List of practice Questions

A solution of \(2\cos^2 x - 3\cos x + 1 = 0\) is
If \(\cos^ 4\theta - \sin^ 4\theta = \frac{1}{2}\),then \(θ=\)
\(\sqrt{\frac{1 + \sin\theta}{1 - \sin\theta}} + \sqrt{\frac{1 - \sin\theta}{1 + \sin\theta}}=\)
The value of \((1 + \cos x)(1 + \cot^2 x)(1 - \cos x)\) =
If A, B and C are angles in a triangle then\(\tan\left(\frac{A + B}{2}\right) \tan\left(\frac{C}{2}\right) \tan + \tan\left(\frac{B + C}{2}\right) \tan\left(\frac{A}{2}\right) + \tan\left(\frac{C + A}{2}\right) \tan\left(\frac{B}{2}\right)\) =
BC is a tower, B is its base. A is a point on a horizontal line passing through B, the angle of elevation of C from A is 60°. From another point D on AB, the angle of elevation is found to be 30°, then BD =
\(\frac{(\sin 30^\circ \cdot \sec 60^\circ + \cos 30^\circ \cdot \csc 60^\circ)}{(\sec 45^\circ \cdot \cot 45^\circ \cdot \csc 45^\circ)}=\)
A square of side 7 cm encloses a circle touching all its four sides. Then the area enclosed between the square and the circle is
The diameter of a sphere is equal to the height of the cone of equal volume. If r and R are the radii of cone and sphere respectively, then r2 =
A man is standing between two lamp posts on a horizontal line dividing the distance between them in the ratio 1:2. The height of man is 2 m. It is noticed that shadow of the man with respect to first lamp post just touches the foot of second lamp post. If the distance between the posts is 30 m, find the height of the first post.
The diagonals of a quadrilateral ABCD intersect at a point O such that AO. DO = BO.CO. Then the quadrilateral is definitely a
An equilateral triangle ABC is such that the side BC is parallel to X-axis. Then the slopes of its sides AB, BC, CA respectively are
The perimeter of the quadrilateral ABCD formed by A(-3, 1), B(0, 5), C(4, 8), D(1, 4) taken in that order is
Q is a point on the line BD dividing the segment internally. AB, PQ and CD are drawn perpendicular to BD. If AB = a, PQ = b and CD = c, then
In a trapezium \(ABCD AB || CD\), the diagonals AC and BD intersect at ‘P’. If \(AB: CD = 2:1\), then area of \(△CPD: \)area of \(△APB = \)
Which of the following combinations of sides and/or angles cannot form a right-angled triangle?
In how many ways can the letters of the word 'PERMUTATIONS' be arranged if vowels are together?
The number of diagonals that can be drawn by joining the vertices of an octagon is:
In a group of children, each child gives a gift to every other. If the number of gifts is 132, then the number of children is:
A 90 kg solution has 10% salt. How much water must be evaporated to have the solution with 20% salt?
There are 200 Prizes of Rs. 100 and Rs. 50 only. If the total amount spent on the prizes is Rs. 12,000, the number of prizes of Rs. 100 is:
A man marks his goods at a price that would give him 20% profit. He sells \( \frac{3}{5} \) of the goods at the marked price and sells the remaining at 20% discount. The gain percent in the whole transaction is:
‘A’ sold a table to ‘B’ at a profit of 15%, later on ‘B’ sold it back to ‘A’ at a profit of 20% there by gaining Rs. 69. How much did ‘A’ pay for the table originally?
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