List of practice Questions

If $x= \frac{1-t}{1+t} ; y= \frac{2t}{1+t}, $ then $\frac{d^{2}y}{dx^{2}} = $
If $f(x) = \begin{cases} \frac{e^{3x} - 1}{4x} & \quad \text{for} x \neq 0 \\ \frac{k + x}{4} & \quad \text{for } x= 0 \end{cases}$ is continuous at $x = 0$, then $k =$
If the tangent to the curve $2y^3 = ax^2 + x^3$ at the point $(a, a)$ cuts off intercepts $\alpha$ and $\beta$ on the coordinate axes where $\alpha^2 + \beta^2 = 61$, then the value of $a$ is
Lengthof the subtangent at $(a, a)$ on the curve $y^2 = \frac{x^2}{2a +x}$ is equal to
If $y=\log \tan\left(\frac{\pi}{4} + \frac{x}{2}\right) ,$ then $ \frac{dy}{dx} = $
If $\sqrt{\frac{x}{y}} + \sqrt{ \frac{y}{x}} = \sqrt{a}$ , then $ \frac{dy}{dx} = $
If $|\vec{a} | = 2 , |\vec{b}| = 7$ and $\vec{a} \times \vec{b} = 3 \hat{i} + 2 \hat{j} + 6\hat{k}$ then the angle between $\vec{a}$ and $\vec{b}$ is
Diffraction effects are more easily detected in the case of sound waves than light waves because
Colour of flower petals is due to
Which one of the following events lead to double fertilization?
Which one of the following is a flagellated protozoan?
Protein synthesis take place in
A tactile organ in Cockroach is
A temporary endocrine gland in humans is
A star $ A $ is 100 times brighter than star $B$. Then $m_B - m_A$ the difference in their apparent magnitudes is
A prehensile tail as in chameleon is an adaptation for
A negative catalyst will
Continuity of cytoplasm from cell to cell is maintained through
The grittiness of the pulp of wood apple is due to
Which of the following statements regarding sclerenchyma is not correct?
In which of following groups of plants, the life cycle includes the gametophytic phase which is dominant, photosynthetic, independent and sexually reproducing?
In which of the following groups, the majority of plants contain the vascular tissue wherein the vessels and companion cells are absent in the xylem and phloem?
In which of the following cells the secondary cell walls are present?
Which of the following is the correct date of publication of the, book entitled 'Speciee Plantarum" authored by Carolus Linnaeus? This date is starting point date for modern plant nomenclature.
The two, more distantly related phyla among the following are