}{a-b}$

$\frac{a+b}{2}$

$\frac{1}{a+b}$

$5^{x} \log _{e} 5$

$5^{x}(\log _{e} 5)^{2}$

$\frac{5^{\mathrm{x}}}{\log _{\mathrm{e}} 5}$

$\frac{5^{\mathrm{x}}}{(\log _{\mathrm{e}} 5)^{2}}$

$1$

$2$

$3$

$\frac{3}{2}$

symmetric matrix

zero matrix

skew symmetric matrix

identity matrix

$8$

$64$

$16$

$4$

$x=1, y=3$

$x=2, y=1$

$x=3, y=3$

$x=3, y=1$

$5$

$0$

$-2$

$-4$

$\frac{5}{9}$

$\frac{1}{3}$

$\frac{4}{7}$

$\frac{3}{8}$

(A) - (IV), (B) - (II), (C) - (I), (D) - (III)

(A) - (II), (B) - (III), (C) - (I), (D) - (IV)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

$66 \pi$

$6.6 \pi$

$3.3 \pi$

$4.4 \pi$

$56\sqrt{3} \ ab$

$56a$

$\frac{ab}{2}$

$3ab$

$\mathrm{I}+\mathrm{A}$

$\mathrm{I}+2 \mathrm{~A}$

$\mathrm{I}-\mathrm{A}$

$\mathrm{A}$

$\log _{e} 3$

$\log _{e} 4-\log _{e} 3$

$\log _{e} 9-\log _{e} 4$

$\log _{e} 3-\log _{e} 2$

$60^{\circ}$

$90^{\circ}$

$120^{\circ}$

$180^{\circ}$

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (I), (B) - (III), (C) - (II), (D) - (IV)

(A) - (II), (B) - (I), (C) - (III), (D) - (IV)

(A) - (II), (B) - (IV), (C) - (III), (D) - (I)

(A) - (I), (B) - (III), (C) - (IV), (D) - (II)

(A) - (I), (B) - (IV), (C) - (III), (D) - (II)

(A) - (II), (B) - (I), (C) - (III), (D) - (IV)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(B) only

(A), (B) and (D) only

(A) and (C) only

(A), (C) and (D) only

$0$

$\frac{\pi}{4}$

$\infty$

$\frac{\pi}{12}$

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (I), (B) - (II), (C) - (IV), (D) - (III)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(B) and (D) only

(A) and (D) only

(A), (C) and (D) only

(B), (C) and (D) only

(A), (B) and (D) only

(A), (B) and (C) only

(A), (B), (C) and (D)

(B), (C) and (D) only

Region A

Region B

Region C

Region D

$16$ sq. units

$\frac{32}{3}$ sq. units

$\frac{8}{3}$ sq. units

$\frac{16}{3}$ sq. units

$\frac{1}{2 \sqrt{\mathrm{x}}} \mathrm{e}^{\mathrm{x}}+\mathrm{C}$

$-\mathrm{e}^{\mathrm{x}} \sqrt{\mathrm{x}}+C$

$-\frac{1}{2 \sqrt{x}} e^{x}+C$

$e^{x} \sqrt{x}+C$

$0$

$\pi$

$\frac{2}{\pi}$

$-\frac{2}{\pi}$

$\left[\begin{array}{ccc}4 & 5 & 7 \\ -3 & -3 & 0 \\ 0 & -3 & -2\end{array}\right]$

$\left[\begin{array}{rrr}-2 & 4 & 2 \\ 4 & -8 & -4 \\ -1 & 2 & 1\end{array}\right]$

$\left[\begin{array}{rrr}5 & 5 & 2 \\ 7 & 6 & 7 \\ -9 & -7 & 0\end{array}\right]$

$\left[\begin{array}{rrr}-2 & 4 & 8 \\ 7 & 5 & 7 \\ -8 & -2 & 6\end{array}\right]$

(A), (C) and (D) only

(A), (B) and (C) only

(A), (B), (C) and (D)

(B), (C) and (D) only

(A), (B) and (D) only

(A), (B) and (C) only

(A), (B), (C) and (D)

(B), (C) and (D) only

$\frac{2}{3},-\frac{1}{3}, \frac{2}{3}$

$-\frac{2}{3},-\frac{1}{3}, \frac{2}{3}$

$\frac{2}{3},-\frac{1}{3},-\frac{2}{3}$

$\frac{2}{3}, \frac{1}{3}, \frac{2}{3}$

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (I), (B) - (II), (C) - (IV), (D) - (III)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

$\frac{\sin ^{2} a}{\sin (a+y)}$

$\frac{\sin (a+y)}{\sin ^{2} a}$

$\frac{\sin (a+y)}{\sin a}$

$\frac{\sin ^{2}(a+y)}{\sin a}$

$\frac{1}{\sqrt{6}} \hat{i}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}+\frac{1}{\sqrt{6}} \hat{\mathrm{k}}$

