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            • 1.

              下列命题中,错误命题的序号是____________.

              \(①\)两个复数不能比较大小;\(②z_{1}\),\(z_{2}\),\(z_{3}∈C\),若\((z_{1}-z_{2})^{2}+(z_{2}-z_{3})^{2}=0\),则\(z_{1}=z_{3}\);

              \(③\)若\((x^{2}-1)+(x^{2}+3x+2)i\)是纯虚数,则实数\(x=±1\);\(④z\)是虚数的一个充要条件是\(z+\overset{\_}{{z}}\,∈R\).

            • 2.

              下列命题正确的序号是      

              \(①\)命题“若\(a > b\),则\({{2}^{a}} > {{2}^{b}}\)”的否命题是真命题;

              \(②\)若命题\(p:"\)\(\dfrac{1}{x-1} > 0 \)\("\),则;\(¬p \)\(:"\)\(\dfrac{1}{x-1}\leqslant 0 \)\("\);

              \(③\)若\(p\)是\(q\)的充分不必要条件,则\(\neg p\)是\(\neg q\)的必要不充分条件;

              \(④\)方程\(a{{x}^{2}}+x+a=0\)有唯一解的充要条件是\(a=\pm \dfrac{1}{2}\).

            • 3.

              下列结论错误命题的个数是

              \(①\)若向量\(\overrightarrow{a}\parallel \overrightarrow{b}\),则存在唯一的实数\(λ\)使得\(\overrightarrow{a}{=}\lambda \overrightarrow{b}\);

              \(②\)已知向量\(\overrightarrow{a}\),\(\overrightarrow{b}\)为非零向量,则“\(\overrightarrow{a}\),\(\overrightarrow{b}\)的夹角为钝角”的充要条件是“\(\overrightarrow{a}\cdot \overrightarrow{b} < 0\)”;

              \(③\)“若\(\theta {=}\dfrac{\pi }{3}\),则\(\cos \theta {=}\dfrac{1}{2}\)”的否命题为“若\(\theta \ne \dfrac{\pi }{3}\),则\(\cos \theta \ne \dfrac{1}{2}\)”;

              \(④\)若命题\(p:\exists {{x}_{0}}\in {R}\),\(x_{0}^{2}-x_{0}+1 < 0\),则\(\neg p:\forall x\in {R}\),\(x^{2}-x+1 > 0\);

              \(⑤\)在\(\triangle ABC\)中,命题“\(\cos B=\sin A\)”是命题“\(\triangle ABC\)是直角三角形”的充要条件.

              A.\(2\)个
              B.\(3\)个
              C.\(4\)个
              D.\(5\)个
            • 4. 给出下列命题:
              \({①}\)命题“若\(b^{2}{-}4ac{ < }0\),则方程\(ax^{2}{+}bx{+}c{=}0(a{\neq }0)\)无实根”的否命题;
              \({②}\)命题“定积分\(\int_{0}^{\sqrt{\pi}}\sqrt{\pi{-}x^{2}}dx{=}\dfrac{\pi^{2}}{4}\)”;
              \({③}\)命题“若\(a{ > }b{ > }0\),则\(\sqrt[3]{a}{ > }\sqrt[3]{b}{ > }0\)”的逆否命题;
              \({④}\)“若\(m{\geqslant }1\),则\(mx^{2}{-}2(m{+}1)x{+}(m{+}3){ > }0\)的解集为\(R\)”的逆命题.
              其中真命题的序号为\(({  })\)
              A.\({①②③}\)
              B.\({①②④}\)
              C.\({②④}\)
              D.\({①②③④}\)
            • 5.

              下列说法正确的个数有

              \(①\)用\(\xi \)刻画回归效果,当\(R^{2}\)越大时,模型的拟合效果越差\(;\)反之,则越好;

              \(②\)可导函数\(f(x)\)在\(x=x_{0}\)处取得极值,则\(f{{{"}}}({x}_{0})=0 \);

              \(③\)归纳推理是由特殊到一般的推理,而演绎推理是由一般到特殊的推理;

              \(④\)综合法证明数学问题是“由因索果”,分析法证明数学问题是“执果索因”.

              A.\(1\)个
              B.\(2\)个
              C.\(3\)个
              D.\(4\)个
            • 6.

