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  • Question 1
    4 / -1

    The number of values of k for which the system of equations (k + 1) x + 8y = 4k and

    kx + (k + 3)y = 3k - 1 has infinitely many solutions is

  • Question 2
    4 / -1

    If \(a_{n}=\frac{\Sigma n}{n !}\), the sum of the infinite series \(\operatorname{da}_{n}\) is

  • Question 3
    4 / -1

    \(\int x^{3} e^{x^{2}} d x\) is equal to

  • Question 4
    4 / -1

    Area of an equilateral triangle is √3 cm2. The length of each side of the triangle is

  • Question 5
    4 / -1

    If \(|\vec{a}|=4,|\vec{b}|=4\) and \(|\vec{c}|=5\) such that \(\vec{a} \perp(\vec{b}+\vec{c})\)
    \(\vec{b} \perp \overrightarrow{(c+a)}\) and \(\vec{c} \perp(\vec{a}+\vec{b}),\) then \(|\vec{a}+\vec{b}+\vec{c}|=\)

  • Question 6
    4 / -1

    Let \(a_{1}, a_{2}, a_{3},\) be terms of an AP. If \(\frac{a_{1}+a_{2}+\ldots+a_{p}}{a_{1}+a_{2}+\ldots a_{q}}=\frac{p^{2}}{q^{2}} p \neq q,\) then \(\frac{a_{6}}{a_{21}}\) equals

  • Question 7
    4 / -1

    If the sum of two of the roots ofx3+px2+qx+r=0is zero, then pq =

  • Question 8
    4 / -1

    The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is

  • Question 9
    4 / -1

    The value of the limit
    \(\lim _{x \rightarrow \frac{\pi}{2}}\left[1^{1 / \cos ^{2} x}+2^{1 / \cos ^{2} x}+3^{1 / \cos ^{2} x}+\ldots \ldots \ldots .+10^{1 / \cos ^{2} x}\right]^{\cos ^{2} x}\)

  • Question 10
    4 / -1

    Let n(U) = 700, n(A) = 200, n(B) = 300 and n(A ∩ B) = 100,

    Then n(Ac∩Bc)=

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