$-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{1}{\sqrt{6}} \hat{\mathrm{j}}-\frac{1}{\sqrt{6}} \hat{\mathrm{k}}$

$-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}+\frac{2}{\sqrt{6}} \hat{\mathrm{k}}$

$-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}-\frac{1}{\sqrt{6}} \hat{\mathrm{k}}$

$\frac{\sqrt{28}}{7}$

$\frac{\sqrt{199}}{7}$

$\frac{\sqrt{328}}{7}$

$\frac{\sqrt{421}}{7}$

even and is strictly increasing in $(0, \infty)$

even and is strictly decreasing in $(0, \infty)$

odd and is strictly increasing in $(-\infty, \infty)$

odd and is strictly decreasing in $(-\infty, \infty)$

(A) and (C) only

(A), (B) and (C) only

(A), (B) and (D) only

(A) and (D) only

$\frac{4}{9}$

$\frac{3}{8}$

$\frac{2}{7}$

$\frac{4}{19}$

$2,-3,-1$

$-2,3,1$

$2,3,-1$

$6,-9,-3$

Symmetric

An Equivalence relation

Transitive

Reflexive

$\frac27$

$\frac17$

$0$

$\frac57$

$\frac{\pi}{3}$

$\pi$

$\frac{\pi}{6}$

$\frac{\pi}{2}$

$3$

$2$

$\frac56$

$6$

There is no real value of x satisfying the above equation.

There is one positive and one negative real value of $x$ satisfying the above equation.

There are two real positive values of x satisfying the above equation.

There are two real negative values of $x$ satisfying the above equation.

15

30

45

90

To calculate and communicate the average growth of a single investment.

To understand and analyse the donations received by a non-government organisation.

To demonstrate and compare the performance of investment advisors.

To compare the historical returns of stocks with a savings account.

$10$

$15$

$17$

$6$

$3 \mathrm{~km}$

$1.5 \mathrm{~km}$

$1.75 \mathrm{~km}$

$1 \mathrm{~km}$

$y \frac{d^{2} y}{d x^{2}}=1$

$\frac{d^{2} y}{d^{2}}-y=0$

$\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0$

$y \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}+1=0$

1

2

3

4

$8 \frac{1}{2} \%$

$8 \frac{16}{23} \%$

$8 \frac{17}{25} \%$

$8 \frac{2}{5} \%$

$\operatorname{maximize} \mathrm{Z}=0.08 \mathrm{x}+0.09 \mathrm{y}$

$\begin{aligned} & x \geq 15000 \\ & y \geq 25000 \\ & x+y \geq 75000 \\ & x \leq y \\ & x, y \geq 0 \end{aligned}$

$\begin{aligned} & \operatorname{maximize} Z=0.08 x+0.09 y \\ & x \geq 15000 \\ & y \leq 25000 \\ & x+y \geq 75000 \\ & x \leq y \\ & x, y \geq 0 \end{aligned}$

$\begin{aligned} & \operatorname{maximize} Z=0.08 x+0.09 y \\ & x \geq 15000 \\ & y \geq 25000 \\ & x+y \leq 75000 \\ & x \geq y \\ & x, y \geq 0 \end{aligned}$

maximize $Z=0.08 x+0.09 y$

$x \geq 15000$

$y \geq 25000$

$x+y \leq 75000$

$\mathrm{x} \leq \mathrm{y}$

$x, y \geq 0$

120 m

150 m

140 m

100 m

$15,25,21$

$15,27,19$

$15,19,26$

$15,19,30$

$\alpha=5 \beta$

$5 \alpha=\beta$

$\alpha=3 \beta$

$4 \alpha=5 \beta$

$(-\infty, 1]$

$[1, \infty)$

$(-\infty, 1) \cup(1, \infty)$

$(-\infty,-1) \cup(-1, \infty)$

12

15

10

14

₹ $79.98$

₹ $15.96$

₹ $16.04$

₹ $80.02$

$100 \mathrm{~cm}^{2}$

$25 \sqrt{3} \mathrm{~cm}^{2}$

$75 \sqrt{3} \mathrm{~cm}^{2}$

$100 \sqrt{3} \mathrm{~cm}^{2}$

$\frac{27}{1331}, \frac{576}{1331}, \frac{243}{1331}$ and $\frac{512}{1331}$

$\frac{27}{1331}, \frac{243}{1331}, \frac{576}{1331}$ and $\frac{512}{1331}$

$\frac{576}{1331}, \frac{27}{1331}, \frac{512}{1331}$ and $\frac{243}{1331}$

$\frac{243}{1331}, \frac{576}{1331}, \frac{512}{1331}$ and $\frac{27}{1331}$

0

1

2

Not Defined

$x+8 y-33=0$

$12 x+y-8=0$

$x+8 y-12=0$

$x+12 y-8=0$

$0.1$

$1.42$

$1.89$

$2.54$