              有下面四个判断,其中正确的个数是(    )

                  \(①\)命题:“设\(a\)、\(b\in R\),若\(a+b\ne 6\),则\(a\neq 3\)或\(b\neq 3\)”是一个真命题

                  \(②\)若“\(p\)或\(q\)”为真命题,则\(p\)、\(q\)均为真命题

                 \(③\)命题“\(\forall a\)、\(b\in R,{{a}^{2}}+{{b}^{2}}\geqslant 2(a-b-1)\)”的否定是:“\(\exists a\)、\(b\in R,{{a}^{2}}+{{b}^{2}}\leqslant 2(a-b-1)\)”

                 \(④\)设非零向量\(a=(x,1)\),\(b=(y,2)\),且向量\(a\)与\(b\)的夹角为\(θ\),则\(xy > -2\)是\(θ\)为锐角的必要不充分条件

              A.\(0\)
              B.\(1\)
              C.\(2\)
              D.\(3\)
            • 7.

              下列命题中正确的是(    )

              A.若\(p∨q\)为真命题,则\(p∧q\)为真命题

              B.若直线\(ax+y-1=0\)与直线\(x+ay+2=0\)平行,则\(a=1\)

              C.若命题“\(∃x∈R\),\(x^{2}+(a-1)x+1 < 0\)”是真命题,则实数\(a\)的取值范围是\(a < -1\)或\(a > 3\)

              D.命题“若\(x^{2}-3x+2=0\),则\(x=1\)或\(x=2\)”的逆否命题为“若\(x\neq 1\)或\(x\neq 2\),则\(x^{2}-3x+2\neq 0\)”
            • 8.

              下列有关命题的说法错误的是(    )

              A.若“\(p∨q\)”为假命题,则\(p\)与\(q\)均为假命题
              B.命题“若\(a < b\),则\(am^{2} < b m^{2}\)”的逆命题是真命题
              C.若命题\(p\):\(∃{x}_{0}∈R,{e}^{{x}_{0}}\geqslant 1 \),则命题\({\,\!}^{┑}p\):\(∀x∈R,{e}^{x} < 1 \)
              D.“\(\sin x=\dfrac{1}{2} \)”的一个必要不充分条件是“\(x=\dfrac{π}{6} \)”
            • 9.

              给出以下四个命题:

              \(①\)动点\(P\)到两定点\({F}_{1}\left(-2,0\right),{F}_{2}\left(2,0\right) \)的距离之和为\(4\),则点\(P\)的轨迹为椭圆;

              \(②P\)为抛物线\({{y}^{2}}=4x\)上一点,\(F\)为焦点,定点\(A\left(2,1\right) \),则\(\left| PF \right|+\left| PA \right|\)的最小值\(3\);

              \(③\)函数\(f(x)=x\cos x-\sin x\)在\(\left(π,2π\right) \)上单调递增;

              \(④\)定义在\(R\)上的可导函数\(f(x) \)满足\(f{{{'}}}\left(1\right)=0 \),\(\left(x-1\right)f{{{'}}}\left(x\right) > 0 \),则\(f(0)+f(2) > 2f(1)\)

              一定成立\(.\)其中,所有真命题的序号是           

            • 10.

              \((1)\)一个正方体的体积为\(8c{{m}^{3}}\),这个正方体的外接球的体积为___________\(c{{m}^{3}}\).

              \((2)\)集合\(A=\{x|{{x}^{2}}-3x-10\leqslant 0\}\),\(B=\{x|m+1⩽x⩽2m−1\} \),若\(A\bigcap B=B\),则实数\(a\)的取值范围是_____.

              \((3)\)已知函数\(f\left(x\right)=\begin{cases}\left(2a-1\right)x+7a-2, & x < 1 \\ {a}^{x}, & x\geqslant 1\end{cases} \)在\(R\)上单调递减,则实数\(a\)的取值范围是___________.

              \((4)\)已知平面\(\alpha ,\beta \),直线\(m,n\),且\(m\bot \alpha \),\(n\subseteq \beta \)给出下列四中说法:

              \(①\)若\(\alpha /\!/\beta \),则\(m\bot n\);     

              \(②\)若\(m\bot n\),则\(\alpha /\!/\beta \);

              \(③\)若\(m/\!/n\),则\(\alpha \bot \beta \);     

              \(④\)若\(\alpha \bot \beta \),则\(m/\!/n\);

              以上说法正确的有________________.

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